developing a construction cost function for …

DEVELOPING A CONSTRUCTION COST FUNCTION FOR

RESIDENTIAL BUILDINGS IN DHAKA CITY- AN ECONOMETRIC APPROACH

JOARDER MD SARWAR MUJIB

DEPARTMENT OF CIVIL ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

(BUET) Dhaka, Bangladesh

April, 20142015

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DEVELOPING A CONSTRUCTION COST FUNCTION FOR

RESIDENTIAL BUILDINGS IN DHAKA CITY- AN ECONOMETRIC APPROACH

By

Joarder Md Sarwar Mujib

A Thesis submitted to the Department of Civil Engineering of Bangladesh

University of Engineering and Technology, Dhaka in partial fulfilment of the requirements for the degree of

MASTER OF SCIENCE IN CIVIL ENGINEERING (STRUCTURAL)

DEPARTMENT OF CIVIL ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING AND

TECHNOLOGY (BUET)

Dhaka, Bangladesh

April, 20154




CERTIFICATE OF APPROVAL The thesis titled “Developing A Construction Cost Function For Residential Buildings In Dhaka City-An Econometric Approach,” submitted by Joarder Md. Sarwar Mujib, Roll No. 1009042310, Session: Oct 2009, has been accepted as satisfactory in partial fulfillment of the requirement for the degree of Master of Science in Civil Engineering (Structural) on 4th April, 2015. Dr. Raquib Ahsan Chairman of the Committee Professor (Supervisor) Dept of Civil Engineering, BUET, Dhaka. Dr. A.M.M. Taufiqul Anwar Member Professor and Head (Ex-Officio)Dept of Civil Engineering,

BUET, Dhaka. Dr. Mahbuba Begum Member Professor Dept of Civil Engineering, BUET, Dhaka. Major Dr. Khondaker Sakil Ahmed Member Instructor Class B (External) Dept of Civil Engineering, Military Institute of Science and Technology (MIST), Dhaka




DECLERATION

This is to certify this thesis work “Developing A Construction Cost Function For Residential Buildings In Dhaka City-An Econometric Approach” has been done by me. Neither of the thesis nor any part of has it been submitted elsewhere for the award of any degree or diploma.

Signature of the Candidate

Joarder Md. Sarwar Mujib




Dedication To my Parents




ACKNOWLEDGEMENT

I would like to express my heartfelt gratitude to Almighty Allah for all my

achievements.

I would like to articulate my gratitude to my present supervisor Dr. Raquib Ahsan, for

his encouragement and guidance of this research, without whose support, this research

work could never finish.

I would like to express my gratefulness to my Ex-supervisor Dr. Zia Wadud who

actually guided me to the concept and let me dream with such an exceptional research

topic. His direction and cordial support allowed me to complete the major part of the

research work.

I am grateful to Dr. Hadiuzzaman who assisted me with his valuable and convincing

suggestion in writing the paper in a befitting manner.

I will do injustice to this acknowledgements if I do not express my gratefulness to

Assistant Professor Kamrul Islam of MIST without whose inspiration and various

guidance probably I could not complete this paper.

I would like to express my sincere thanks to my committee members. Dr. A.M.M.

Taufiqul Anwar, Dr. Mahbuba Begum and Maj Dr. Khondaker Sakil Ahmed,

Engineers for their valuable advices, comments and supports. I strongly believe that I

was able to improve the paper and my knowledge further due to their insightful

comments.

I gratefully acknowledge the contribution of various authors who have been referred

in preparation of this thesis. My extended grateful acknowledgement to Damodar N.

Gujrati, Sangeetha, G.S. Maddala and C.R, Kothari whose books who have directly

helped me to develop the concept of the research and also the methodology by writing




the books on Econometrics and Research Methodology.

I would like to express the recognition of my wife Umme Salma and my two

daughters Tahsinah Sarwar and Tahiyat Sarwar who have always inspired me

throughout the research.

Finally I like to acknowledge the contribution of the students of CE-11, CE-12 and

CE-13 of MIST who assisted me in data collection.

ABSTRACT

The preliminary cost estimate of a new building project is very significant which

provides the basis for the clients' budgeting, funding and controlling the project costs.

It is also the starting point on which the stakeholders decide whether to accept or

reject the project in question. A cost model should represent the significant cost items

in a form which will allow analysis and prediction of cost according to changes in the

design variables and price of cost elements. Only then it can be utilized in the

decision-making process. Considering the above fact the main objectives of this

research is to identify the possible cost elements and developing a general cost

function for residential building at Dhaka city. The developed model is then validated

to be useful for future study in this regards.

For the above study primary and secondary data were collected from the developers

of Dhaka city and Bangladesh Bureau of Statistics respectively. Total three models

were formulated using multiple linear regression (MLR) on 85 data with 26

independent variables (IV) and construction cost per sq. ft as dependent variable

(DV). Model-1 integrated construction materials' cost and labour wage and explained

91.4% of variability with standard error 65.461. Model-2 incorporated only design

variables as IV and explained only 32.9% variability with standard error 185.938.

Model-3 took account of all the variables explaining an increase of 0.5% of variability

only. Sand and Paint cost with Mason wage could describe the construction cost,

whereas design related variables displayed little influence on the DV. Models and

variables were statistically significant below 5% level. All models met MLR

assumptions and found suitable after cross validation and sensitivity analysis. Hence it

Comment [ja1]: Please correct.




is concluded that model with materials' cost and wage explain the DV better.

However, a discrepancy is observed here, as steel and cement were not found

statistically significant whereas, these cause the maximum cost in reality. Conversely,

sand and paint being smaller in cost is contributing in these models. Foundation and

Structural systems is more important cost contributor but these are not statically

significant in our case. Concrete Strength, Steel Grade did not show desired

indication as in reality. This discrepancy might be because of data being collected

from developers of various standards and in different time frames, when sudden rise

and fall of the materials' cost took place. At the end, it could be noted that an

estimated project cost is not directly calculated from project components rather an

approximate indication of the cost derived from minimum possible number of

variables.

TABLE OF CONTENTS

CERTIFICATE OF APPROVAL………………………………………………….ii

DECLARATION……………………………………………………………………iii

ACKNOWLEDGEMENT………………………………………………………….v

ABSTRACT…………………………………………………………………………vi

TABLE OF CONTENTS...................................................................................... vii

LIST OF APPENDICES........................................................................................ xiv

LIST OF TABLES................................................................................................. xv

LIST OF FIGURES.................................................................................................xiii

ABSTRACT............................................................................................................xviii

CHAPTER ONE

INTRODUCTION........................................................................................................1

1.1 General..............................................................................................................1

1.2 Background and Present State of The Problem.................................................2

1.3 Objectives..........................................................................................................6

1.4 Outcomes/Benefits of the Study........................................................................6

1.5 Scope...................................................................................................................7

1.6 Methodology.....................................................................................................7

1.7 Guides to the Thesis..........................................................................................8




CHAPTER TWO

LITERATURE REVIEW............................................................................................9

2.1 Introduction.......................................................................................................9

2.2 Various Research..............................................................................................9

2.3 Conclusion.......................................................................................................15

CHAPTER THREE

RESEARCH METHOD.............................................................................................16

3.1 Approaches to the Research.............................................................................16

3.2 Outline of Methodology...................................................................................16

3.3 Desk Study.......................................................................................................17

3.4 Pilot Field Survey.............................................................................................17

3.5 Formulation of Research Questionnaire..........................................................18

3.6 Data Collection for Main Research..................................................................20

3.7 Sampling Method Sample Size........................................................................20

3.8 Historical Analysis of Cost and Data...............................................................21

3.9 Statistical Analysis...........................................................................................21

3.10 Model Development........................................................................................22

CHAPTER FOUR

THE THEORETICAL ASPECTS OF THE DATA ANALYSIS AND

DEVELOPMENT OF COST MODEL....................................................................23

4.1 Introduction......................................................................................................23

4.2 Regression Analysis.........................................................................................23

4.3 Simple Regression Model..............................................................................24

4.4 Multiple Linear Regression (MLR): An Overview.........................................24

4.5 Important Definitions and Clarifications.........................................................25

4.5.1 Descriptive

Statistics...................................................................................25

4.5.2 Inferential Statistics....................................................................................25

4.5.3 Estimation Statistics....................................................................................26

4.5.4 Confidence Intervals...................................................................................26

4.5.5 Parameter Estimation..................................................................................26

4.5.6 Hypothesis Testing Statistics......................................................................26

4.6 Assumptions of MLR Analysis and Relevant Tests........................................26

4.6.1 Note to SPSS...............................................................................................29

4.7 Decision Rules for Development of Cost Model……………….....................29




4.7.1 Descriptive

Statistics...................................................................................29

4.7.2 Correlation Matrix......................................................................................30

4.7.3 Curve Fit.....................................................................................................31

4.7.4 Histogram and Box Plot..............................................................................32

4.7.5 Data Sorting and Finalizing........................................................................33

4.8 Decision Rule for Model Development………………....................................33

4.9 Data Processing and Analysis..........................................................................34

4.9.1 Methods of Linear Regression for The

Model............................................34

4.9.2 Mode of Analysis for Final Model.............................................................35

4.9.3 Test of Significance....................................................................................35

4.9.4 Approaches to Analysis of Final Model.....................................................36

4.10 General Information About Model-1...............................................................36

4.11 Model With Enter Method...............................................................................36

4.11.1 Interpretation of The Model........................................................................37

4.11.2 The Variables Considered in The Model....................................................38

4.11.3 Model Summary.........................................................................................38

4.11.4 ANOVA......................................................................................................38

4.11.5 Coefficient..................................................................................................38

4.11.6 Concluding Remarks of The Model by Enter Method...............................38

4.12 Model With Stepwise Regression....................................................................39


4.12.2 The Variables Considered In The Model....................................................41

4.12.3 Model Summary.........................................................................................41

4.12.4 ANOVA......................................................................................................41

4.12.5 Coefficient..................................................................................................41

4.12.6 Practical Significance.................................................................................42

4.12.7 Concluding Remarks of The Models With Stepwise Regression...............42

4.13 Model With Backward Elimination Method....................................................42



4.13.3 Model Summary.........................................................................................45

4.13.4 ANOVA......................................................................................................46

4.13.5 Coefficient..................................................................................................46


4.13.7 Concluding Remarks of the Models with Backward Elimination..............46

4.14 Model with Forward Selection Method...........................................................46

4.14.1 Interpretation of the Model Output Derived From Forward Selection......48




4.15 Concluding Remarks for Step 1………….......................................................48

4.16 Description of Step 2……...............................................................................49

4.17 Model with Backward Elimination Method....................................................49




4.19 Model with Backward Elimination Method.....................................................53

4.19.1 Concluding Remarks of The Models With Backward Elimination............55

4.20 Model With Forward Selection Method...........................................................55

4.20.1 Concluding Remarks of The Models with Forward Selection...................56

4.21 Model With Backward Elimination Method....................................................56



4.22.1 Concluding Remarks of the Models with Forward Selection.....................60

4.23 Final Conclusion...............................................................................................60

4.24 General Information about Model-2.................................................................62

4.25 Model Enter Method........................................................................................62



4.25.3 Model Summary.........................................................................................64

4.25.4 ANOVA......................................................................................................64

4.25.5 Coefficient..................................................................................................64

4.25.6 Concluding Remarks of The Model By Enter Method...............................64

4.26 Model with Backward Elimination Method-........................................64

4.26.1 Interpretation of the Model.........................................................................71

4.26.2 The Variables Considered In the Model.....................................................71

4.26.3 Model Summary.........................................................................................72

4.26.4 ANOVA......................................................................................................72

4.26.5 Coefficient..................................................................................................72



4.27 Model with Forward Selection Method-..............................................73



4.27.3 Model Summary and ANOVA...................................................................75

4.27.4 Coefficient..................................................................................................75


4.27.6 Concluding Remarks of The Models With Forward

Selection...................75

Formatted: Indent: Hanging: 0.25"





4.28 Model with Backward Elimination Method-........................................75



4.28.3 Model Summary.........................................................................................82

4.28.4 ANOVA......................................................................................................82

4.28.5 Coefficient..................................................................................................82

4.28.6 Concluding Remarks of The Models With Backward Elimination-

2.........83

4.29 Model with Forward Selection Method-2........................................................83



4.29.3 Model Summary and ANOVA...................................................................84

4.29.4 Coefficient..................................................................................................84


4.29.6 Concluding Remarks of The Models With Stepwise Regression...............85

4.30 Model with Backward Elimination Method-3.................................................85



4.30.3 Model Summary.........................................................................................91

4.30.4 ANOVA......................................................................................................91

4.30.5 Coefficient..................................................................................................91


4.31 Model with Forward Selection Method-3………………................................92



4.31.3 Model Summary And ANOVA..................................................................93

4.31.4 Concluding Remarks of The Analysis With Design Variables..................94

4.32 General Information about Model-3................................................................94

4.32.1 Model Enter Method...................................................................................94

4.32.2 Interpretation of The Model And Concluding Remarks By Enter Method........96

4.32.3 Concluding Remarks of The Model By Enter Method...............................96

4.33 Backward Elimination Method-1.....................................................................96

4.33.1 Interpretation of the Model and Concluding Remarks by Backward

Elimination Method-1...............................................................................

109

4.33.2 Concluding Remarks of the Model by Enter Method...............................109

4.34 Forward Selection Method-1..........................................................................110





4.34.1 Interpretation of The Model And Concluding Remarks By Forward

Selection Method-1...................................................................................

112

4.34.2 Concluding Remarks of The Model By Forward Selection Method-1.....112

4.35 Backward Elimination Method-1...................................................................113

4.35.1 Interpretation of The Model And Concluding Remarks By Backward


125

4.35.2 Concluding Remarks of The Model By Backward Elimination Method-1...126

4.36 Forward Selection Method-2.........................................................................

126



128

4.36.2 Concluding Remarks of The Model By Enter Method.............................128




140

4.37.2 Concluding Remarks of The Model By Backward Elimination Method-1.....140

4.38 Forward Selection Method-3......................................................................... 140



142

4.38.2 Concluding Remarks of The Model By Forward Selection-3..................143




154


4.40 Forward Selection-4.......................................................................................156

4.40.1 Interpretation of The Model and Concluding Remarks By Forward


156

4.40.2 Concluding Remarks of The Model By Forward Selection-4..................156




167








176





185


4.44 The Final Model.............................................................................................186

CHAPTER FIVE

EMPERICAL RESULTS AND DISCUSSIONS...................................................188

5.1 Introduction....................................................................................................188

5.2 Boxplot And Identification Of Outliers.........................................................188

5.2.1 Boxplot of 87 Data....................................................................................189

5.3 Histogram of DV............................................................................................189

5.4 Descriptive Statistics......................................................................................191

5.5 Explanation of Result from SPSS Output (Model-1).....................................192

5.5.1 Model Summary (Model-1)......................................................................192

5.5.2 Analysis of Variance (Model-1)...............................................................194

5.5.3 Coefficients...............................................................................................197

5.5.4 Collinearity Statistics................................................................................199

5.5.5 Residual Statistics.....................................................................................200

5.6 Histogram of Residuals..................................................................................203

5.7 Normal P-P Plot of Standardized Residual (Model-1)..................................204

5.8 Scatter Plot of Standardized Residuals..........................................................205

5.9 Validation of The Model................................................................................206

5.10 Sensitivity Analysis........................................................................................206

5.11 Explanation of Result from SPSS Output (Model-1).....................................209



5.11.3 Coefficients (Model-2).............................................................................210



5.13 Normal P-P Plot of Standardized Residual (Model-1)...................................212

5.14 Scatter Plot of Standardized Residuals...........................................................214




5.15 Validation of the Model.................................................................................215

5.16 Sensitivity Analysis.......................................................................................215

5.17 Explanation of Result from SPSS Output (Model-1)………………….........216



5.17.3 Coefficients (Model-2).............................................................................217



5.19 Normal P-P Plot of Standardized Residual (Model-1)...................................219

5.20 Scatter Plot of Standardized Residuals..........................................................220

5.21 Validation of The Model................................................................................222

5.22 Sensitivity Analysis........................................................................................223

5.23 Discussion on Empirical Result…………………………………………….224

5.23.1 The Data...................................................................................................224

5.23.2 The Model…………………………………………………………….…224

5.23.3 Comparison of the Models……………………………………………...226

5.23.4 Overall Significance…………………………………………………….226

5.23.5 Individual Significance……………………………………………….....227

5.23.6 Testing of Assumptions………………………………………………...227

5.23.7 Residual Statistics……………………………………………………....228

5.23.8 Cross validation on Data……………………………………………..…229

5.23.9 Sensitivity Analysis……………………………………………………..230

5.23.10 Conclusions………………………………………………………....231

CHAPTER SIX

CONCLUSIONS AND RECOMMENDATIONS.................................................233

6.1 Introduction....................................................................................................233

6.2 Conclusion......................................................................................................235

6.3 Limitations of the Study…………………………………………………….236

6.4 Recommendation And Future Study..............................................................237

REFERRENCES......................................................................................................238




LIST OF APPENDICES

APPENDIX-A (Survey on Residential Building-Dhaka) PART A......................241

APPENDIX-B (Survey on Residential Building-Dhaka) PART B......................245

APPENDIX-C (SPECIMEN OF SAMPLE DATA IN SPREADSHEET)….....247

APPENDIX-D (DESCRIPTIVE STATISTICS).................................................249

APPENDIX-E (PEARSON CORRELATIONS MATRIX)................................251

APPENDIX-F (BIVARIATE DATA ANALISIS AND CURVE FITTING)…259

APPENDIX-G (BOXPLOT AND HISTOGRAM).............................................307

APPENDIX-H (VALIDATION OF MODELS).................................................336




LIST OF TABLES

Table 4.1 Variables Entered/Removed.................................................................36

Table 4.2 Model Summary...................................................................................36

Table 4.3 ANOVA................................................................................................36

Table 4.4 Coefficients..........................................................................................37



Table 4.7 ANOVA................................................................................................39




Table 4.11 ANOVA................................................................................................43




Table 4.15 ANOVA................................................................................................47



Table 4.18 ANOVA................................................................................................49



Table 4.21 ANOVA................................................................................................51



Table 4.24 ANOVA................................................................................................53



Table 4.27 ANOVA................................................................................................55



Table 4.30 ANOVA................................................................................................57



Table 4.33 ANOVA...............................................................................................59



Table 4.36 ANOVA................................................................................................61

Comment [ja2]: There shouldn't be two tables with the same caption.






Table 4.39 ANOVA................................................................................................64



Table 4.42 ANOVA................................................................................................72



Table 4.45 ANOVA................................................................................................75



Table 4.48 ANOVA................................................................................................82



Table 4.51 ANOVA................................................................................................85



Table 4.54 ANOVA................................................................................................92



Table 4.57 ANOVA................................................................................................95



Table 4.60 ANOVA................................................................................................98

Table 4.61 Coefficients........................................................................................100

Table 4.62 Model Summary.................................................................................111

Table 4.63 ANOVA..............................................................................................111



Table 4.66 ANOVA..............................................................................................115



Table 4.69 ANOVA..............................................................................................128



Table 4.72 ANOVA..............................................................................................131



Table 4.75 ANOVA..............................................................................................143






Table 4.78 ANOVA..............................................................................................146



Table 4.81 ANOVA..............................................................................................157



Table 4.84 ANOVA..............................................................................................160



Table 4.87 ANOVA..............................................................................................171



Table 4.90 ANOVA..............................................................................................181


Table 5.1 Descriptive Statistics.....................................................................192

Table 5.2 Model Summary (Model-1)............................................................194

Table 5.3 ANOVA (Model-1).......................................................................196

Table 5.4 Coefficients (Model-1)...................................................................198

Table 5.5 Residuals Statistics (Model-1)...........................................................201

Table 5.6 Model Summary (Model-2)............................................................211

Table 5.7 ANOVA (Model-2).......................................................................211

Table 5.8 Coefficients..................................................................................212

Table 5.9 Residuals Statistics........................................................................213

Table 5.10 Model Summary (Model-3)...........................................................218

Table 5.11 ANOVA (model-3).......................................................................218

Table 5.12 Coefficients (model-3)...................................................................219

Table 5.13 Residuals Statistics (Model-3)..........................................................220

Table 5.14 Comparison of the Models.............................................................227




LIST OF FIGURES

Figure 5.1 Boxplot of Construction Cost-87 Data............................................190

Figure 5.2 Boxplot of Construction Cost-85 Data..............................................191

Figure 5.3 Histogram of Construction Cost.....................................................192

Figure 5.4 Histogram of Residuals (Model-1)..................................................205

Figure 5.5 Normal P-P Plot of Standardized Residual (Model-1).......................206

Figure 5.6 Scattered Plot of Standardized Residual vs. Standardized Predicted

Value (Model-1)................................................................................. 207

Figure 5.7 Sensitivity Analysis of Model-1 Variables (DV vs IV).....................210

Figure 5.8 Histogram of Standardized Residuals (Model-2)...............................214

Figure 5.9 Normal P-P Plot of Standardized Residuals (Model-2).....................215

Figure 5.10 Scatter Plot of Standardized Residuals vs. Standardized Predicted

Value (Model-2).................................................................................215

Figure 5.11 Sensitivity Analysis of Model-2 Variables (DV vs. IV)....................217

Figure 5.12 Histogram of Standard Residuals (Model-3)......................................221

Figure 5.13 Normal P-P Plot of Standardized Residuals (Model-3).....................222

Figure 5.14 Scatter Plot of Standardized Residuals vs. Standardized Predicted

Value (Model-3)................................................................................223

Figure 5.15 Sensitivity Analysis of Model-3 Variables (DV vs. IV)...................224




CHAPTER ONE

INTRODUCTION

1.1 Introduction

Any prospective client who is interested in building a structure would first ask the

question “How much will the project cost?” Naturally the next question would be

“how accurate is this figure as answered in response to the first question?" The

preliminary cost estimate of a new building project remains a benchmark throughout

the project period. This estimate provides the basis for the constructor's (a developer,

an agency or an individual) budgeting, funding and controlling the construction costs.

This is also the starting point on which the stakeholders decide whether to accept or

reject the project in question. At the same time a client who is interested to purchase

the whole or a part of the building would also be interested to know the same as to

how far he will bargain for the price. Again a land owner who is interested to get his

building constructed in joint venture with a developer will also be interested in the

same question as to fix the signing money and percentage of his share. A bidder who

prepares himself to get a similar contract by bidding is also required to prepare the

minimum and maximum price he may have to spend for the project. All these

institutions, agencies and individuals primarily focus on the answers of these two

questions. However, regular construction experiences reveal that purely prediction

sometimes ends up in non-pragmatic conclusions.

Cost modeling may be defined as the symbolic representation of a system in terms of

the factors, which influence its cost. In other words, a model represents the significant

cost items of a building in a form which will allow analysis and prediction of cost to

be undertaken according to changes in the design variables and direct cost elements.

The idea is to prepare a model such that it would simulate both current and future

situations and the problems of early cost estimation may be taken care of, thereby, it

can be used in the decision-making process.

1.2 Background and Present State of the Problem




Dhaka - the Capital city of Bangladesh is known to be one of the most populated

megacities of the world. The residential areas are gradually adapting the dynamic

changes in patterns for rapid growth of the city population. However, these areas have

lost much of their residential characteristics in order to cope with rapid urbanization.

The traditional urban housing system in Dhaka has undergone many radical

transformations over the past few decades. The continuous growth has given scope of

large scale housing project in and around the city. As a result huge private developers

have emerged to take the opportunity and construct medium to high rise buildings to

meet up the scarcity of accommodations. The major clients are higher middle class to

upper class of the society. The location and importance of nearby features have a

great effect of valuation perception both for the people as well as the developers. The

developers generally undertake projects through mutual agreements with land owner

rather than purchasing land. A decision is often required to be taken by the clients/

land owners whether they should agree to the proposal of the developers. Naturally,

the question comes in mind of the prospective client or land owner “Is their cost

perception about the project reasonable? Or “Are the developer’s bargain

acceptable?”

A building project can only be regarded as successful, once it is delivered in time, at

the appropriate price and quality providing the client with a high level of satisfaction.

One important influence on this is the authenticity of the cost estimates prepared

during the various phases, especially in the conception phase. Often the quality of the

project, along with the ability to construct and complete on schedule largely depends

on the accuracy of cost estimates made in the design phase. Since cost has been

identified as one of the measures of function and performance of a building, it should

be capable of being modeled so that a tentative design can also be indicated. This will

assist in providing greater understanding and possibility of predicting the cost effect

for changing the design variables.

It is clear that, early cost estimates are accepted as approximations that includes some

degree of uncertainty. If it is too high then it may discourage the prospective client

from proceeding further with the scheme. Conversely, if the estimate is too low, it

may result in wasted development efforts, dissatisfaction on the part of the client,

such as obtaining lower than expected returns or even litigation.




The principal components of the cost of any construction facility include the market

prices of construction materials and the wage agreements. Besides these, few design

parameters like foundation types, structural forms, slab systems etc also involve cost

as they occupy additional costs in terms of materials and labour wage. Design

variables like concrete strength, steel reinforcement grade, plinth area, number of

stories, size of lobby, number of basements, number of stairs and number of toilets

also contribute some variations in cost. Other parameters like plumbing and electrical

system (Transformer, generator and lift capacity), location and accessibility, time and

season, climatic conditions, availability and interest rates of capital, demand for

construction, political and economic climates etc. also incur variations in cost. While

several of these factors could be constant for a given project, the design style still

could be varied in order to select the most economical option. It is in fact customary

that for any project, the designer will make liaison with the client considering several

economical design solutions. The factors that have economic consequences in various

design options are identified and examined, and thus, these often form the basis of

selecting the most suitable and appropriate proposal for the prospective client to

embark upon.

There have been sporadic attempts to develop cost models in Bangladesh and other

countries. These include efforts in U.S.A.(Texas), Nigeria, UK, Korea, Turkey,

Australia and a few more countries. The scope and purpose of research, modeling

methodology, data used and geographic coverage vary significantly from each other

in all these studies. It is particularly noticeable that, there has not been sufficient

research that provides any correlation or clear indications of the degree to which

changes in the construction parameters of the building (materials' cost and design

variables) would affect its cost with regards to Dhaka city.

In our country a few government organizations like Public Works Department

(PWD), Military Engineering Services (MES), Local Government Engineering

Department (LGED), City Corporation prepare schedule of rates for their own

buildings at the interval of five to ten years. Each organization makes some

amendments as the price of construction materials, labour wage and cost of

machineries change. MES prepare the cost estimate of individual item (work) per unit

volume which includes cost of materials, labour, income tax, value added tax and

contractors profit, also a few other cost adding some additional percentages. They




make contracts of any building by referring the cost per unit volume/ area of each

item as applicable. If any part of the integrated cost changes between the approvals of

the two consecutive schedules of rates, re-fixing is not possible without going to the

origin of cost. A few more estimating techniques used in our country at the pre-design

phase of the construction project do not seem to have any fixed procedure. Small to

medium firms take account of their recently completed project and make some

adjustment on cost with additional cost of 10% to 25% as unforeseen. Only the

renowned firms make the cost estimation based on design and quantity surveying by

preparing a Bill of Quantity (BOQ). If any changes take place in terms of only a

single design variable such as foundation, floor system, structural forms etc. each time

the firms have to redesign and calculate the BOQ separately time and again. This

eventually results in additional time and cost of overall design. Nobody follows a

unique tool to make a quick estimate considering all design variables and functional

parameters. Few developers use Microsoft Project to control their construction

project. It is not possible for anybody other than an engineer, who has adequate

knowledge on the construction process to involve in the above procedure stated. At

the same time a statistician who is interested to study the trends of construction cost

for drawing macroeconomic inference will not be able to follow the existing

procedure without having prior knowledge of construction engineering.

The cost model may be considered satisfactory to the researcher if the variation

generates on application is within the acceptable economic tolerance limit. The

probable cost function that would be identified in this research involves all possible

cost items and design variables and makes a generalized equation. Most interesting

aspect of this model is that, the estimators have options to change any design

variables at any stage and amend the estimated cost. At the same time, persons

without having the adequate knowledge on building may estimate the cost. The model

is expected to be more versatile and fits the residential buildings with almost all types

of design parameters. It is also expected that the multiple regression model, planned

for the present research, may unfold a new avenue for the researchers of Bangladesh

for making further study with both numerical and categorical design variables to

develop any cost function for Bangladesh in particular. Present study is carried out

with only panel data. But this approach can be used for both Time Series and Pooled




data also. This model can be effectively planned for cost function of other disciplines

also.

Econometrics, the result of a certain outlook on the role of economics,

consists of the application of mathematical statistics to economic data to

lend empirical support to the models constructed by mathematical

economics and to obtain numerical results. The art of the

econometrician consists in finding the set of assumptions that are both

sufficiently specific and sufficiently realistic to allow him to take the best

possible advantage of the data available to him. Linear Regression is the

most important tool of Econometrics and multiple regression provides a

powerful method to analyze multivariate data creating linear function of the cost

variables. Construction cost involves huge numbers of independent variables. To deal

with these massive variables Bill of Quantity (BOQ) method is very prolonged and

also burdensome. More so, it is not comprehensible for the people not concerned in

construction. There are many who are interested to know the cost but have no

opportunity to conceptualize the matter. Hence, if a researcher make it usable by all

stakeholders, it will be a unique one and very effective for the mass people.

Regression analyses are usually driven by a theoretical or conceptual model that can

be drawn in the form of a path diagram. The path diagram provides the model for

setting the regression and what statistics to examine. If one assumes linear relations

between variables, it provides a ‘road map’ to a set of theoretically guided linear

equations that can be analyzed by multiple regression methods. Multiple regression is

widely used to estimate the size and significance of the effects of a number of

independent variables on a dependent variable. Before a complete regression analysis

can be performed, the assumptions concerning the original data must be made.

Ignoring the regression assumptions contribute to wrong validity estimates. When the

assumptions are not met, the results may upshot in errors, or over- or under-estimation

of significance of effect size. Meaningful data analysis relies on the researcher’s

understanding and testing of the assumptions and the consequences of violations. The

old research shows that the researchers are drawing their own conclusions after testing

the assumptions and results of the statistical tests.




1.3 Objectives

The aim of this research is to study the residential building construction cost to

develop an early cost estimating construction cost model for Dhaka city. The specific

objectives are:

To identify all possible cost elements of the residential building construction.

Developing a general construction cost function for residential building at

Dhaka city for pre-design construction project cost predictions.

To validate the model as how it explains the unit cost (construction cost per

square feet) in other words to verify the effectiveness of the model.

1.4 Outcomes/Benefits of the Study

The benefits which could be derived from the research are as follows:

The model when developed is going to facilitate the method of predicting pre-

design construction cost for anybody who have no or little knowledge about

the construction process. Probably it is going to establish the first ever initial

cost predicting model for construction cost in Bangladesh by an econometric

approach, basing on which other researchers can develop other cost predicting

models.

The research is going to unveil some of the factors that affect construction

cost, and hence will draw estimator's attention to inculcate the effects of those

factors in their initial estimates to nullify or reduce the end effects.

The research findings also serves as the researcher's contribution to existing

knowledge, and should form the basis for other related further research works.

The expected outcome of the present study would be beneficial to estimate the

probable cost of construction per square foot during inception phase by the

stakeholders (constructors, developers, land owner, government agencies,

researcher etc.).

To identify the design variables (numeric and non numeric) those have the

largest effect or have no or little effect on total cost.




1.5 Scope

This work seeks to find out a quick estimation method to be used by different

stakeholders interested in predicting the initial pre-design construction cost. The

scope of the research is limited to only Reinforced Cement Concrete (RCC) buildings

in Dhaka city. The primary data were collected from developers and secondary data

were obtained from Statistical Year Book. Variation in quality of materials and

workmanship is not considered here. For interpreting secondary data, few

construction engineering judgments were made which may vary in reality. Cost of

materials, assumed/collected, was considered as constant, although it may vary over

the project duration for some materials. The research has been carried out purely on

available data which was sorted out on the basis of engineering judgment and market

study. Monetary value of cost of materials and other expenditure was perceived in the

accounting scale. Time value of money such as bank interest and other miscellaneous

cost was not taken into consideration.

1.6 Methodology

The research is planned to employ an econometric modeling approach for developing

a general cost function equation for residential building at Dhaka city. Almost 275

building projects data with more than 100 variables were collected. However after

scrutiny, only 25 variables have finally been considered for the study. The data were

sorted in spread sheet and finally 206 data sets have been selected for the research.

Multiple regression analysis has been adopted as it is most suitable for analyzing

these types of data set. The statistical software SPSS and MS Excel 2007 were used as

the tools for this research. In the proposed study primary cross-sectional data were

collected from different developers who construct residential building at Dhaka.

Initially a pilot project was carried out to identify the issue and finally a full survey

was conducted. At first all probable cost elements were identified by the pilot project

and from that, final survey questionnaires were prepared. There are both qualitative

and quantitative variables. Few of the potential variables are price of construction

materials, total plinth area, foundations types, structural form, floor system, locations

etc. An appropriate econometric model was developed using the SPSS platform.

Relevant statistical tests were carried out to determine the best possible model.




1.7 Organization of the Thesis

The thesis was presented in Six (6) chapters as follows:

Chapter1: gives the introduction which also includes background of the research,

outlines the aims and objectives. It also states the benefits, scope and method of the

research briefly.

Chapter 2: presents the available literature on the various methods of initial cost

predictions and basic approaches to cost estimation.

Chapter 3: presents the methodology and shows the general approach to the research.

Chapter 4: gives the general overview of the principle of regression analysis and its

application in the model development. This chapters also shows the research data

analysis process and steps to empirical model development

Chapter 5: presents the optimized result with descriptive statistics concerning the

variables associated with final empirical model. This chapter also shows the

discussion of the result found.

Chapter 6: contains the conclusions drawn from the research, the researcher's

contribution to knowledge and recommendations for further research.




CHAPTER TWO

LITERATURE REVIEW

2.1 Introduction

Construction cost estimation is one of the most challenging responsibilities in order to

ensure proper allocation of funding resources among different phases and events of

construction. It plays a vital role in decision making process of various stakeholders

such as owner, contractors, sub-contractors, designer, consultants etc. Thus the

successful completion and extent of a construction project largely depend on initial or

conceptual cost estimation. Previous researches emphasize on the accuracy of

conceptual cost estimation. Various approaches namely Regression Analysis, Neural

Network, Case Based Reasoning were adopted by different research groups to

minimize the gap between estimation and final project cost. A large number of

variables related to project thus introduced by the authors to incorporate maximum

uncertainties and deviation of the real project. Some of these variables are highly

sensitive to location of the project. Literature review reveals some study in the context

of U.K, USA, Nigeria and Turkey etc. But similar study related to Bangladesh in

particular Dhaka being the one of the most populated city is neither conducted nor

effort was taken. That is why; the necessity of development of a cost estimation

model in the context of Bangladesh is then initiated in order to incorporate local

project related variables.

2.2 Various Researches

Khosrowshahi and Kaka (1996), Lowe et al. (2006), Kantanantha and Leelakriangsak

(2012), Skitmore and Thomas Ng (2003), Ganiyu and Zubairu (2010), Hollar et al.

(2010) used the regression model to predict the cost of different construction project

in terms of different variables. However, the limitations of the regression model were

studied by Kim et al. (2004), Amusanet et al. (2013), Jamshid Sodikov (2005) as a

comparative approach. Their study concluded that Neural Network can estimate the

cost more accurately than that of the traditional Regression Analysis. Khosrowshahi

and Kaka (1996) describes a simple predictive model for estimation of project cost




and duration of U.K. housing project. The predictive model is based on regression

analysis by iteration contain predictors which based on their statistical performance.

Cost and duration were separately evaluated through two different models where the

cost model was independent of duration model. Hollar et al. (2010) describe an

approach for the development of a regression model to predict preliminary

engineering costs. Study result shows that, multiple linear regressions modeling also

show promises as a tool that support improvement in PE estimate preparation as well

as cost budgeting which can be used for effective distribution of funding resources to

capital project. Ganiyu and Zubairu (2010) identifies six most important design

related variables as complexity in design and construction, advancement in

technology, percentage of repetitive element, special issues and scope of work to

affect the ultimate project cost. Time given by the client for bid evaluation,

importance of project to be delivered and the need for the project completion are three

main time/cost related factors. Beside this, contractors and consultants previous

experience and adequacy of plant and equipment’s also plays significant role for

project cost estimation model. The factors were then incorporated in the predictive

cost model using principle components regression analysis. Later Lowe et al. (2006)

shows that multiple regression techniques can be more effective to predict the

construction cost of buildings rather than the traditional methods of cost estimation. In

their study the regression models were developed for cost\m2, log of cost and log of

cost\m2 rejecting the raw costs. Total six models were obtained by performing both

forward and backward stepwise analyses. Throughout the models total 19 different

variables were used. Among all six models log of backward model is considered as

the best one that gives an R2 of 0.661 and MAPE of 19.3%. The data used in the

model were collected from 286 United Kingdom construction projects. In another

study, Lowe et al. (2007) establishes a relationship among the project strategic, site

related and design related variables with the total construction cost. The study uses

data of 286 construction project in U.K. which were then validated using regression

analysis and neural network cost models. Use of different regression techniques were

observed in the study of Skitmore and Thomas Ng (2003). They describe the

deviation of the actual construction time and cost of construction project from the

contract time and cost. A set of 93 Australian construction projects were used to

develop several models for actual construction time and cost prediction. Different

analysis like forward regression, Standard cross-validation regression was conducted




to develop a model for forecasting actual construction time when client sector,

contractor selection method, contractual arrangements, project type, contract period

and contract sum are known. Then the sensitivity analysis of the model was done

since the prediction of actual construction time and cost is based on the estimated

contract period and contract sum. After that, the practical application was examined

by plotting different curves that helps the client to select the perfect project type to

minimize the variation between actual and contract time and cost.

Li et al. (2005) made an endeavor to develop a regression cost model for office

buildings in Hong Kong to predict the cost estimation at initial stage of any

construction project. Multiple regression analysis involving few variables had been

done to develop cost modeling. Historical data of 37 office buildings in Hong Kong,

constructed in different years, had been collected to develop the cost model that

included detailed information on the final construction cost, average floor area, total

floor area, average storey height, total building height, number of storey above

ground, number of basements and types of construction. The final construction cost

data were adjusted by the construction price index and categorized as dependent

variable while the rest data were categorized as independent variables. The

relationship between the final construction cost and the independent variables was

made by using the computer software (SPSS-17 package) to find the most accurate

equation. 7 samples out of 14 reinforced concrete buildings and 11 samples out of 23

steel buildings were randomly selected for verifying the result. Result shows that total

floor area and total building height entered into the final regression model equation

and resulted in more than 96% of the accuracy for reinforced concrete office

buildings. Total floor area, average floor area and total building height remained in

final equation and yielded over 95% of accuracy for steel office buildings. The major

limitation of the study was that, it was only considered for office buildings in Hong

Kong. But the research methodology is universal which can be applicable for other

residential and non-residential buildings as well. The reliability of the cost models

could be further enhanced by inclusion of more number of buildings. Continuous

updating the data can be a possible option to meet the future trend which is changing

frequently due to dynamic nature of construction industry.




In a different study on cost estimation of electrical and communication system for

industry Kantanantha and Leelakriangsak (2012) describes three different

methodologies namely Multiple Regression Analysis (MRA), Multiple Regression

Analysis Incorporating Genetic Algorithm (MRA-GA) and Neural Network. Result

shows that the electrical and communication system is composed of ten sub-systems

and the cost can be classified into five main components. The floor area and provision

of Air conditioning systems are considered as input variables and the cost as output

variable. Accuracy of the methods is measured by Root mean Squared Error (RMSE)

and the MRA-GA model provides a little lower RMSE than other two models.

Though MRA-GA model provides lower RMSE but it doesn’t prove it as the best

technique. Rather MRA-GA and NN technique takes time to develop whereas the

MRA is quick is providing the result. In his study Kim et. al. (2004) presented a

comparative study on the performance of three different construction cost estimation

models based on multiple regression analysis (MRA), neural network (NN) and the

case based reasoning (CBR) with respect to the data of 530 historical cases. Result

shows that the NN estimating model was more accurate than other two methods

whereas the CBR shows better performance considering long term use, availability of

information from result and time versus accuracy tradeoffs. Amusan et al. (2013) uses

the Artificial Neural Network (ANN) model to estimate the construction cost of

building projects. Their study shows that the neural network model is more accurate

than the traditional regression analysis with a maximum range variation of 7.42

percent. The corruption escalator factor and the inflation buffer factors were included

in the model for obtaining the actual performance of the model. A similar study of

Jamshid Sodikov (2005) suggested that, in the conceptual phase of a project the cost

estimation usually calculated on approximation and it leads to a great inaccuracy.

ANN could be a useful tool to help solve problems which come from the cost

estimation at the conceptual phase. Therefore, the development of an ANN model of

cost estimation should be focused by incorporating methods like Fuzzy Logic, Case

Based Reasoning etc.

However some other methodologies were also adopted by many researchers. For

instance, Cheng et. al. (2010) constructed an evolutionary estimate at completion

(EAC) model to estimate the final cost of the project based on the evolutionary

support vector machine interface model (ESIM). The two artificial intelligence




approaches fast messy genetic algorithm (FMGA) and support vector machine (SVM)

were merged to generate the ESIM model. The probable project performance and

risks associated with the project are taken into consideration to construct the EAC

model and hence the performance of the model was found satisfactory which was

validated using real applications. Somerville (1999) introduces a new set of micro-

data on housing construction cost to construct the quality controlled, hedonic cost

series based on this data set. Result shows that, the hedonic cost series can better

estimate the supply of new single family housing than the existing housing supply

studies. The study also shows that housing starts are cost elastic and the endogenous

behavior of the construction cost in the new housing supply functions. Skomrlj and

Radujković describes the S-curve methodology to establish a relationship between the

project cost and duration of the project based on 24 terminated high rise building

project data sets. The analysis shows that relationship between the cost and the

duration of a building project exists. The study was concluded with the mathematical

modelling of the time-cost distribution using regression methods of analysis. Yaman

and Tas (2007) introduced a computer based cost estimation process for the

construction project sector of Turkey. Automated cost estimation software was

developed based on the functional elements of building construction. The use of this

software was only limited within the educational purposes and its use in different

sectors with different database are not yet justified.

Relationships between variables were also studied by different researchers in order to

capture the most accurate cost estimation techniques using those relationships. As an

example, Blackman and Picken (2011) examine the relationship of height and

construction cost of high rise building in Shanghai. The total construction cost and the

elemental costs were considered as the basis of the relationship. Curves explained the

relationship between height and cost of the residential buildings at Hong Kong as

observed in the previous research of the authors was not similar with the height-cost

relationship of the present one. Thus the study suggests applying different sets of

criteria in the judgment of height in different locations to obtain the actual

relationship. Choudhury and Rajan investigated if there is a relationship between cost

and time for construction of residential structures in Texas. Having a realistic timeline

with respect to budget is important in construction business, so a time-cost model is

necessary prior to planning. This study analyzes the data of 55 different projects in




Texas over a period of 5 years. Result shows that the cost and time were found to be

positively correlated and an empirical relationship was developed based on

Bromilow's model. Windpao and Iyagba (2007) predicted the future levels of housing

construction cost in terms of present cost of construction and the economic factors in

Nigeria. The model was constructed using economic factors as the primary indicators

of future construction cost. Result shows that a positive relation but no specific

relation exist between housing construction cost and interest rates. The study includes

seven theoretical indicators such as BMP, IRT, PPI, FER, LCT, NDI, and MSP.

Among them six are directly related to housing cost. There are some limitations about

the achieved data that is the interest rate in not the on-going rates that is charged by

financial institution. Moreover Nigeria is not responsive in building material price,

interest rates and land price. Finally, a positive relationship was exhibited between

housing construction cost and building material cost, property price, foreign exchange

rates, labor cost etc. Thus, it can also be said that the future levels of cost in a

developing country like Nigeria can be determined from estimated levels of labor

costs. Choudhury and Sanampudi (2008) describe the relationship between the

construction cost and time for industrial and commercial project in India. The model

developed by Bromilowis was proved to be an unrivaled conductor in the construction

sector to predict the construction time, no matter whether it is commercial or

industrial. Total cost, and duration of construction are not the only variables in this

model. There are some more variables those have impact on construction sector, such

as change orders, category of structure, procurement method etc. There are two bad

impact of change order issue in this field, one of those is budgetary changes and the

other one is schedule changes. These two changes might be the cause of unwanted

losses. They follow “Design-Bid-Build” method. There are two more methods

included in procurement method, Design-Build and Construction Management at

Risk. Choosing one of these depends on the nature of the project. The objective of

their research was to determine the time-cost relationship in commercial and

Industrial projects and also the effect of change orders on construction time. Primary

data analysis tool was The SPSS software. Study shows that category of structure is a

dummy variable and it has minor effect on construction sector. With these additional

variables, the model has been modified to cope with more efficiency all over the

world. The result shows there are significant amount of relationship between cost and




time, change of order and time in industrial and commercial project. It indicates in

industrial project the total time is lower than the commercial.

2.3 Conclusion

From the above literature review we can identify that most of the researcher used

basically three techniques to study the construction cost these are Artificial Neural

Network, Multiple Linear Regression and Case Based Reasoning. Almost everybody

used basically two software SPSS and MATLAB except one who has developed

software to use this for officially. All the researches related to prediction of project

cost were conducted outside of Bangladesh with different political situation, different

environment and some for addressing few burning requirements. The studies at

abroad were conducted considering project or construction cost as Dependent

Variable and one or more Independent Variables. A few researches took only building

height and duration as independent variables and another took design variables as

independent variables. There were few studies in Bangladesh but none of them was on

cost prediction. None of these Bangladeshi works was done on the basis of

engineering aspect rather mostly on social aspects. Considering the above fact I

personally felt a study should be carried out on the parameter of Bangladesh, Dhaka

city in particular as it is one of the most populated and a city of massive constructions.

I planned to make three models, firstly; models with materials' cost and wage, then;

model with design variables and finally; model with both.




CHAPTER THREE

RESEARCH METHOD

3.1 Approaches to the Research

This chapter describes the method or the steps adopted in a systematic order so as to

organize the whole work properly. It is an attempt to arrange the research work in a

methodical order which will direct towards the achievement of the aim and objectives.

3.2 Outline of Methodology

The research is planned to employ an econometric approach for developing a general

cost function equation for residential building at Dhaka city. Multiple regression

model was used as the technique of analysis [4, 9]. The statistical software SPSS-17

and Excel 2007 were used as tools of this research [11]. In the proposed study primary

cross-sectional data was collected from different developers who construct residential

building at Dhaka city. There was also time series data but this was not taken into

consideration as the data were not in equal interval. Initially a pilot project was

carried out to identify the issue as well as the probable cost elements. From the

experience of pilot survey a final survey questionnaires were prepared. There were

both qualitative and quantitative variables. Then a full survey was conducted. An

appropriate econometric model was then developed using basically the SPSS

platform. Relevant statistical tests were carried out to determine the best possible

model. Few statistical tests were also conducted using Excel 2007. The various

procedures followed were as listed below:

a. Desk Study

b. Pilot Field Survey

c. Formulation of Research Questionnaire

d. Data Collection for Main Research

e. Sampling Methods and Sample Size

f. Historical Analysis of Cost Data

g. Statistical Analysis of Data

h. Model Building

i. Conclusion

Comment [ja3]: In the last chapter, you quoted reference by last names of the authors. In this chapter you are using numbers. Citation of reference has to be consistent in the entire thesis.




3.3 Desk Study

This involved detail examination of the existing methods and reviewing other relevant

literature on construction cost predictions and similar study at home and abroad by

different authors. Initial study was done by going through the previous thesis

conducted at BUET; hence the lists of thesis paper in Civil Engineering library,

BUET were studied. Finding no paper based on Econometrics, I started going through

the books of Econometrics from different library. As this subject was completely new

to me so finally I selected two books on Econometrics by Gujrati and Mandala to

perceive the concept of Econometrics. I carried out a bird's eye view of the paper on

internet and went insight the problem as how the historical researches were done. As

it is the statistical procedure I had to learn SPSS statistical software to know how the

software demands the data. Finally I selected multiple regression analysis to be my

tool of study for prediction of residential building construction cost per square feet.

As the study was based on primary data and there was no such research in context of

Bangladesh it was actually very difficult to make the respondents motivated to allow

collecting the data from office. The respondents were the private developers of

Dhaka. Moreover, in Bangladesh the data are not readily available in private sector. I

also studied availability of data from secondary source which are different

publications from Bangladesh Bureau of Statistics.

3.4. Pilot Field Survey

A pilot study was carried out by preparing initial questionnaires to identify the cost

elements and also the issue. After studying the data collected from pilot survey a all

probable cost elements were identified by the pilot project. For pilot project only few

developers were selected who were readily available and ready to expose their cost

data which are actually secret within the office of the firms. From that a final survey

questionnaires were prepared. There were both qualitative and quantitative variables.

It was also identified that many important and required data would not be readily

available with the respondents. So I studied Statistical Year Books and Bulletins

published by Bangladesh Bureau of Statistics as to inquire about the availability of

secondary price and wage data which are not readily available to the developers.

Upon the development of the structural questionnaire, a pilot study was conducted on




a random sample of 4 construction firms. This pilot study served the following

purposes:

a. Test the adequacy of the questions

b. Detect gray areas or ambiguous questions

c. Expand or compress the questions or choices, as may be required

d. Review the adequacy of the spaces allowed for each question

e. Estimate the average time required to fill out the questionnaire, and

determine whether it is reasonable or not.

3.5 Formulation of Research Questionnaire

The questionnaires of survey were formed to collect the historical data from the

construction firms aimed at developing the proposed cost estimation function of the

residential building at Dhaka city. Well structured closed-ended questionnaires were

designed, vetted and tested. These questionnaires were set in line with the specific

objectives and the aim. There were open ended questions too whose answer would

have much spread or fully numeric. There are two set of questionnaires for each

completed building (provided in Appendix A and B). The questionnaire of Part A was

comprised of a total 49(forty nine) questions spread across eight sections. To ensure

unbiased responses, completion of personal data was made optional. The

questionnaire of Part B was comprised of a total 9(nine) questions which are mainly

the cost data. In addition to these secondary data from construction firm I had to

collect three publication from Bangladesh Bureau of Statistics for many data

regarding wages of construction labour, helper, painter and prices of construction

materials (like sand and brick) and paint. I had to collect carrying cost of construction

materials from the above stated publications. The themes of the questionnaires are as

follows:

Part A:

a. Project Location, Contract and Year: This section was comprised of

financial year, location, plot, road number and some other general

information.




b. Foundation Data: This section has questions about foundation depth,

types etc.

c. Frames, Floor and Shape: This section was comprised of asking

questions like structural form, floor system and building shape.

d. Details of Flat: This section includes total area, plinth area, and

basement, number of flat per floor (with sizes and facilities), number of

stories, parking, lobby size, toilet, bathroom (with facilities), stair case and

fire fighting facilities.

e. Material Information: In this section we asked information regarding

concrete strength, reinforcement grade, partition wall, doors, windows,

tiles, paint, few community facilities, electric substation, gas connection, lift,

generator and pump facilities.

f. State of Luxury: This section asked only state of luxury.

g. Cost Data: This section is comprised of asking cost data like

construction cost, total cost, delay (if any) and additional expenditure of

the project.

h. Any Other Information: This section was intentionally prepared to give

freedom of respondents to provide additional information about cost

which I may miss in the questionnaire.

Part B:

a. State of Luxury: This question was asked also in Part A.

b. Cost/ Expenditure of Data as a Percentage of Total Cost: In this section

cost data of previous part was repeated and in addition asked the cost of plan

& design (architectural, structural, plumbing and electrical).

c. Overhead Cost: This section includes establishment cost and salary of

manager, site engineer and security personnel).

d. Government Taxes & Fees: This section includes fees and taxes for

plan pass, permission etc. by RAJUK, City Corporation and also fees for

electric and gas connection.




e. Misc Cost: (% of Total Cost): In this section the respondents were

asked expenditure and cost regarding materials and wages of structural,

plumbing, electrical, interior decoration, painting etc.

Secondary Data Sources:

a. Statistical Year Book 2011.

b. Statistical pocket Book 2013 and

c. Monthly Statistical Bulletin-Bangladesh, February 2013

3.6 Data Collection for Main Research

Well structured open and closed-ended questionnaires were designed, vetted and

tested as stated in paragraph 3.5. These questionnaires were set in line with the

specific objectives and the aim. The respondents were the private construction firms

who are involved with Dhaka based construction. Only data regarding residential

building were collected through a well trained team of civil engineering students. One

set of questionnaire (Part A and B) was for only one building which was later filled in

one row of spread sheet. There was single dependent variable (construction cost per

square foot) and as good as 93 independent variables. All these 94 variables were

collected from primary source that is the developers and construction firms. In

addition to these there were more 7 secondary cost data collected from the secondary

source (from the publication of Bangladesh Bureau of Statistics). There were also

many categorical variables as stated in paragraph 3.5. The data collecting process

was a huge and heavy task. The data were not readily available with the firms.

Moreover many developer firms denied sharing their data to outsiders. It took almost

two years to collect data of 278 buildings out of which many were incomplete and

unusable for missing of prime cost information. The target group was the members of

REHAB. However for lack of response from the reputed firm few data was also

collected from out of target group.




3.7 Sampling Method and Sample Size

Stratified sampling method was used for data collection. The strata were higher class,

higher middle class and lower middle class. The questionnaires were distributed in

such a way that the total respondents would be a fair representative of the planned

population. The target groups of respondents were the members of REHAB.

Distribution was such that the samples were taken from all well defined residential

area of new Dhaka. However for lack of response from few reputed firm some data

was also collected from out of target group. As the study was planned to create a

multiple regression model, it was decided to collect data such that the minimum

numbers of data is equal or more than total variable after sorting them. In order to

achieve this, a sample size it was decided to collect minimum 300 data from field and

get a minimum of 110 valid data so that it gives at least a size equal or more than total

numbers of variables.

3.8 Historical Analysis of Cost Data

A detailed cost analysis on eighty five (85) completed projects selected out of two

hundred and eighty (280), which were systematically selected through econometric

process by conducting relevant statistical tests all of which were located within Dhaka

city. Sample Spread Sheet Data is shown in Appendix C. As this was done on

stratified sampling the whole Dhaka was initially divided into seven zones. Later the

zone was reduced depending on correlation coefficients. The probable cost elements

were collected from the primary sources. Few data regarding prices and wages were

collected through the publications of Bangladesh Bureau of Statistics (BBS). Detailed

examinations of completed projects were analyzed on the basis of practical

significance and outliers were omitted through box plots. This also involved cost

finding out if any correlation and trend between the various elements existed. A

critical study and analysis was also done on the ratio of cost to area.




3.9 Statistical Analysis

This involved the use of relevant statistical formulae such as correlation coefficients,

regression analysis using SPSS 17.0 and also testing the significance of the statistical

values to support the survey results. The relative importance of the major factors that

affect the initial cost of construction at Dhaka city, their interdependency and test of

significance were also tested.

3.10 Model Development

The development of the model was based on the historical cost analysis that was

carried out on a 106 completed passed projects. The various costs elements were

taken as collected from survey. Few cost data regarding prices and wages were taken

from the publications of BBS. All numerical and categorical variables of respective

building of the projects were input in SPSS 17.0 and regression analysis was done

base upon which the model was developed. Statistical overview, data analysis process

and model development is described in Chapter 4 in thread bear.




CHAPTER FOUR

THE THEORETICAL ASPECTS OF THE DATA

ANALYSIS AND DEVELOPMENT OF COST MODEL

4.1 Introduction

This chapter deals with the theoretical aspects of multiple linear regression (MLR)

analysis in short with assumptions and statistical tests to support for the justification

of the model on the statistical point of view. In the process practical significance will

be considered as to justify the result on the basis of reality. It also shows the steps

and processes of data analysis using SPSS-17 to build final empirical model. This

chapter basically shows the process to reach the final model. The analysis details will

be shown in chapter 5.

4.2 Regression Analysis

Regression analysis is the statistical method which is the main tool of

econometrics. It is concerned with the study of the dependence of a variable

(DV) Y, on a set of independent variables (IV) X1, X2 …, Xk with the view to:

(a) Formulating a mathematical model to represent the statistical relation;

(b) Estimating the model parameters and;

(c) Using the model to make inferences about the DV, that is, to predict or

the primary variable, describe the behaviour of the primary variable, (Y),

based on the IV the influencing variable, (Xi).

(d) The primary variable, (Y), measures the effect or response resulting from a

certain combination of factors under specified conditions. It establishes

the relationship between variables and the effect of a change in one variable

on the other.




4.3 Simple Regression Model

This model has only one predictor variable and is the simplest regression relation in

which the regression function is a linear function of the predictor variable. The

simplelin ear regression model is given by the equation;

Yi= βo +β1Xi +ε

Where,

Yi - is the value of the response variable in the ith observation.

Xi - is the known value of the predictor variable in the ith observation.

ε - is the random error term or the “stochastic disturbance” which caters for the errors

due to chance and neglected factors which are assumed not important.

β1 - gives the intercept on y-axis, and are the regression parameters.

βo - measures the slope of the linear model.

4.4. Multiple Linear Regression (MLR): An Overview

Multiple linear regressions are a regression that involves more than one independent

variable. It is a straightforward extension of simple linear regression and is one of the

most widely used techniques. The purpose of multiple regression is to predict a single

variable from one or more independent variables. Multiple regression with many

predictor variables is an extension of linear regression with two predictor variables. A

linear transformation of the X variables is done so that the sum of squared deviations

of the observed and predicted Y is a minimum. The computations are more complex,

however, because the interrelationships among all the variables must be taken into

account in the weights assigned to the variables. The interpretation of the results of a

multiple regression analysis is also the prediction of Y is accomplished by the

following equation:

Yi = β1+ β2 X2k+ β3 X3k +··········+ βk Xjk+uk

Where,

- is the value of the response variable in the ith observation.

i

i




- are the values of ith observation of the jth independent variable;

…. - are the population regression coefficients which indicate the effect of a

given X on Y

- is the intercept which indicates the expected value of Y when all of the X

are Zero;

εi- is the ith observation of the disturbance or stochastic (error) term i

=1, 2 ...n, j =1, 2,…, k.

Multiple regression also allows you to determine the overall fit (variance explained)

of the model and the relative contribution of each of the predictors to the total

variance explained.

4.5. Important Definitions and Clarifications:

4.5.1 Descriptive Statistics

Descriptive statistics allow a researcher to describe or summarize their data. For

example, descriptive statistics for a study using subjects might include the sample

size, mean, median, mode, standard error, Skewness, Kurtosis etc. Descriptive

statistics are often briefly presented at the beginning of the Results chapter.

4.5.2 Inferential Statistics

Inferential statistics are usually the most important part of a dissertation's statistical

analysis. Inferential statistics are used to allow a researcher to make statistical

inferences that is draw conclusions about the study population based upon the sample

data. Most of my thesis results chapter will focus on presenting the results of

inferential statistics used for your data. There are two main types of Inferential

Statistics, estimation and hypothesis testing.

4.5.3 Estimation Statistics

Estimation statistics are used to make estimates about population values based on

sample data. There are two types of estimation statistics, confidence intervals and

parameter estimation.




4.5.4 Confidence Intervals

These statistics allow us to establish a range that has a known probability of

capturing the true population value. There are many different confidence interval

formulas, for example for estimating the population mean, or the percentage of a

characteristic in the population.

4.5.5 Parameter Estimation

Parameter estimation statistics allow us to make inferences about how well a

particular model might describe the relationship between variables in a population.

Examples of parameter estimation statistics include a linear regression model, a

logistic regression model, and the Cox regression model.

4.5.6 Hypothesis Testing Statistics

Hypothesis testing statistics allow us to use Statistical Data Analysis to make

statistical inferences about whether or not the data we gathered support a particular

hypothesis. There are many hypothesis testing procedures. Some of these are the T-

Test, F-Test etc. "T" and "F" test can be tested by level of significance also.

4.6 Assumptions of MLR Analysis and Relevant Tests

When we choose to analyze any set of data using multiple regression, part of the

process involves checking to make sure that the data to analyze can actually be

analyzed using multiple regression. We need to do this because it is only appropriate

to use multiple regression if the data "passes" few assumptions that are required for

multiple regression to give a suitable result. In practice, checking for these

assumptions just adds a little bit more time to the analysis, requiring clicking a few

more buttons in SPSS Statistics.

Before introducing to these assumptions, it is to be understood if, when analyzing

the data using SPSS Statistics, one or more of these assumptions is violated (i.e., not

met). This is not uncommon when working with real-world data rather than

textbook examples, which often only show as how to carry out multiple regression




when everything goes well! Following are the assumptions made in the present

thesis for MLR analysis:

o Assumption #1: Linear regression model - The regression model is linear in

parameter (coefficient) not necessarily linear in variables. Based on this

assumption the model is set linear from the beginning.

o Assumption #2: Dependent variable should be measured on a continuous scale

(i.e., it is either an interval or ratio variable).

o Assumption #3: There have to be two or more independent variables, which

can be either continuous (i.e., an interval or ratio variable) or categorical (i.e.,

an ordinal or nominal variable). The independent variables may be

dichotomous, trichotomous or even more. We need to introduce dummy

variables to deal with it categorical variables.

o Assumption #4: The data must not show multicollinearity, which occurs when

we have two or more independent variables that are highly correlated with

each other. This leads to high R2 value but Standard Error also become high,

thereby creating insignificant "t" ratio with high level of significance which is

not desirable. We can check this assumption by Tolerance or VIF values. The

guidelines are the VIF and Tolerance value should be maximum 10 and

minimum 0.2 respectively. If these conditions are not met we can solve these

by three ways, these are increasing the sample size, transformation of

variables or removing a variables.

o Assumption #5: The data needs to show homoscedasticity, which is where the

variances along the line of best fit remain similar as one moves along the line.

To check this assumption, we need to plot the standardized residuals against

the un-standardized predicted values during you analyze of data. In this plot

the points should not have any systematic pattern; rather it should be random

over the graph.

o Assumption #6: There should be no significant outliers, high leverage

points or highly influential points. Outliers, leverage and influential points are

different terms used to represent observations in the data set that are in some

way unusual when we wish to perform a multiple regression analysis. These




different classifications of unusual points reflect the different impact they have

on the regression line. All these points can have a very negative effect on the

regression equation that is used to predict the value of the dependent variable

based on the independent variables. This can change the output that SPSS

Statistics produces and reduce the predictive accuracy of your results as well as

the statistical significance. Fortunately, when using SPSS Statistics to run

multiple regression on the data, we can detect possible outliers by "Box and

Whiskers Plot" and other techniques and check for influential points in SPSS

Statistics using a measure of influence known as Cook's Distance, before

presenting some practical approaches in SPSS Statistics to deal with any

influential points we might have. Box plot will be discussed in this chapter

under separate sub heading.

o Assumption #7: Finally, one needs to check that the residuals (errors) are not

serially correlated or have autocorrelation, approximately normally distributed.

We can easily check this using the Durbin-Watson statistic, which is a simple

test to run using SPSS Statistics. Two more common methods to check this

assumption include using: (a) a histogram (with a superimposed normal curve)

and a Normal P-P Plot; or (b) a Normal Q-Q Plot of the studentized residuals.

We will limit to Durbin Watson (DW) Test. If the value of DW is close to 0

(zero), it indicates strong positive serial correlation and if same is close to 4

(four), it indicates strong negative serial correlation. As a guideline statisticians

use the value to be within the range of 1.5 to 2.5, which means no

autocorrelation exist.

4.6.1 Note to SPSS

SPSS-17 formulates the linear model by selecting linear regression model and first

three assumptions are met automatically. In output file if level of significance

becomes less than 0.05 for "F" and "t" statistics then the 5th and 6th assumptions are

met automatically - a fact which is will be observed in Chapter 5. Assumption 6 needs

to be checked by Box and Whisker Plots for each variables formulating the models.

Finally the 7th assumption can be checked from output of the residual plot. There are

more three assumptions which are also met in the process of data collecting, sorting

and analysis. These are:




Assumption #8:Number of observations must be greater than number of parameter.

Assumption #9:The value of independent should be stochastic.

Assumption #10:The regression model is correctly specified.

4.7 Decision Rules for Development of Cost Model

Before development of cost model we need to check few Descriptive Statistics

(Appendix D), Correlation Matrix (Appendix E), Curve Fit (Appendix H), Histogram

(for normal distribution) and Boxplot (for outliers) (Appendix I).

4.7.1 Descriptive Statistics:

From the Descriptive Statistics (Appendix D) we get a clear idea about the quality of

data and also its reliability. N=106 mean during analysis all 106 numbers of data is

considered and it was valid. From Range, Minimum and Maximum value we get the

reliability whether the data seem to be of normal value. Standard Error, Standard

Deviation and Variance give us the idea about dispersion of data. Skewness measures

the asymmetry and gives an idea about mean, mode and median's direction. On the

other hand, Kurtosis measures the peak of the curve. Skewness and Kurtosis measure

the shape of the curve. Interpretation of skewness and kurtosis are as under:

Skewness quantifies how symmetrical the distribution is.

A symmetrical distribution has a skewness of 0 (zero).

Positive value indicates a positive skewness i.e., an asymmetrical distribution

with a long tail to the right.

Negative value indicates a negative skewness i.e., an asymmetrical distribution

with a long tail to the left.

The skewness is unit less.




Any threshold or rule of thumb is arbitrary, but here is one: If the skewness is

greater than 1.0 (or less than -1.0), the skewness is substantial and the

distribution is far from symmetrical.

Kurtosis quantifies whether the shape of the data distribution matches the

Gaussian distribution.

A Gaussian distribution has a kurtosis of 0.

A flatter distribution has a negative kurtosis

A distribution more peaked than a Gaussian distribution has a positive

kurtosis.

Kurtosis has no units.

The value that Prism reports is sometimes called the excess kurtosis since the

expected kurtosis for a Gaussian distribution is 0.0.

An alternative definition of kurtosis is computed by adding 3 to the value

reported by Prism. With this definition, a Gaussian distribution is expected to

have a kurtosis of 3.0.

Anybody interested in data may take an overview whether the data set can be

used in other model.

4.7.2 Correlation Matrix:

Correlation matrix shows Pearson's Correlation Coefficient between two variables. In

our study we have total 28 variables including dependent one. The result as shown in

"Appendix E" shows 5% to 10% level of significance by two tailed test. "**" sign

denotes that the correlation is significant at the 0.01 level (2-tailed) of significance

and "*" sign denotes the correlation is significant at the 0.05 level (2-tailed) of

significance. From this matrix we can also manually chose which variable will

generate better model with high coefficient of determination (R2) value i.e., Goodness

of Fit. It also guides us in advance the possibilities of multicollinearity. In row "1" IV

"Sand Price" and "Mason Wage" have value of maximum multiple coefficients of

correlation (R) with the DV, so there is possibility that these two variables will remain




in final model. On the other hand in row "5" IV "Sand Price and "Steel Price" have

high value of R, so if sand remains in final model, steel should not remain due to high

VIF or low tolerance.

4.7.3 Curve Fit:

SPSS can generate 11 types of curves from bivariate regression. These are as follows:

(1) Linear E(Yt)=β0+β1t

(2) Logarithmic E(Yt)= β0+ β1ln(t)

(3) Inverse E(Yt)= β0+ β1/t

(4) Quadratic E(Yt)= β0+ β1t+β2t2

(5) Cubic E(Yt)= β0+ β1t+β2t2+β3t3

(6) Compound E(Yt)= β0βt1

(7) Power E(Yt)= β0t β1

(8) S E(Yt)=exp(β0+β1/t)

(9) Growth E(Yt)=exp(β0+ β1t)

(10) Exponential E(Yt)= β0e β1t

(11) Logistic E(Yt)=(1u+ β0βt1)−1

All the independent variables (IV) were tested as function of dependent variables

(DV) and found the various R2, "F" statistics for each curve and corresponding level

of significance with probable coefficient as to predict the best curve for each IV with

DV (Appendix F). In the process if need be transformation decision will be easier in

case of less value of R2.

4.7.4 Histogram and Box Plot:




Histograms measure whether the distributions normal or not and Boxplots find the

outliers (Appendix G). In descriptive statistics, a box plot is a convenient way of

graphically depicting groups of numerical data through their quartiles. Box plots may

also have lines extending vertically from the boxes (whiskers) indicating variability

outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-

and-whisker diagram. Outliers may be plotted as individual points. Box plots are non-

parametric: they display variation in samples of a statistical population without

making any assumptions of the underlying statistical distribution. The spacing

between the different parts of the box indicates the degree of dispersion (spread)

and skewness in the data, and show outliers. In addition to the points themselves, they

allow one to visually estimate various L-estimators, notably the inter quartile

range, mid hinge, range, mid-range, and tri mean. Box plots can be drawn either

horizontally or vertically. Any data not included between the whiskers is plotted as an

outlier with a dot, small circle, or star, but occasionally this is not done. Box plot

shows the first (bottom of box) and third (top of box) quartiles (equivalently the 25th

and 75th percentiles), the median (the horizontal line in the box), the range (excluding

outliers and extreme scores) (the "whiskers" or lines that extend from the box show

the range), outliers (a circle represents each outlier the number next to the outlier is

the observation number.) An outlier is defined as a score that is between 1.5 and 3 box

lengths away from the upper or lower edge of the box (remember the box represents

the middle 50 percent of the scores). An extreme score is defined as a score that is

greater than 3 box lengths away from the upper or lower edge of the box. Individual

points above or below 3 box heights are considered extreme outliers, and are marked

with asterisks Points for individuals that fall above or below 1.5 to 3.0 box heights

from the top or bottom of the filled box are considered outliers.

4.7.5 Data Sorting and Finalizing

Initially we summarized 285 data sets in spreadsheet. There were many missing value

and few unusual data. So, 106 data were sorted and finalized for analysis. After

consulting box plot in "Appendix G", the data having extreme outliers were removed.

The examples are serial 204, 205 and 206 in Figure G-1 and serial 4, 1, 49 1nd 53 in

Figure G-3. Finally 85 data were sorted after removing the extreme outliers. This data

formed the basis for analysis.




4.8 Decision Rule for Model Development

The model was interpreted based on the following statistical parameters to investigate

the relationship between the independent variables and the construction cost.

Statistical tests were conducted to confirm the reliability of output. Then the practical

significance was observed for accepting the model. Till such time both are mate

numbers of iteration was conducted. The decision was taken at every level by

statistical inference and also practical significance. These are described below in

short:

Firstly: From the "Model Summary" we will decide to accept the model if

Large Coefficient of determination-square, R2 (Goodness of Fit).

Large Adjusted R2 with minimum decrease in value with R2.

Minimum Standard Error (SE)

Secondly: From the "ANOVA" table we will decide to accept the model if

Overall model is significant at 5% level of significance which is tested by

"F" statistics from SPSS output.

Thirdly: From the "Coefficient" table we will decide to accept the model if

All the variables in the model must be individually statistical significant at

5% of level by "T" statistics and significance value from SPSS output;

and

Finally: We have to check practical significance of each coefficient from "Coefficient

Table". The decision rule is that, if the algebraic sign is same in the coefficient as it is

in practice: we will decide to consider that individual variable in model, if otherwise

we will drop the variable till the condition is met. These four steps will continue till

formulation of final model. If in the process value of R2 reduce substantially or SE

increase much we will go for transformation or non linear model.

4.9 Data Processing and Analysis

We will use SPSS-17 as a tool of statistics to develop the final model. This will be an

empirical model which will strictly depend on my data. In SPSS there are five




methods of linear regression analysis. In the first step I will use four methods.

4.9.1 Methods of Linear Regression for the Model

Enter Method: This method does not eliminate any variable rather show probable

coefficients (parameter), B against all IV in selected with individual "T" statistics and

level of significance. This method gives an idea about all the IV and its contribution

to the model. If sig value for each IV is not less than or equal to 0.050 (5%) then we

reject the model.

i. Stepwise Regression: This method carry out regression by taking IV one after

another considering "F" statistics sig at 5% to 10% of sig. This method enters a

variable if probability of "F" statistics is less than or equal to 0.5 and remove if the

same crosses 0.100. The method works with all variables and stops after checking all

and gives the best model with the variables whose "T" stat is at minimum 10% level

of sig. It gives summary of the all models it considered to be sig.

ii. Backward Elimination: This method carries out regression by taking all the IV

in the first go and removes one after another if "F" statistics is not sig and P value

crosses 0.100. This process continues till it gets a model with all the variables to be

statistically significance at minimum 10% level. This method also gives summary of

the all models it considered be it statically significant or not.

iii. Forward Selection: This method is somewhat like stepwise regression except it

does not enter new variables if "F" statistics sig is more than 5%.

4.9.2 Mode of Analysis for Final Model

Initially, regression will be carried out by all four methods till the results from all are

same. If a single method shows better result in the process, that method will

considered for modeling till the formulation of final model. Once, models are derived

from various methods, the model, with maximum R2 and minimum SE, will be

selected provided the P value is less than or equal to 0.050. All the methods produce

similar tables and figures like "Model Summary", "ANOVA", "Coefficient",




"Excluded Variable", "Residual Statistics" etc. depending on the selection of the

options. During iteration and till formulation of final model, only "Model Summary",

"ANOVA" and "Coefficient" will be considered. For the final model, other details

will be discussed in Chapter 5. In Chapter 5, all the assumption not tested in this

section, will be tested and additional two steps will also be carried out. These are:

a. Check the validity of the model by fitting with new sets of data those

are not considered during regression.

b. Carry out sensitivity analysis to check which IV contributes at what

percentage.

4.9.3 Test of Significance

In this chapter each model will be explained basically for Test of Significance under

three heading. These are "The Model Summary", "ANOVA" and "Coefficient". If

model is significant in all three tests, we will test for practical significance. If it

qualifies in all the Tests we will accept the model.

4.9.4 Approaches to Analysis of Final Model

a. Empirical Model with only Materials' Costs as Independent Variables.

b. Empirical Model with only Design Variables as Independent

Variables.

c. Empirical Model with all variables under study.

These three models types will be analyzed in three different sections separately.

4.10 General Information about Model-1(Step-1)

This section will show analysis of the model with the variables concerning materials'

costs only. The process will be followed as stated in paragraph 4.8 to 4.9.3 above. In

all model Construction Cost per square feet is Dependent Variable. The variable will

be analyzed by four methods first. Then two methods will be chosen up to the end to

get better and reasonable result. If the overall and individual significance of the model




and variables remain below 5% level then the variables will be observed for practical

significance. The practical significance is judged by coefficient sign (+/-). The sign of

coefficient must be same as it is in reality. If any variable is such that increase of it

increases the cost of construction then the coefficient sign must be positive.

4.11 Model With Enter Method

The model is done by Enter method using SPSS-17. The Tables are as follows:

Table 4.1: Variables Entered/Removed

Model Variables Entered Variables

Removed

Method

1 Transport, Cement, Steel,

Paint, Brick, Sand, Carpenter,

Helper, Mason

. Enter

All requested variables entered.

Table 4.2: Model Summary

Model R R Square Adjusted R Square Std. Error of the Estimate

1 .966 .932 .925 66.721

Predictors: (Constant), Transport, Cement, Steel, Paint, Brick, Sand, Carpenter,

Helper, Mason

Table 4.3: ANOVA

Model Sum of

Squares

df Mean

Square

F Sig.

1 Regression 4731763.724 9 525751.525 118.102 .000a

Residual 342779.195 77 4451.678

Total 5074542.920 86

Predictors: (Constant), Transport, Cement, Steel, Paint, Brick, Sand, Carpenter,

Helper, Mason

Table 4.4: Coefficients

Model Unstandardized

Coefficients

Standardized

Coefficients

B Std. Error Beta t Sig.

1 (Constant) -891.499 242.603 -3.675 .000

Steel .000 .002 -.004 -.094 .925




Cement .274 .362 .031 .756 .452

Brick -.027 .028 -.126 -.976 .332

Sand .197 .123 .185 1.603 .113

Paint 1.574 .400 .285 3.936 .000

Mason 4.839 1.978 .678 2.446 .017

Helper 1.414 1.402 .199 1.009 .316

Carpenter -.948 .627 -.140 -1.512 .135

Transport -.148 .072 -.099 -2.060 .043

4.11.1 Interpretation of the Model

This aspect attempt to explain the statistical parameters that is used to further

explain the model better and gives it a better understanding.

4.11.2 The Variables Considered In the Model

Table 4.1 shows that by the Enter Methods 9 independent variables (IV) were entered

with Construction Cost as dependent variable (DV). The IV are Transport, Cement,

Steel, Paint, Brick, Sand, Carpenter, Helper and Mason. All the variables were

considered but none was rejected.

4.11.3 Model Summary

Referring to Table 4.2, the value of R2 and Adjusted R2 are 0.932 and 0.925. There is

no considerable change between R2 and Adjusted R2. This means that the model can

explain 93.24% of the variability with the 9 variables. The Standard Error (SE)

66.721 which is very small in regards to the DV in question.

4.11.4 ANOVA

Referring to Table 4.3, the F ratio for degree of freedom (df) 9 and 77 is 118.102

which is acceptable with 0.000 level of significance (Confidence Interval 99.99%).

The critical F ratio for df (9, 77) for P value 0.005 is 2.00387212 which is less than

F=118.102. That means the overall model is significant. F critical is not always

required to find. If P value is less than or equal to 0.050 than F ratio will always be

significant. So, from next onward I will not bring F critical if P value is less than or

equal to 0.050. As P value is 0.000, the overall model is good.




4.11.5 Coefficient

Referring to Table 4.4, the only Paint, Mason and Transport is significant at 5% level.

Other variables are not significant as shown in the last column (Sig.). Necessity of

checking other values is of no use. So we cannot accept the model with all these

variables. So we have to try another model.

4.11.6 Concluding Remarks of the Model by Enter Method

Model cannot be accepted because individual level of significance crossed 5%.

4.12 Model with Stepwise Regression

The model is done by Stepwise Regression method using SPSS-17. The Tables are as

follows:


Model Variables Entered

Variables Removed Method

1 Mason .

Stepwise (Criteria: Probability-of-F-to-enter

<= .050, Probability-of-F-to-remove >= .100).

2 Paint .

Stepwise (Criteria: Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).

3 Brick .

Stepwise (Criteria: Probability-of-F-to-enter

<= .050, Probability-of-F-to-remove >= .100).

4 Transport . Stepwise (Criteria: Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).



1 .935a .874 .873 86.611

2 .953b .908 .905 74.689

3 .959c .920 .917 70.070

4 .963d .927 .923 67.291

Table 4.7: ANOVA

Model Sum of Squares df Mean Square F Sig.

1 Regression 4436924.912 1 4436924.912 591.480 .000a




Residual 637618.007 85 7501.388

Total 5074542.920 86

2 Regression 4605955.827 2 2302977.913 412.837 .000b

Residual 468587.093 84 5578.418

Total 5074542.920 86

3 Regression 4667034.447 3 1555678.149 316.855 .000c

Residual 407508.473 83 4909.741

Total 5074542.920 86

4 Regression 4703243.627 4 1175810.907 259.673 .000d

Residual 371299.292 82 4528.040

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -357.338 76.820 -4.652 .000

Mason 6.678 .275 .935 24.320 .000

2 (Constant) -971.082 129.692 -7.488 .000

Mason 5.515 .317 .772 17.379 .000

Paint 1.351 .245 .245 5.505 .000

3 (Constant) -1004.041 122.029 -8.228 .000

Mason 7.693 .685 1.077 11.224 .000

Paint 1.021 .249 .185 4.110 .000

Brick -.062 .018 -.290 -3.527 .001

4 (Constant) -1012.919 117.232 -8.640 .000

Mason 8.003 .667 1.121 11.993 .000

Paint 1.163 .244 .211 4.770 .000

Brick -.055 .017 -.258 -3.223 .002

Transport -.188 .067 -.125 -2.828 .006








Table 4.5 shows that the Stepwise Regression has produced four models

automatically. IV are included in the model successively one after another. If we go

through Correlation Matrix in Appendix E we will find Mason has the maximum

Pearson's Correlation Coefficient value with Construction Cost which is 0.943 and

then with Sand (0.919). That is why the Mason is included in the first model. But in

the second model it has not chosen Sand even after being the second highest

correlation. The reason is it is collinear with Mason which would generate problem of

multicollinearity. With this types logic the models has included Paint, Brick and

Transport in the successive models. As I discussed in paragraph 4.6.1 in the Notes to

SPSS that the model generated by SPSS automatically meet few assumptions during

the analysis process.


Referring to Table 4.6, the value of R2 of 4 models are 0.874, 0.908, 0.920 and o.927

serially. Corresponding Adjusted R2 are 0.873, 0.905, 0.917 and 0.927. There is no

considerable change between R2 and Adjusted R2. This means that the models can

explain 87.4%, 90.8%, 92% and 92.3% of the variability respectively. Corresponding

Standard Errors (SE) are 86.611, 74.689, 70.070 and 67.291which are very small in

regards to the DV in question. We can confirm that Model 4 is the best in

consideration to others in respect of R2, Adjusted R2 and SE. The best model is 4th

one and next come 3rd, 2nd and 1st from the bottom up to top.

4.12.4 ANOVA

Referring to Table 4.7, the F ratio in context of all models with degree of freedom (df)

(1, 85), (2, 84), (3, 83) and (4, 82) are acceptable with 0.000 level of significance

(Confidence Interval 99.99%). As I discussed in paragraph 4.11.4 above that F critical

is not required to find if P value is less than or equal to 0.050 than F ratio will always

be significant. In these models P value is less than or equal to 0.000 for all models

that means the overall model is significant at 0.00 level. All the models are

acceptable.




4.12.5 Coefficient

Referring to Table 4.8, all the models have P value less than 0.050. So we can accept

the models with the variables each have considered. Now we will check practical

significance in the next paragraph.

4.12.6 Practical Significance

Referring to Table 4.8, in 4th model each of the variables is individually significant

below 5% level. But the coefficients of Brick and Transport is negative i.e., If the cost

of Brick and Transportation is decreased the Construction Cost will increase and vice

versa. So, model will be rejected. Similar is the case with 3rd one where coefficient of

Brick is negative. In real world it is never true. So we cannot accept neither model 3

and nor 4 from practical significance point of view. So here comes which one to

select. Between model 1 and 2, 2nd Model provides better Goodness of Fit (R2) and

minimum SE. R2 =0.908 and SE=74.689.

4.12.7 Concluding Remarks of the Models with Stepwise Regression:

Model 2 may be accepted with R2 =0.908 and SE=74.689.

4.13 Model with Backward Elimination Method

The model is done by Backward Elimination method using SPSS-17. The Tables are

as follows:



Variables

Removed Method





Variables

Removed Method

1 Transport, Cement, Steel,

Paint, Brick, Sand,

Carpenter, Helper, Mason

. Enter

2 . Steel

Backward (criterion: Probability

of F-to-remove >= .100).

3 . Cement



4 . Brick



5 . Helper





1 .966a .932 .925 66.721

2 .966b .932 .926 66.296

3 .965c .932 .926 66.116

4 .965d .931 .926 66.064

5 .965e .930 .926 66.041

Table 4.11: ANOVA

Model

Sum of

Squares df Mean Square F Sig.

1 Regression 4731763.724 9 525751.525 118.102 .000a

Residual 342779.195 77 4451.678

Total 5074542.920 86

2 Regression 4731724.086 8 591465.511 134.573 .000b

Residual 342818.834 78 4395.113

Total 5074542.920 86

3 Regression 4729212.382 7 675601.769 154.555 .000c

Residual 345330.538 79 4371.273




Model

Sum of


Total 5074542.920 86

4 Regression 4725387.768 6 787564.628 180.450 .000d

Residual 349155.152 80 4364.439

Total 5074542.920 86

5 Regression 4721268.598 5 944253.720 216.502 .000e

Residual 353274.322 81 4361.411

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -891.499 242.603 -3.675 .000

Steel .000 .002 -.004 -.094 .925

Cement .274 .362 .031 .756 .452

Brick -.027 .028 -.126 -.976 .332

Sand .197 .123 .185 1.603 .113

Paint 1.574 .400 .285 3.936 .000

Mason 4.839 1.978 .678 2.446 .017

Helper 1.414 1.402 .199 1.009 .316

Carpenter -.948 .627 -.140 -1.512 .135

Transport -.148 .072 -.099 -2.060 .043

2 (Constant) -894.861 238.442 -3.753 .000

Cement .271 .359 .031 .756 .452

Brick -.027 .027 -.129 -1.012 .315

Sand .197 .122 .184 1.612 .111

Paint 1.574 .397 .285 3.964 .000

Mason 4.822 1.958 .675 2.463 .016

Helper 1.428 1.386 .201 1.030 .306




Model

Unstandardized

Coefficients

Standardized

Coefficients


Carpenter -.948 .623 -.140 -1.522 .132

Transport -.148 .071 -.098 -2.071 .042

3 (Constant) -801.229 203.196 -3.943 .000

Brick -.025 .027 -.118 -.935 .352

Sand .222 .117 .208 1.894 .062

Paint 1.581 .396 .286 3.992 .000

Mason 4.581 1.926 .641 2.378 .020

Helper 1.632 1.356 .230 1.204 .232

Carpenter -.942 .621 -.139 -1.516 .133

Transport -.162 .069 -.108 -2.368 .020

4 (Constant) -769.537 200.195 -3.844 .000

Sand .271 .105 .254 2.586 .012

Paint 1.702 .374 .308 4.551 .000

Mason 4.048 1.839 .567 2.202 .031

Helper 1.257 1.294 .177 .971 .334

Carpenter -1.206 .553 -.178 -2.181 .032

Transport -.171 .068 -.114 -2.526 .014

5 (Constant) -879.098 165.349 -5.317 .000

Sand .203 .078 .190 2.607 .011

Paint 1.644 .369 .298 4.455 .000

Mason 5.748 .562 .805 10.220 .000

Carpenter -1.200 .553 -.177 -2.171 .033

Transport -.182 .067 -.121 -2.714 .008





Table 4.9 shows that the Backward Elimination Method of Regression has produced




five models automatically. At the first model all the 9 IV are included in the model.

In the each successive step single variable is removed one after another depending on

P value greater than or equal to 0.100. It removes the variable first whose P value is

maximum. If we check Table 4.4 (Coefficient of Enter Method) we will find the Steel

has maximum P value (0.925), so the steel is removed in the second model. This way

it removes IV one after another till it gets all the IV to be statistically significant. In

the Final Model (5th) five variables Sand, Paint, Mason and Transport were retained.


Referring to Table 4.10 the value of R2 of model 1, 2 and 3 is 0.932 and for other two

these are 0.931 and 0.930, Corresponding Adjusted R2 of model 1 is 0.925 and for

other four models it is same (0.926). There is no considerable change between R2 and

Adjusted R2. This means that the models can explain more than 93% of the

variability. Corresponding Standard Errors (SE) are 66.721, 66.289, 66.116, 66.064

and 66.041 which are very small in regards to the DV in question. We can confirm

that all the Models are good having fractional variation in goodness of fit and SE.

4.13.4 ANOVA

Referring to Table 4.11, the F ratios are acceptable with 0.000 level of significance

(Confidence Interval 99.99%) for all models. All the models are good.

4.13.5 Coefficient

Referring to Table 4.12, only in 5th model each variable is individually statistically

significant below 5% level. So we can accept only the model 5 with all these

variables. Now we will check practical significance in the next paragraph.


Referring to Table 4.12, in 5th model each variable is individually significant below




5% level. But the coefficients of Carpenter and Transport is negative i.e., If the wage

of Carpenter and Transportation Cost is decreased the Construction Cost will increase

and vice versa. In real world it is never true. So we cannot accept the model from

practical significance point of view.

4.13.7 Concluding Remarks of the Models with Backward Elimination

None of the models are acceptable because they do not qualify to be both statically

and practically significant.

4.14 Model with Forward Selection Method

The model is done by Forward Selection method using SPSS-17. The Tables are as

follows:


Model

Variables

Entered

Variables

Removed Method

1 Mason . Forward (Criterion: Probability-of-F-to-enter <= .050)

2 Paint . Forward (Criterion: Probability-of-F-to-enter <= .050)

3 Brick . Forward (Criterion: Probability-of-F-to-enter <= .050)

4 Transport . Forward (Criterion: Probability-of-F-to-enter <= .050)

Table 4.14 Model Summary

Model R

R

Square Adjusted R Square Std. Error of the Estimate

1 .935a .874 .873 86.611

2 .953b .908 .905 74.689

3 .959c .920 .917 70.070

4 .963d .927 .923 67.291

Table 4.15 ANOVA

Model

Sum of





Model

Sum of


1 Regression 4436924.912 1 4436924.912 591.480 .000a

Residual 637618.007 85 7501.388

Total 5074542.920 86

2 Regression 4605955.827 2 2302977.913 412.837 .000b

Residual 468587.093 84 5578.418

Total 5074542.920 86

3 Regression 4667034.447 3 1555678.149 316.855 .000c

Residual 407508.473 83 4909.741

Total 5074542.920 86

4 Regression 4703243.627 4 1175810.907 259.673 .000d

Residual 371299.292 82 4528.040

Total 5074542.920 86

Table 4.16 Coefficients

Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -357.338 76.820 -4.652 .000

Mason 6.678 .275 .935 24.320 .000

2 (Constant) -971.082 129.692 -7.488 .000

Mason 5.515 .317 .772 17.379 .000

Paint 1.351 .245 .245 5.505 .000

3 (Constant) -1004.041 122.029 -8.228 .000

Mason 7.693 .685 1.077 11.224 .000

Paint 1.021 .249 .185 4.110 .000

Brick -.062 .018 -.290 -3.527 .001

4 (Constant) -1012.919 117.232 -8.640 .000

Mason 8.003 .667 1.121 11.993 .000

Paint 1.163 .244 .211 4.770 .000

Brick -.055 .017 -.258 -3.223 .002

Transport -.188 .067 -.125 -2.828 .006




4.14.1 Interpretation of the Model Output Derived From Forward Selection

The information of Table 4.13, 4.14, 4.15 and 4.16 are same as stated in Stepwise

Regression (Table 4.5, 4.6, 4.7 and 4.8). We will not discuss the tables here.

4.15 Concluding Remarks for Step 1.

If we compare output of all four methods we neither can accept any result from Enter

Method (Statistically Insignificant by Paragraph 4.11.6) nor from Backward

Elimination Method (Practically Insignificant by Paragraph 4.13.6). We can accept

Model 2 derived from both Stepwise Regression and Forward Selection method).

The model is as under (R2= 0.908, Adjusted R2=0.905 and SE= 74.689)

Construction = ̶ 971+ 5.516 × (Mason) + 1.351 × (Paint)

Here,

Construction = Construction Cost (Taka/sq ft)

Mason = the Wage of a Mason (Taka/Day) and

Paint = Price of Paint (Taka/ Gallon)

4.16 Description of Step 2.

In this step we will drop the Enter Method and the Stepwise Regression rather we will

model and analyze with Forward Selection and Backward Elimination Methods. Both

are expected to be useful. Model with highest R2 value and lowest SE value will be

considered if statistically significant at 5% level. If the model is not practically

significant for any individual variable we will drop that variable manually from being

regressed and analyze by both method. This will continue till a model is derived with

both statically significant at 5% level and also practically significant. From now

onward only three main tables (Model Summary, ANOVA and Coefficient) will be

explained.




4.17 Model with Backward Elimination Method

The model is done by Backward Elimination method using SPSS-17 in the similar

way we performed the regression in Step-1. At first we will drop Transport Cost from

the variable list and then perform the Backward Elimination with remaining 8 IV.

The Tables are as follows:



1 .964a .929 .921 68.094

2 .964b .929 .922 67.662

3 .963c .927 .922 67.930

4 .963d .927 .922 67.857

Table 4.18: ANOVA


1 Regression 4712868.006 8 589108.501 127.049 .000a

Residual 361674.913 78 4636.858

Total 5074542.920 86

2 Regression 4712867.483 7 673266.783 147.060 .000b

Residual 361675.437 79 4578.170

Total 5074542.920 86

3 Regression 4705388.326 6 784231.388 169.952 .000c

Residual 369154.594 80 4614.432

Total 5074542.920 86

4 Regression 4701567.242 5 940313.448 204.210 .000d

Residual 372975.678 81 4604.638

Total 5074542.920 86





Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -971.454 244.409 -3.975 .000

Steel 1.696E-5 .002 .000 .011 .992

Cement .471 .357 .053 1.319 .191

Brick -.037 .028 -.172 -1.320 .191

Sand .176 .125 .165 1.409 .163

Paint 1.621 .407 .293 3.978 .000

Mason 4.404 2.007 .617 2.194 .031

Helper 1.795 1.418 .253 1.265 .209

Carpenter -1.158 .632 -.171 -1.833 .071

2 (Constant) -971.089 240.441 -4.039 .000

Cement .471 .353 .053 1.335 .186

Brick -.037 .027 -.172 -1.344 .183

Sand .176 .124 .165 1.418 .160

Paint 1.620 .405 .293 4.004 .000

Mason 4.406 1.988 .617 2.217 .030

Helper 1.793 1.403 .252 1.278 .205

Carpenter -1.158 .628 -.171 -1.845 .069

3 (Constant) -1135.540 203.923 -5.568 .000

Cement .580 .344 .066 1.685 .096

Brick -.028 .026 -.131 -1.053 .296

Sand .099 .109 .093 .910 .366

Paint 1.598 .406 .289 3.937 .000

Mason 6.401 1.236 .896 5.180 .000

Carpenter -1.277 .623 -.189 -2.049 .044

4 (Constant) -1260.111 150.984 -8.346 .000

Cement .633 .339 .072 1.869 .065

Brick -.044 .019 -.207 -2.271 .026

Paint 1.634 .404 .296 4.049 .000

Mason 7.338 .682 1.027 10.751 .000

Carpenter -1.177 .613 -.174 -1.921 .058





If we consult the Output in Table 4.17, 4.18 and 4.19 we get four models. But we can

come in a conclusion that none of the models are acceptable because they do not

qualify to be both statically and practically significant.


The model is done by Forward Selection method using SPSS-17 in the similar way we

performed the regression in Step-1. Here also we will drop Transport Cost from the

variable list and then perform the Forward Selection with remaining 8 IV. The Tables

are as follows:



1 .935a .874 .873 86.611

2 .953b .908 .905 74.689

3 .959c .920 .917 70.070

Table 4.21: ANOVA


1 Regression 4436924.912 1 4436924.912 591.480 .000a

Residual 637618.007 85 7501.388

Total 5074542.920 86

2 Regression 4605955.827 2 2302977.913 412.837 .000b

Residual 468587.093 84 5578.418

Total 5074542.920 86

3 Regression 4667034.447 3 1555678.149 316.855 .000c

Residual 407508.473 83 4909.741

Total 5074542.920 86





Model

Unstandardized Coefficients

Standardized

Coefficients


1 (Constant) -357.338 76.820 -4.652 .000

Mason 6.678 .275 .935 24.320 .000

2 (Constant) -971.082 129.692 -7.488 .000

Mason 5.515 .317 .772 17.379 .000

Paint 1.351 .245 .245 5.505 .000

3 (Constant) -1004.041 122.029 -8.228 .000

Mason 7.693 .685 1.077 11.224 .000

Paint 1.021 .249 .185 4.110 .000

Brick -.062 .018 -.290 -3.527 .001


If we consult the Output in Table 4.20, 4.21 and 4.22 we get three models. Model 3 is

not acceptable for being practically insignificant. But other two models are acceptable

because they qualify to be both statically and practically significant. Model 2 with 2

IV (Mason and Paint) have greater R2 (0.908) value and smaller SE (74.689) so we

select this model at this stage. If we check with paragraph 4.15 then we find that

model is same as finalize in Step -1.

4.19 Model with Backward Elimination Method (Step-3)


way we performed the regression in Step-1. Here also we will both drop Transport

and Brick Cost from the variable list and then perform the Forward Selection with

remaining 7 IV. The Tables are as follows:






1 .963a .927 .921 68.414

2 .963b .927 .922 68.002

3 .962c .926 .922 67.975

4 .961d .924 .920 68.556

Table 4.24: ANOVA

Model

Sum of


1 Regression 4704790.252 7 672112.893 143.601 .000a

Residual 369752.667 79 4680.414

Total 5074542.920 86

2 Regression 4704599.595 6 784099.932 169.561 .000b

Residual 369943.325 80 4624.292

Total 5074542.920 86

3 Regression 4700273.508 5 940054.702 203.448 .000c

Residual 374269.411 81 4620.610

Total 5074542.920 86

4 Regression 4689149.838 4 1172287.459 249.427 .000d

Residual 385393.082 82 4699.916

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -907.737 240.716 -3.771 .000

Steel .000 .002 -.008 -.202 .841

Cement .445 .358 .050 1.243 .218

Sand .250 .112 .234 2.228 .029

Paint 1.801 .386 .326 4.669 .000




Model

Unstandardized

Coefficients

Standardized

Coefficients


Mason 3.576 1.915 .501 1.867 .066

Helper 1.305 1.375 .184 .949 .346

Carpenter -1.562 .555 -.231 -2.815 .006

2 (Constant) -913.217 237.742 -3.841 .000

Cement .437 .354 .050 1.236 .220

Sand .252 .111 .236 2.260 .027

Paint 1.806 .382 .327 4.725 .000

Mason 3.521 1.885 .493 1.868 .065

Helper 1.320 1.365 .186 .967 .336

Carpenter -1.571 .550 -.232 -2.856 .005

3 (Constant) -1053.270 188.483 -5.588 .000

Cement .529 .341 .060 1.552 .125

Sand .177 .080 .166 2.204 .030

Paint 1.754 .378 .318 4.637 .000

Mason 5.254 .584 .736 8.999 .000

Carpenter -1.587 .549 -.234 -2.888 .005

4 (Constant) -924.756 170.755 -5.416 .000

Sand .190 .081 .178 2.356 .021

Paint 1.740 .381 .315 4.561 .000

Mason 5.460 .573 .765 9.523 .000

Carpenter -1.592 .554 -.235 -2.872 .005


If we consult the Output in Table 4.23, 4.24 and 4.25 we get four models. But we can

come in a conclusion that none of the models are acceptable because they do not

qualify to be both statically and practically significant.



performed the regression in Step-1. Here also we will drop Transport and Brick Cost

from the variable list and then perform the Forward Selection with remaining 8 IV.




The Tables are as follows:



1 .935a .874 .873 86.611

2 .953b .908 .905 74.689

3 .959c .919 .916 70.410

4 .961d .924 .920 68.556

Table 4.27: ANOVA


1 Regression 4436924.912 1 4436924.912 591.480 .000a

Residual 637618.007 85 7501.388

Total 5074542.920 86

2 Regression 4605955.827 2 2302977.913 412.837 .000b

Residual 468587.093 84 5578.418

Total 5074542.920 86

3 Regression 4663062.523 3 1554354.174 313.530 .000c

Residual 411480.396 83 4957.595

Total 5074542.920 86

4 Regression 4689149.838 4 1172287.459 249.427 .000d

Residual 385393.082 82 4699.916

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -357.338 76.820 -4.652 .000

Mason 6.678 .275 .935 24.320 .000

2 (Constant) -971.082 129.692 -7.488 .000

Mason 5.515 .317 .772 17.379 .000

Paint 1.351 .245 .245 5.505 .000

3 (Constant) -1177.267 136.524 -8.623 .000

Mason 6.441 .405 .902 15.908 .000




Model

Unstandardized

Coefficients

Standardized

Coefficients


Paint 2.191 .339 .397 6.467 .000

Carpenter -1.883 .555 -.278 -3.394 .001

4 (Constant) -924.756 170.755 -5.416 .000

Mason 5.460 .573 .765 9.523 .000

Paint 1.740 .381 .315 4.561 .000

Carpenter -1.592 .554 -.235 -2.872 .005

Sand .190 .081 .178 2.356 .021

4.20.1. Concluding Remarks of the Models with Forward Selection

If we consult the Output in Table 4.26, 4.27 and 4.28 we get four models. Model 3

and 4 are not acceptable for being practically insignificant. But other two models are

acceptable because they qualify to be both statically and practically significant.

Model 2 with 2 IV (Mason and Paint) have greater R2 (0.908) value and smaller SE

(74.689) so we select this model at this stage. If we check with paragraph 4.15 then

we find that model is same as finalize in Step -1.

4.21 Model with Backward Elimination Method (Step-4)


way we performed the regression in Step-1. Here also we will drop Transport Cost,

Brick Cost and Carpenter Wage from the variable list and then perform the Forward

Selection with remaining 6 IV. The Tables are as follows:



1 .959a .920 .914 71.313

2 .959b .920 .915 70.943

3 .958c .919 .915 70.953

4 .957d .916 .913 71.487




Table 4.30: ANOVA


1 Regression 4667701.200 6 777950.200 152.974 .000a

Residual 406841.719 80 5085.521

Total 5074542.920 86

2 Regression 4666876.572 5 933375.314 185.454 .000b

Residual 407666.347 81 5032.918

Total 5074542.920 86

3 Regression 4661729.527 4 1165432.382 231.498 .000c

Residual 412813.393 82 5034.310

Total 5074542.920 86

4 Regression 4650383.655 3 1550127.885 303.331 .000d

Residual 424159.265 83 5110.353

Total 5074542.920 86


Model


Standardized

Coefficients


1 (Constant) -662.219 233.869 -2.832 .006

Steel .000 .002 -.017 -.403 .688

Cement .450 .373 .051 1.207 .231

Sand .306 .115 .286 2.651 .010

Paint 1.022 .280 .185 3.648 .000

Mason 2.493 1.956 .349 1.275 .206

Helper 1.406 1.433 .198 .981 .329

2 (Constant) -670.824 231.683 -2.895 .005

Cement .434 .369 .049 1.176 .243

Sand .309 .114 .290 2.706 .008

Paint 1.025 .279 .186 3.679 .000

Mason 2.366 1.920 .331 1.232 .221

Helper 1.439 1.423 .203 1.011 .315

3 (Constant) -820.923 177.920 -4.614 .000




Model


Standardized

Coefficients


Cement .534 .356 .061 1.501 .137

Sand .229 .082 .214 2.794 .006

Paint .959 .271 .174 3.540 .001

Mason 4.244 .488 .594 8.696 .000

4 (Constant) -690.457 156.419 -4.414 .000

Sand .242 .082 .226 2.949 .004

Paint .942 .273 .171 3.455 .001

Mason 4.450 .472 .623 9.426 .000


If we consult the Output in Table 4.29, 4.30 and 4.31 we get four models. We can

come in a conclusion that only models-4 is acceptable because they qualify to be both

statically and practically significant. This model has better goodness of fit and smaller

SE (R2= 0.916, Adjusted R2=0.913 and SE= 71.487). Model described in paragraph

4.15 had R2= 0.908, Adjusted R2=0.905 and SE= 74.689

The present model is as under

Construction= -690.457+ 4.45 × (Mason) + 0.942 × (Paint) + 0.242 × (Sand)

Here,




Sand= Price of Sand (Taka/ 100 cft)



performed the regression in Step-1. Here also we will drop Transport and Brick Cost

and Wage of Carpenter from the variable list and then perform the Forward Selection




with remaining 6 IV. The Tables are as follows:



1 .935a .874 .873 86.611

2 .953b .908 .905 74.689

3 .957c .916 .913 71.487

Table 4.33: ANOVA


1 Regression 4436924.912 1 4436924.912 591.480 .000a

Residual 637618.007 85 7501.388

Total 5074542.920 86

2 Regression 4605955.827 2 2302977.913 412.837 .000b

Residual 468587.093 84 5578.418

Total 5074542.920 86

3 Regression 4650383.655 3 1550127.885 303.331 .000c

Residual 424159.265 83 5110.353

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -357.338 76.820 -4.652 .000

Mason 6.678 .275 .935 24.320 .000

2 (Constant) -971.082 129.692 -7.488 .000

Mason 5.515 .317 .772 17.379 .000

Paint 1.351 .245 .245 5.505 .000

3 (Constant) -690.457 156.419 -4.414 .000

Mason 4.450 .472 .623 9.426 .000

Paint .942 .273 .171 3.455 .001

Sand .242 .082 .226 2.949 .004




4.22.1 Concluding Remarks of the Models with Forward Selection

If we consult the Output in Table 4.32, 4.33 and 4.34 we get four models. Model 3 is

the best and acceptable for being qualified to be both statically and practically

significant. Model 3 with 3 IV (Mason, Paint and Sand) have greater R2 (0.908) value

and smaller SE (74.689) so we select this model at this stage. If we check with

paragraph 4.15 then we find that model is same as finalize in Step -1.

4.23 Final Conclusion (Model-1)

Comparing all facts three models are significant in both statistically and practically.

But the model derived from paragraph 4.21.1 has the maximum R2 and minimum SE

(R2= 0.916, Adjusted R2=0.913 and SE= 71.487). So this one is the final model. The

equation is as under:

Here,




Sand= Price of Sand (Taka/ 100 cft)

Construction= -690.457+ 4.45 × Mason + 0.942 × Paint + 0.242 × Sand




4.24 General Information about Model-2

This section will show analysis of the model with the design variables those might

influence building construction costs. The process will be followed as stated in

paragraph 4.8 to 4.9.3 above. In all model Construction Cost per square feet is

Dependent Variable.

4.25 Model Enter Method (Step-1)

The model is done by Enter method using SPSS-17.



1 .760 .578 .474 176.114

a. Predictors: (Constant), Lift, Steel Grade, Stair, Deep Foundation, Corner,

Duration, Concrete, Toilet, Rd-1, Basement, Lobby, Transformer, Story, Plinth,

Rd-2, Area Generator.

Table 4.36: ANOVA


1 Regression 2934420.328 17 172612.960 5.565 .000a

Residual 2140122.591 69 31016.269

Total 5074542.920 86





Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) 2173.389 304.252 7.143 .000

Duration -16.739 3.429 -.431 -4.881 .000

Corner 60.598 74.294 .117 .816 .418

Rd_1 -1.346 1.898 -.076 -.709 .481

Rd_2 -2.218 2.355 -.156 -.942 .349

Deep_Foundation -17.785 43.430 -.036 -.410 .683

Basement 11.566 51.196 .021 .226 .822

Area 35.696 24.267 .493 1.471 .146

Plinth -.104 .044 -.671 -2.367 .021

Story 35.522 16.422 .237 2.163 .034

Lobby .085 .284 .031 .301 .764

Toilet -6.900 5.185 -.150 -1.331 .188

Stair -43.440 18.411 -.200 -2.359 .021

Concrete -.101 .061 -.160 -1.663 .101

Steel_Grade -1.733 4.265 -.042 -.406 .686

Transformer .174 .231 .082 .750 .456

Generator .149 .462 .032 .322 .749

Lift 23.722 6.903 .393 3.437 .001





Enter Method considered 17 independent variables (IV) were entered with

Construction Cost as dependent variable (DV). The IV are Lift, Steel Grade, Stair,

Deep Foundation, Corner, Duration, Concrete, Toilet, Rd-1, Basement, Lobby,

Transformer, Story, Plinth, Rd-2, Area Generator. All the variables were considered

but none was rejected.





Referring to Table 4.35, the value of R2 and Adjusted R2 are 0.578 and 0.474. There is

considerable change between R2 and Adjusted R2. This means that the model can

explain 57.8% of the variability with the 17 variables. The Standard Error (SE) is

176.114 which is a bit more considering the Model-1.

4.25.4 ANOVA

Referring to Table 4.36, the F ratio for degree of freedom (df) 17 and 69 is 5.565

which is acceptable with 0.000 level of significance (Confidence Interval 99.99%).

The critical F ratio for df (17, 69) for P value 0.005 is 2.00387212 which is less than

F=5.565. That means the overall model is significant. F critical is not always

required to find. If P value is less than or equal to 0.050 than F ratio will always be

significant. So, from next onward I will not bring F critical if P value is less than or

equal to 0.050. As P value is 0.000, the overall model is good.

4.25.5 Coefficient

Referring to Table 4.37, the only duration, plinth, storey, concrete strength, steel

grade and lift are significant at 5% level. Other variables are not significant as shown

in the last column (Sig.). Necessity of checking other values is of no use. So we

cannot accept the model with all these variables. So we have to try another model.


Model cannot be accepted because individual level of significance crossed 5% for

many variables.

4.26 Model with Backward Elimination Method-1


as follows:






1 .760 .578 .474 176.114

2 .760 .578 .481 174.917

3 .760 .577 .488 173.774

4 .760 .577 .495 172.647

5 .759 .576 .501 171.582

6 .758 .575 .506 170.654

7 .757 .573 .510 169.975

8 .755 .571 .514 169.298

9 .748 .559 .508 170.388

10 .741 .549 .503 171.320

11 .732 .535 .494 172.762

12 .725 .525 .490 173.515

13 .717 .514 .484 174.435

Table 4.39: ANOVA


1 Regression 2934420.328 17 172612.960 5.565 .000

Residual 2140122.591 69 31016.269

Total 5074542.920 86

2 Regression 2932837.323 16 183302.333 5.991 .000

Residual 2141705.597 70 30595.794

Total 5074542.920 86

3 Regression 2930526.031 15 195368.402 6.470 .000

Residual 2144016.889 71 30197.421

Total 5074542.920 86

4 Regression 2928445.437 14 209174.674 7.018 .000

Residual 2146097.483 72 29806.909

Total 5074542.920 86

5 Regression 2925401.079 13 225030.852 7.644 .000

Residual 2149141.841 73 29440.299

Total 5074542.920 86

6 Regression 2919444.398 12 243287.033 8.354 .000

Residual 2155098.522 74 29122.953





Total 5074542.920 86

7 Regression 2907687.355 11 264335.214 9.149 .000

Residual 2166855.565 75 28891.408

Total 5074542.920 86

8 Regression 2896249.013 10 289624.901 10.105 .000

Residual 2178293.907 76 28661.762

Total 5074542.920 86

9 Regression 2839078.114 9 315453.124 10.866 .000

Residual 2235464.806 77 29032.010

Total 5074542.920 86

10 Regression 2785208.295 8 348151.037 11.862 .000

Residual 2289334.625 78 29350.444

Total 5074542.920 86

11 Regression 2716660.970 7 388094.424 13.003 .000

Residual 2357881.949 79 29846.607

Total 5074542.920 86

12 Regression 2665946.690 6 444324.448 14.758 .000

Residual 2408596.229 80 30107.453

Total 5074542.920 86

13 Regression 2609911.791 5 521982.358 17.155 .000

Residual 2464631.129 81 30427.545

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) 2173.389 304.252 7.143 .000

Duration -16.739 3.429 -.431 -4.881 .000

Corner 60.598 74.294 .117 .816 .418

Rd_1 -1.346 1.898 -.076 -.709 .481

Rd_2 -2.218 2.355 -.156 -.942 .349

Deep_Foundation -17.785 43.430 -.036 -.410 .683

Basement 11.566 51.196 .021 .226 .822

Area 35.696 24.267 .493 1.471 .146




Model

Unstandardized

Coefficients

Standardized

Coefficients


Plinth -.104 .044 -.671 -2.367 .021

Story 35.522 16.422 .237 2.163 .034

Lobby .085 .284 .031 .301 .764

Toilet -6.900 5.185 -.150 -1.331 .188

Stair -43.440 18.411 -.200 -2.359 .021

Concrete -.101 .061 -.160 -1.663 .101

Steel_Grade -1.733 4.265 -.042 -.406 .686

Transformer .174 .231 .082 .750 .456

Generator .149 .462 .032 .322 .749

Lift 23.722 6.903 .393 3.437 .001

2 (Constant) 2171.266 302.038 7.189 .000

Duration -16.685 3.398 -.429 -4.911 .000

Corner 61.349 73.714 .119 .832 .408

Rd_1 -1.373 1.882 -.078 -.730 .468

Rd_2 -2.206 2.338 -.155 -.943 .349

Deep_Foundation -15.935 42.361 -.032 -.376 .708

Area 34.701 23.702 .479 1.464 .148

Plinth -.101 .042 -.656 -2.398 .019

Story 36.368 15.880 .242 2.290 .025

Lobby .077 .279 .028 .275 .784

Toilet -6.961 5.143 -.151 -1.353 .180

Stair -43.696 18.251 -.201 -2.394 .019

Concrete -.104 .059 -.165 -1.756 .084

Steel_Grade -1.687 4.231 -.041 -.399 .691

Transformer .175 .230 .083 .763 .448

Generator .144 .458 .031 .313 .755

Lift 24.176 6.560 .400 3.686 .000

3 (Constant) 2169.309 299.982 7.231 .000

Duration -16.474 3.288 -.424 -5.010 .000

Corner 62.918 73.013 .122 .862 .392

Rd_1 -1.429 1.859 -.081 -.769 .445

Rd_2 -2.255 2.316 -.159 -.974 .334

Deep_Foundation -16.202 42.073 -.033 -.385 .701




Model

Unstandardized

Coefficients

Standardized

Coefficients


Area 36.158 22.950 .499 1.576 .120

Plinth -.102 .042 -.661 -2.436 .017

Story 36.523 15.766 .243 2.317 .023

Toilet -7.109 5.081 -.154 -1.399 .166

Stair -44.341 17.981 -.204 -2.466 .016

Concrete -.106 .058 -.169 -1.826 .072

Steel_Grade -1.523 4.161 -.037 -.366 .715

Transformer .177 .228 .084 .774 .442

Generator .117 .445 .025 .262 .794

Lift 24.391 6.470 .404 3.770 .000

4 (Constant) 2171.396 297.931 7.288 .000

Duration -16.406 3.257 -.422 -5.038 .000

Corner 63.723 72.475 .123 .879 .382

Rd_1 -1.430 1.846 -.081 -.774 .441

Rd_2 -2.292 2.297 -.161 -.998 .322

Deep_Foundation -17.281 41.600 -.035 -.415 .679

Area 37.746 21.995 .521 1.716 .090

Plinth -.104 .041 -.676 -2.573 .012

Story 36.382 15.655 .242 2.324 .023

Toilet -7.229 5.028 -.157 -1.438 .155

Stair -45.006 17.687 -.207 -2.545 .013

Concrete -.110 .056 -.175 -1.976 .052

Steel_Grade -1.291 4.040 -.031 -.320 .750

Transformer .171 .226 .081 .757 .451

Lift 24.903 6.130 .412 4.063 .000

5 (Constant) 2112.998 233.863 9.035 .000

Duration -16.309 3.223 -.420 -5.061 .000

Corner 61.987 71.826 .120 .863 .391

Rd_1 -1.504 1.821 -.085 -.826 .412

Rd_2 -2.312 2.282 -.163 -1.013 .314

Deep_Foundation -18.516 41.165 -.038 -.450 .654

Area 38.616 21.692 .533 1.780 .079

Plinth -.105 .040 -.681 -2.608 .011




Model

Unstandardized

Coefficients

Standardized

Coefficients


Story 35.731 15.426 .238 2.316 .023

Toilet -7.213 4.996 -.157 -1.444 .153

Stair -45.062 17.577 -.207 -2.564 .012

Concrete -.114 .054 -.180 -2.090 .040

Transformer .134 .192 .064 .696 .489

Lift 24.919 6.092 .412 4.091 .000

6 (Constant) 2087.033 225.403 9.259 .000

Duration -16.240 3.201 -.418 -5.073 .000

Corner 64.738 71.178 .125 .910 .366

Rd_1 -1.312 1.760 -.074 -.745 .459

Rd_2 -2.387 2.263 -.168 -1.055 .295

Area 39.229 21.532 .542 1.822 .073

Plinth -.106 .040 -.688 -2.655 .010

Story 36.705 15.190 .245 2.416 .018

Toilet -7.479 4.934 -.162 -1.516 .134

Stair -44.489 17.436 -.204 -2.552 .013

Concrete -.112 .054 -.178 -2.075 .042

Transformer .120 .189 .057 .635 .527

Lift 24.970 6.058 .413 4.122 .000

7 (Constant) 2072.320 223.317 9.280 .000

Duration -15.992 3.165 -.411 -5.053 .000

Corner 75.775 68.751 .147 1.102 .274

Rd_1 -1.079 1.715 -.061 -.629 .531

Rd_2 -2.743 2.184 -.193 -1.256 .213

Area 41.670 21.102 .575 1.975 .052

Plinth -.107 .040 -.695 -2.698 .009

Story 36.518 15.127 .243 2.414 .018

Toilet -7.428 4.914 -.161 -1.512 .135

Stair -45.368 17.311 -.208 -2.621 .011

Concrete -.108 .053 -.171 -2.020 .047

Lift 24.615 6.008 .407 4.097 .000

8 (Constant) 2052.985 220.312 9.319 .000

Duration -15.760 3.131 -.405 -5.034 .000




Model

Unstandardized

Coefficients

Standardized

Coefficients


Corner 90.741 64.249 .176 1.412 .162

Rd_2 -3.521 1.794 -.248 -1.963 .053

Area 43.930 20.711 .606 2.121 .037

Plinth -.111 .039 -.716 -2.813 .006

Story 34.972 14.866 .233 2.352 .021

Toilet -7.452 4.894 -.162 -1.523 .132

Stair -45.326 17.242 -.208 -2.629 .010

Concrete -.111 .053 -.176 -2.105 .039

Lift 24.531 5.982 .406 4.101 .000

9 (Constant) 2043.504 221.628 9.220 .000

Duration -15.943 3.148 -.410 -5.064 .000

Rd_2 -1.575 1.156 -.111 -1.362 .177

Area 43.634 20.843 .602 2.093 .040

Plinth -.110 .040 -.712 -2.780 .007

Story 30.894 14.677 .206 2.105 .039

Toilet -8.174 4.899 -.177 -1.669 .099

Stair -41.814 17.172 -.192 -2.435 .017

Concrete -.098 .052 -.156 -1.879 .064

Lift 26.063 5.921 .431 4.402 .000

10 (Constant) 1944.499 210.516 9.237 .000

Duration -16.347 3.151 -.421 -5.187 .000

Area 40.147 20.799 .554 1.930 .057

Plinth -.103 .039 -.666 -2.610 .011

Story 34.186 14.556 .228 2.349 .021

Toilet -7.487 4.899 -.163 -1.528 .131

Stair -39.984 17.213 -.184 -2.323 .023

Concrete -.082 .051 -.130 -1.600 .114

Lift 26.841 5.926 .444 4.530 .000

11 (Constant) 1863.303 205.416 9.071 .000

Duration -16.894 3.157 -.435 -5.350 .000

Area 32.419 20.345 .448 1.594 .115

Plinth -.106 .040 -.686 -2.667 .009

Story 39.389 14.272 .262 2.760 .007




Model

Unstandardized

Coefficients

Standardized

Coefficients


Stair -41.059 17.343 -.189 -2.367 .020

Concrete -.066 .051 -.105 -1.304 .196

Lift 27.765 5.944 .459 4.671 .000

12 (Constant) 1649.818 124.529 13.248 .000

Duration -17.062 3.169 -.439 -5.385 .000

Area 27.365 20.059 .378 1.364 .176

Plinth -.098 .039 -.637 -2.494 .015

Story 38.600 14.321 .257 2.695 .009

Stair -38.645 17.319 -.178 -2.231 .028

Lift 28.177 5.962 .466 4.726 .000

13 (Constant) 1595.189 118.541 13.457 .000

Duration -17.047 3.185 -.439 -5.352 .000

Plinth -.047 .013 -.307 -3.706 .000

Story 44.252 13.781 .295 3.211 .002

Stair -36.745 17.355 -.169 -2.117 .037

Lift 31.015 5.617 .513 5.522 .000




4.26.2 The Variables Considered in the Model

Referring to Table 4.38, 4.39 and 4.40 we can see that the Backward Elimination

Method of Regression has produced 13 (thirteen) models automatically. At the first

model all the IV are included. In the each successive step single variable is removed

one after another depending on P value greater than or equal to 0.100. It removes the

variable first whose P value is highest. This way it removes IV one after another till it

gets all the IV to be statistically significant. In the Final Model (13th) five variables

Duration, Plinth, Storey, Stair and Lift were retained.





Referring to Table 4.38 the value of R2 of model 13 is 0,514, Corresponding Adjusted

R2 of model 1 is 0.484. There is considerable change between R2 and Adjusted R2.

This model can explain 51.4% of the variability. Corresponding Standard Errors (SE)

174.435 which is slightly more than that of Enter Method. We can confirm that the

Model is workable.

4.26.4 ANOVA


(Confidence Interval 99.99%) for the model.

4.26.5 Coefficient





Referring to Table 4.40, in 13th model each variable is individually statistically

significant below 5% level. But the coefficients of Duration and Stair are are negative

i.e., If the Duration or Number of Stair is decreased the Construction Cost will

increase and vice versa. In real world it is never true. So we cannot accept the model

from practical significance point of view.


None of the models are acceptable because they do not qualify to be both statically

and practically significant.




4.27 Model with Forward Selection Method-1


follows:



1 .457a .209 .200 217.320

2 .587b .344 .328 199.064

3 .648c .420 .399 188.348

4 .698d .487 .462 178.101

5 .717e .514 .484 174.435

Table 4.42: ANOVA


1 Regression 1060174.072 1 1060174.072 22.448 .000a

Residual 4014368.848 85 47227.869

Total 5074542.920 86

2 Regression 1745912.754 2 872956.377 22.030 .000b

Residual 3328630.165 84 39626.550

Total 5074542.920 86

3 Regression 2130132.885 3 710044.295 20.015 .000c

Residual 2944410.035 83 35474.820

Total 5074542.920 86

4 Regression 2473509.283 4 618377.321 19.495 .000d

Residual 2601033.637 82 31719.922

Total 5074542.920 86

5 Regression 2609911.791 5 521982.358 17.155 .000e

Residual 2464631.129 81 30427.545

Total 5074542.920 86





Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) 1246.103 57.905 21.520 .000

Lift 27.625 5.831 .457 4.738 .000

2 (Constant) 1621.177 104.608 15.498 .000

Lift 32.229 5.454 .533 5.909 .000

Duration -14.591 3.508 -.375 -4.160 .000

3 (Constant) 1712.529 102.795 16.660 .000

Lift 37.767 5.428 .625 6.958 .000

Duration -13.923 3.325 -.358 -4.188 .000

Plinth -.045 .014 -.292 -3.291 .001

4 (Constant) 1513.643 114.465 13.224 .000

Lift 29.639 5.696 .490 5.203 .000

Duration -15.776 3.194 -.406 -4.939 .000

Plinth -.050 .013 -.323 -3.830 .000

Story 46.193 14.040 .308 3.290 .001

5 (Constant) 1595.189 118.541 13.457 .000

Lift 31.015 5.617 .513 5.522 .000

Duration -17.047 3.185 -.439 -5.352 .000

Plinth -.047 .013 -.307 -3.706 .000

Story 44.252 13.781 .295 3.211 .002

Stair -36.745 17.355 -.169 -2.117 .037





Table 4.41 shows that the Forward Selection method has produced five models

automatically. IV are included in the model successively one after another. In the first

model it has included Lift and there after duration, Plinth, Storey and finally Stairs

successively in each model.




4.27.3 Model Summary and ANOVA

Referring to Table 4.41 and 4.42, the value of R2 of 5 models are between 0.209 to

0.514 and Corresponding Adjusted R2 are between 0.200 and 0.484. There is no


explain 20.9% to 51.4% of the variability respectively. Corresponding Standard

Errors (SE) lie between 217.320 and 174.435 which are very big but considerable in

regards to the DV in question. We can confirm that all the models are statistically

significant but model 5 is the best in consideration to others in respect of R2, Adjusted

R2 and SE.

4.27.4 Coefficient

Referring to Table 4.43, all the models have P value less than 0.050. So we can accept

the models with the variables each have considered. Now we will check practical

significance in the next paragraph.


Referring to Table 4.43, in 1st model the variable Lift is individually significant

practical purpose. But the coefficients of Duration and Stair are negative which is not

real. So, all models will be rejected except model-1.

4.27.6 Concluding Remarks of the Models with Forward Selection:




as follows:






1 .658 .433 .303 202.806

2 .658 .433 .313 201.373

3 .658 .433 .322 199.984

4 .657 .432 .331 198.663

5 .657 .432 .340 197.362

6 .657 .432 .348 196.102

7 .657 .431 .357 194.857

8 .654 .428 .361 194.221

9 .644 .415 .355 195.122

10 .636 .405 .352 195.562

11 .623 .388 .342 197.065

12 .606 .367 .328 199.182

13 .591 .349 .317 200.761

Table 4.45: ANOVA


1 Regression 2195416.511 16 137213.532 3.336 .000

Residual 2879126.409 70 41130.377

Total 5074542.920 86

2 Regression 2195413.031 15 146360.869 3.609 .000

Residual 2879129.889 71 40551.125

Total 5074542.920 86

3 Regression 2195010.075 14 156786.434 3.920 .000

Residual 2879532.844 72 39993.512

Total 5074542.920 86

4 Regression 2193448.025 13 168726.771 4.275 .000

Residual 2881094.895 73 39467.053

Total 5074542.920 86

5 Regression 2192104.335 12 182675.361 4.690 .000

Residual 2882438.584 74 38951.873

Total 5074542.920 86

6 Regression 2190354.238 11 199123.113 5.178 .000

Residual 2884188.682 75 38455.849





Total 5074542.920 86

7 Regression 2188870.317 10 218887.032 5.765 .000

Residual 2885672.602 76 37969.376

Total 5074542.920 86

8 Regression 2169965.312 9 241107.257 6.392 .000

Residual 2904577.607 77 37721.787

Total 5074542.920 86

9 Regression 2104886.778 8 263110.847 6.911 .000

Residual 2969656.142 78 38072.515

Total 5074542.920 86

10 Regression 2053239.434 7 293319.919 7.670 .000

Residual 3021303.486 79 38244.348

Total 5074542.920 86

11 Regression 1967760.130 6 327960.022 8.445 .000

Residual 3106782.790 80 38834.785

Total 5074542.920 86

12 Regression 1861000.620 5 372200.124 9.382 .000

Residual 3213542.300 81 39673.362

Total 5074542.920 86

13 Regression 1769537.457 4 442384.364 10.976 .000

Residual 3305005.462 82 40304.945

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) 1801.105 339.178 5.310 .000

Corner 104.697 84.919 .203 1.233 .222

Rd_1 -.436 2.175 -.025 -.201 .842

Rd_2 -4.340 2.665 -.306 -1.628 .108

Deep_Foundat

ion -9.936 49.978 -.020 -.199 .843

Basement -5.839 58.813 -.010 -.099 .921

Area 52.513 27.662 .725 1.898 .062




Model

Unstandardized

Coefficients

Standardized

Coefficients


Plinth -.117 .050 -.758 -2.325 .023

Story 22.880 18.674 .152 1.225 .225

Lobby -.237 .318 -.086 -.746 .458

Toilet -10.612 5.906 -.230 -1.797 .077

Stair -33.900 21.082 -.156 -1.608 .112

Concrete -.146 .069 -.232 -2.112 .038

Steel_Grade 1.140 4.864 .028 .234 .815

Transformer .002 .263 .001 .009 .993

Generator -.136 .528 -.029 -.257 .798

Lift 22.299 7.942 .369 2.808 .006

2 (Constant) 1799.917 311.414 5.780 .000

Corner 104.823 83.204 .203 1.260 .212

Rd_1 -.434 2.143 -.025 -.202 .840

Rd_2 -4.346 2.585 -.306 -1.681 .097

Deep_Foundat

ion -9.905 49.512 -.020 -.200 .842

Basement -5.816 58.341 -.010 -.100 .921

Area 52.567 26.844 .726 1.958 .054

Plinth -.117 .050 -.758 -2.352 .021

Story 22.871 18.519 .152 1.235 .221

Lobby -.237 .315 -.086 -.752 .454

Toilet -10.611 5.863 -.230 -1.810 .075

Stair -33.916 20.855 -.156 -1.626 .108

Concrete -.146 .069 -.232 -2.127 .037

Steel_Grade 1.162 4.186 .028 .278 .782

Generator -.136 .523 -.029 -.260 .796

Lift 22.295 7.878 .369 2.830 .006

3 (Constant) 1800.943 309.096 5.826 .000

Corner 104.456 82.549 .202 1.265 .210

Rd_1 -.420 2.123 -.024 -.198 .844

Rd_2 -4.353 2.567 -.307 -1.696 .094

Deep_Foundat

ion -10.844 48.274 -.022 -.225 .823

Area 53.073 26.178 .733 2.027 .046




Model

Unstandardized

Coefficients

Standardized

Coefficients


Plinth -.118 .048 -.766 -2.465 .016

Story 22.426 17.848 .149 1.257 .213

Lobby -.233 .310 -.085 -.751 .455

Toilet -10.586 5.818 -.230 -1.820 .073

Stair -33.763 20.655 -.155 -1.635 .106

Concrete -.145 .067 -.230 -2.163 .034

Steel_Grade 1.133 4.147 .027 .273 .785

Generator -.134 .519 -.029 -.257 .798

Lift 22.065 7.480 .365 2.950 .004

4 (Constant) 1800.337 307.040 5.864 .000

Corner 110.324 76.516 .213 1.442 .154

Rd_2 -4.631 2.133 -.326 -2.172 .033

Deep_Foundat

ion -8.600 46.611 -.017 -.185 .854

Area 53.683 25.824 .741 2.079 .041

Plinth -.119 .047 -.773 -2.519 .014

Story 22.117 17.662 .147 1.252 .214

Lobby -.225 .306 -.082 -.737 .464

Toilet -10.596 5.779 -.230 -1.833 .071

Stair -33.682 20.514 -.155 -1.642 .105

Concrete -.145 .067 -.230 -2.177 .033

Steel_Grade .929 3.989 .023 .233 .817

Generator -.129 .515 -.028 -.250 .803

Lift 22.010 7.425 .364 2.964 .004

5 (Constant) 1793.686 302.920 5.921 .000

Corner 110.114 76.006 .213 1.449 .152

Rd_2 -4.590 2.107 -.323 -2.178 .033

Area 53.534 25.642 .739 2.088 .040

Plinth -.119 .047 -.773 -2.535 .013

Story 22.735 17.227 .151 1.320 .191

Lobby -.225 .304 -.082 -.742 .460

Toilet -10.710 5.709 -.232 -1.876 .065

Stair -33.337 20.295 -.153 -1.643 .105




Model

Unstandardized

Coefficients

Standardized

Coefficients


Concrete -.143 .066 -.227 -2.185 .032

Steel_Grade .833 3.929 .020 .212 .833

Generator -.119 .509 -.026 -.234 .816

Lift 22.007 7.376 .364 2.983 .004

6 (Constant) 1827.620 255.516 7.153 .000

Corner 111.731 75.139 .216 1.487 .141

Rd_2 -4.573 2.092 -.322 -2.186 .032

Area 52.872 25.288 .730 2.091 .040

Plinth -.118 .047 -.767 -2.542 .013

Story 23.114 17.025 .154 1.358 .179

Lobby -.216 .299 -.079 -.724 .471

Toilet -10.669 5.669 -.232 -1.882 .064

Stair -33.264 20.162 -.153 -1.650 .103

Concrete -.139 .063 -.221 -2.230 .029

Generator -.097 .495 -.021 -.196 .845

Lift 21.809 7.270 .361 3.000 .004

7 (Constant) 1816.626 247.730 7.333 .000

Corner 110.635 74.457 .214 1.486 .141

Rd_2 -4.547 2.074 -.320 -2.192 .031

Area 51.548 24.220 .712 2.128 .037

Plinth -.116 .045 -.754 -2.575 .012

Story 22.992 16.906 .153 1.360 .178

Lobby -.206 .292 -.075 -.706 .483

Toilet -10.554 5.603 -.229 -1.884 .063

Stair -32.605 19.754 -.150 -1.650 .103

Concrete -.137 .061 -.217 -2.256 .027

Lift 21.358 6.855 .353 3.116 .003

8 (Constant) 1804.368 246.313 7.326 .000

Corner 104.139 73.644 .201 1.414 .161

Rd_2 -4.352 2.049 -.306 -2.124 .037

Area 48.440 23.738 .669 2.041 .045

Plinth -.116 .045 -.751 -2.572 .012

Story 22.066 16.800 .147 1.313 .193




Model

Unstandardized

Coefficients

Standardized

Coefficients


Toilet -10.336 5.576 -.224 -1.854 .068

Stair -30.654 19.496 -.141 -1.572 .120

Concrete -.135 .060 -.214 -2.232 .029

Lift 21.029 6.816 .348 3.085 .003

9 (Constant) 1940.212 224.585 8.639 .000

Corner 84.349 72.421 .163 1.165 .248

Rd_2 -4.183 2.055 -.295 -2.036 .045

Area 58.407 22.597 .806 2.585 .012

Plinth -.129 .044 -.835 -2.918 .005

Toilet -12.136 5.430 -.263 -2.235 .028

Stair -32.770 19.519 -.151 -1.679 .097

Concrete -.134 .061 -.213 -2.216 .030

Lift 23.645 6.549 .391 3.610 .001

10 (Constant) 1902.895 222.789 8.541 .000

Rd_2 -2.333 1.306 -.164 -1.786 .078

Area 56.314 22.576 .777 2.494 .015

Plinth -.126 .044 -.816 -2.850 .006

Toilet -12.536 5.431 -.272 -2.308 .024

Stair -28.798 19.262 -.132 -1.495 .139

Concrete -.122 .060 -.194 -2.042 .045

Lift 24.606 6.512 .407 3.779 .000

11 (Constant) 1830.636 219.155 8.353 .000

Rd_2 -2.175 1.312 -.153 -1.658 .101

Area 53.970 22.694 .745 2.378 .020

Plinth -.122 .045 -.793 -2.751 .007

Toilet -12.856 5.469 -.279 -2.351 .021

Concrete -.111 .060 -.176 -1.855 .067

Lift 24.408 6.560 .404 3.720 .000

12 (Constant) 1713.592 209.703 8.172 .000

Area 51.346 22.882 .709 2.244 .028

Plinth -.115 .045 -.747 -2.577 .012

Toilet -12.279 5.516 -.267 -2.226 .029

Concrete -.090 .059 -.142 -1.518 .133




Model

Unstandardized

Coefficients

Standardized

Coefficients


Lift 25.880 6.570 .428 3.939 .000

13 (Constant) 1411.688 67.156 21.021 .000

Area 43.086 22.402 .595 1.923 .058

Plinth -.107 .045 -.690 -2.381 .020

Toilet -10.506 5.434 -.228 -1.933 .057

Lift 26.604 6.604 .440 4.028 .000











Area, Plinth, Toilet and Lift were retained.


Referring to Table 4.44 the value of R2 of model 13 is 0.049 that means this model

can explain 44.4% of the variability and corresponding Standard Errors (SE) is

200.76 which .

4.28.4 ANOVA



4.28.5 Coefficient

Referring to Table 4.46, no model is individually statistically significant below 5%

level. So we cannot accept any model with its integral variables.




4.28.6 Concluding Remarks of the Models with Backward Elimination-2

None of the models are acceptable because they do not qualify to be statically

significant below 5% level of significance.



follows:



1 .457a .209 .200 217.320

2 .549b .301 .285 205.463

Table 4.48: ANOVA


1 Regression 1060174.072 1 1060174.072 22.448 .000a

Residual 4014368.848 85 47227.869

Total 5074542.920 86

2 Regression 1528477.131 2 764238.566 18.103 .000b

Residual 3546065.788 84 42215.069

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) 1246.103 57.905 21.520 .000

Lift 27.625 5.831 .457 4.738 .000

2 (Constant) 1340.618 61.663 21.741 .000

Lift 30.280 5.570 .501 5.437 .000

Toilet -14.141 4.246 -.307 -3.331 .001








Table 4.47 shows that the Forward Selection method has produced two models


model it has included Lift in the first model and added Toilet in the second model.


Referring to Table 4.47 and 4.48, the value of R2 of 2 models are 0.209 and 0.301 that

means the models can explain means that the models can explain 20.9% and 30.1% of

the variability respectively. Corresponding Standard Errors (SE) are 217.320 and

205.463 which are very big but considerable in regards to the DV in question. We can

confirm that both the models are statistically significant but model 2 is the best in

consideration to one in respect of R2, Adjusted R2 and SE.

4.29.4 Coefficient

Referring to Table 4.49, all the models have P value less than 0.050 for coefficient. So

we can accept the models with the variables each have considered. Now we will

check practical significance in the next paragraph.


Referring to Table 4.49, in 1st model the variable Lift is individually significant

practical purpose. But the coefficient of Toilet is negative which is not real. So,

model-2 will be rejected and model-1 will be accepted.




4.29.6 Concluding Remarks of the Models with Stepwise Regression:




as follows:



1 .638 .406 .281 205.964

2 .638 .406 .291 204.529

3 .638 .406 .301 203.125

4 .637 .406 .310 201.757

5 .637 .406 .319 200.466

6 .637 .406 .328 199.188

7 .636 .405 .335 198.056

8 .634 .402 .341 197.230

9 .618 .382 .328 199.167

10 .607 .368 .321 200.234

11 .596 .355 .315 200.987

12 .587 .344 .312 201.457

13 .579 .335 .311 201.646

Table 4.51: ANOVA


1 Regression 2062651.380 15 137510.092 3.242 .000

Residual 3011891.539 71 42421.008

Total 5074542.920 86

2 Regression 2062629.675 14 147330.691 3.522 .000

Residual 3011913.245 72 41832.128

Total 5074542.920 86

3 Regression 2062593.497 13 158661.038 3.845 .000

Residual 3011949.423 73 41259.581

Total 5074542.920 86





4 Regression 2062308.888 12 171859.074 4.222 .000

Residual 3012234.031 74 40705.865

Total 5074542.920 86

5 Regression 2060551.064 11 187322.824 4.661 .000

Residual 3013991.856 75 40186.558

Total 5074542.920 86

6 Regression 2059184.700 10 205918.470 5.190 .000

Residual 3015358.220 76 39675.766

Total 5074542.920 86

7 Regression 2054141.350 9 228237.928 5.819 .000

Residual 3020401.570 77 39225.994

Total 5074542.920 86

8 Regression 2040368.193 8 255046.024 6.557 .000

Residual 3034174.727 78 38899.676

Total 5074542.920 86

9 Regression 1940822.716 7 277260.388 6.990 .000

Residual 3133720.204 79 39667.344

Total 5074542.920 86

10 Regression 1867053.886 6 311175.648 7.761 .000

Residual 3207489.033 80 40093.613

Total 5074542.920 86

11 Regression 1802470.815 5 360494.163 8.924 .000

Residual 3272072.104 81 40395.952

Total 5074542.920 86

12 Regression 1746572.227 4 436643.057 10.759 .000

Residual 3327970.693 82 40585.008

Total 5074542.920 86

13 Regression 1699671.708 3 566557.236 13.934 .000

Residual 3374871.211 83 40661.099

Total 5074542.920 86





Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) 1663.863 335.608 4.958 .000

Corner 118.170 85.904 .229 1.376 .173

Rd_1 -.449 2.209 -.025 -.203 .840

Rd_2 -4.428 2.706 -.312 -1.636 .106

Deep_Foundation -19.798 50.449 -.040 -.392 .696

Basement -1.350 59.674 -.002 -.023 .982

Area 40.455 27.253 .558 1.484 .142

Plinth -.119 .051 -.772 -2.333 .023

Story 29.375 18.606 .196 1.579 .119

Lobby -.191 .321 -.070 -.595 .553

Stair -34.284 21.409 -.158 -1.601 .114

Concrete -.121 .069 -.192 -1.761 .083

Steel_Grade 1.086 4.940 .026 .220 .827

Transformer -.008 .268 -.004 -.028 .978

Generator -.045 .534 -.010 -.085 .933

Lift 22.548 8.064 .373 2.796 .007

2 (Constant) 1664.046 333.174 4.995 .000

Corner 118.091 85.235 .228 1.385 .170

Rd_1 -.445 2.188 -.025 -.203 .839

Rd_2 -4.431 2.686 -.312 -1.650 .103

Deep_Foundation -20.007 49.250 -.041 -.406 .686

Area 40.584 26.456 .560 1.534 .129

Plinth -.120 .049 -.774 -2.428 .018

Story 29.267 17.860 .195 1.639 .106

Lobby -.191 .317 -.069 -.601 .550

Stair -34.250 21.208 -.157 -1.615 .111

Concrete -.121 .067 -.192 -1.801 .076

Steel_Grade 1.082 4.902 .026 .221 .826

Transformer -.008 .265 -.004 -.029 .977

Generator -.045 .530 -.010 -.084 .933

Lift 22.494 7.650 .372 2.940 .004




Model

Unstandardized

Coefficients

Standardized

Coefficients


3 (Constant) 1667.843 305.033 5.468 .000

Corner 117.683 83.520 .228 1.409 .163

Rd_1 -.453 2.156 -.026 -.210 .834

Rd_2 -4.414 2.607 -.311 -1.693 .095

Deep_Foundation -20.122 48.758 -.041 -.413 .681

Area 40.414 25.633 .558 1.577 .119

Plinth -.119 .049 -.773 -2.450 .017

Story 29.291 17.719 .195 1.653 .103

Lobby -.191 .314 -.070 -.608 .545

Stair -34.195 20.978 -.157 -1.630 .107

Concrete -.121 .067 -.192 -1.814 .074

Steel_Grade 1.010 4.211 .024 .240 .811

Generator -.044 .525 -.009 -.083 .934

Lift 22.501 7.593 .372 2.963 .004

4 (Constant) 1666.169 302.317 5.511 .000

Corner 117.395 82.886 .227 1.416 .161

Rd_1 -.445 2.139 -.025 -.208 .836

Rd_2 -4.405 2.587 -.310 -1.703 .093

Deep_Foundation -19.631 48.072 -.040 -.408 .684

Area 39.854 24.567 .550 1.622 .109

Plinth -.119 .047 -.767 -2.508 .014

Story 29.263 17.596 .195 1.663 .101

Lobby -.186 .306 -.068 -.607 .545

Stair -33.886 20.508 -.156 -1.652 .103

Concrete -.120 .064 -.190 -1.869 .066

Steel_Grade .934 4.083 .023 .229 .820

Lift 22.289 7.101 .369 3.139 .002

5 (Constant) 1665.591 300.369 5.545 .000

Corner 123.675 76.687 .239 1.613 .111

Rd_2 -4.701 2.144 -.331 -2.193 .031

Deep_Foundation -17.316 46.465 -.035 -.373 .710

Area 40.557 24.178 .560 1.677 .098

Plinth -.120 .047 -.775 -2.570 .012




Model

Unstandardized

Coefficients

Standardized

Coefficients


Story 28.944 17.417 .193 1.662 .101

Lobby -.178 .302 -.065 -.590 .557

Stair -33.838 20.375 -.155 -1.661 .101

Concrete -.120 .064 -.190 -1.883 .064

Steel_Grade .725 3.933 .018 .184 .854

Lift 22.256 7.054 .368 3.155 .002

6 (Constant) 1696.183 248.797 6.818 .000

Corner 125.264 75.715 .242 1.654 .102

Rd_2 -4.688 2.129 -.330 -2.202 .031

Deep_Foundation -16.357 45.878 -.033 -.357 .722

Area 40.240 23.963 .556 1.679 .097

Plinth -.119 .046 -.773 -2.581 .012

Story 29.364 17.157 .196 1.711 .091

Lobby -.173 .299 -.063 -.578 .565

Stair -33.872 20.245 -.156 -1.673 .098

Concrete -.117 .061 -.185 -1.911 .060

Lift 22.178 6.997 .367 3.170 .002

7 (Constant) 1674.415 239.818 6.982 .000

Corner 124.994 75.281 .242 1.660 .101

Rd_2 -4.618 2.108 -.325 -2.190 .032

Area 40.023 23.819 .553 1.680 .097

Plinth -.120 .046 -.776 -2.608 .011

Story 30.649 16.679 .204 1.838 .070

Lobby -.176 .297 -.064 -.593 .555

Stair -33.340 20.075 -.153 -1.661 .101

Concrete -.115 .060 -.182 -1.896 .062

Lift 22.299 6.949 .369 3.209 .002

8 (Constant) 1666.456 238.444 6.989 .000

Corner 119.186 74.329 .231 1.603 .113

Rd_2 -4.449 2.080 -.313 -2.139 .036

Area 37.570 23.358 .519 1.608 .112

Plinth -.119 .046 -.772 -2.608 .011

Story 29.722 16.536 .198 1.797 .076




Model

Unstandardized

Coefficients

Standardized

Coefficients


Stair -31.659 19.790 -.145 -1.600 .114

Concrete -.113 .060 -.180 -1.884 .063

Lift 22.002 6.901 .364 3.188 .002

9 (Constant) 1563.631 231.871 6.744 .000

Corner 101.177 74.193 .196 1.364 .177

Rd_2 -3.855 2.067 -.271 -1.865 .066

Area 33.296 23.433 .460 1.421 .159

Plinth -.114 .046 -.735 -2.465 .016

Story 32.165 16.627 .214 1.934 .057

Concrete -.098 .060 -.156 -1.634 .106

Lift 21.780 6.968 .360 3.126 .002

10 (Constant) 1551.203 232.934 6.659 .000

Rd_2 -1.701 1.341 -.120 -1.269 .208

Area 32.657 23.554 .451 1.386 .169

Plinth -.114 .046 -.738 -2.461 .016

Story 27.598 16.374 .184 1.686 .096

Concrete -.084 .059 -.133 -1.410 .162

Lift 23.617 6.873 .391 3.436 .001

11 (Constant) 1451.398 220.083 6.595 .000

Area 29.965 23.546 .414 1.273 .207

Plinth -.106 .046 -.689 -2.310 .023

Story 30.151 16.311 .201 1.848 .068

Concrete -.069 .058 -.109 -1.176 .243

Lift 24.349 6.875 .403 3.542 .001

12 (Constant) 1229.526 113.675 10.816 .000

Area 24.953 23.212 .344 1.075 .286

Plinth -.099 .046 -.641 -2.164 .033

Story 28.941 16.317 .193 1.774 .080

Lift 24.810 6.879 .411 3.606 .001

13 (Constant) 1182.600 105.058 11.257 .000

Plinth -.052 .015 -.340 -3.559 .001

Story 33.968 15.647 .226 2.171 .033

Lift 27.456 6.430 .454 4.270 .000














Duration, Plinth, Storey and Lift were retained.


Referring to Table 4.50 the value of R2 of model 13 is 0.335, corresponding Adjusted

R2 of model 1 is 0.331 There is no considerable change between R2 and Adjusted R2.

This model can explain 33.5% of the variability and corresponding Standard Errors

(SE) 201.646 which slightly more than that of Enter Method. We can confirm that the

Model is workable.

4.30.4 ANOVA



4.30.5 Coefficient








Referring to Table 4.52, in 13th model each variable is individually statistically

significant below 5% level and also all the coefficients Plinth, Storey and Lift are

practically significant. So we can accept the model from all significance points of

view. This model is accepted. The equation will be as under:

Construction Cost =1182.600 -0.052x (Plinth) +33.968x (Storey) +27.456x (Lift)

Where;

Construction Cost = Construction Cost (Taka/sft)

Plinth= Plinth Area (sft/floor)

Storey=Number of Storey and

Lift=Total Capacity of Lift in the building.



follows:



1 .457a .209 .200 217.320

2 .545b .297 .280 206.054

3 .579c .335 .311 201.646

Table 4.54: ANOVA


1 Regression 1060174.072 1 1060174.072 22.448 .000a

Residual 4014368.848 85 47227.869

Total 5074542.920 86

2 Regression 1508045.109 2 754022.554 17.759 .000b

Residual 3566497.811 84 42458.307

Total 5074542.920 86

3 Regression 1699671.708 3 566557.236 13.934 .000c

Residual 3374871.211 83 40661.099

Total 5074542.920 86





Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) 1246.103 57.905 21.520 .000

Lift 27.625 5.831 .457 4.738 .000

2 (Constant) 1363.044 65.657 20.760 .000

Lift 33.819 5.848 .560 5.783 .000

Plinth -.049 .015 -.314 -3.248 .002

3 (Constant) 1182.600 105.058 11.257 .000

Lift 27.456 6.430 .454 4.270 .000

Plinth -.052 .015 -.340 -3.559 .001

Story 33.968 15.647 .226 2.171 .033





Table 4.53 shows that the Forward Selection method has produced three models


model it has included Lift and there after Plinth and finally Storey successively in

each model.


Referring to Table 4.53 and 4.54, the values of R2 of three models are between 0.209

to 0.335 and Corresponding Adjusted R2 are between 0.200 and 0.311. There is no


explain 20.9% to 33.5% of the variability respectively. Corresponding Standard

Errors (SE) are between 217.320 and 201.646 which are very big but considerable in

regards to the DV in question. We can confirm that all the models are statistically

significant but model 3 is the best in consideration to others in respect of R2, Adjusted

R2 and SE. This model is basically same as derived from paragraph 4.13.6




4.31.4 Concluding Remarks of the Analysis with Design Variables:

The Final equation of the model with design variables will be as under where with R2

=0.335 and SE=201.646

Construction Cost =1182.600 -0.052x (Plinth) +33.968x (Storey) +27.456x (Lift)

Where;

Construction Cost = Construction Cost (Taka/sft)


Storey=Number of Storey and

Lift=Total Capacity of Lift in the building.

4.32 General Information about Model-3

This section will show analysis of the model with all variables concerning building

costs. The process will be followed as stated in paragraph 4.8 to 4.9.3 above. In all

model Construction Cost per square feet is Dependent Variable.

4.32.1 Model Enter Method (All Variables)

The model is done by Enter method using SPSS-17.



1 .977a .954 .934 62.433

a. Predictors: (Constant), Lift, Steel_Grade, Stair, Pile, Corner, Dual, Duration,

Toilet, Concrete, Rd_1, Lobby, Cement, Generator, Steel, Transformer, Transport,

Story, Paint, Plinth, Brick, Rd_2, Sand, Carpenter, Area, Helper, Mason

Table 4.57: ANOVA


1 Regression 4840671.653 26 186179.679 47.765 .000a

Residual 233871.266 60 3897.854

Total 5074542.920 86




a. Predictors: (Constant), Lift, Steel_Grade, Stair, Pile, Corner, Dual, Duration,

Toilet, Concrete, Rd_1, Lobby, Cement, Generator, Steel, Transformer, Transport,

Story, Paint, Plinth, Brick, Rd_2, Sand, Carpenter, Area, Helper, Mason


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -991.186 340.589 -2.910 .005

Steel .000 .002 -.022 -.515 .608

Cement .173 .369 .020 .468 .641

Brick -.060 .032 -.283 -1.889 .064

Sand .071 .137 .066 .519 .606

Paint 1.407 .442 .255 3.185 .002

Mason 5.793 2.170 .811 2.670 .010

Helper 1.542 1.574 .217 .980 .331

Carpenter -.223 .879 -.033 -.254 .801

Transport -.158 .081 -.105 -1.949 .056

Duration -4.034 2.357 -.104 -1.712 .092

Corner 12.710 28.964 .025 .439 .662

Rd_1 -.674 .709 -.038 -.950 .346

Rd_2 .362 .932 .025 .388 .699

Pile -.858 15.968 -.002 -.054 .957

Dual 18.410 22.615 .025 .814 .419

Area -20.912 9.301 -.289 -2.248 .028

Plinth .033 .017 .215 1.923 .059

Story 6.708 6.569 .045 1.021 .311

Lobby .045 .110 .016 .406 .686

Toilet -.092 2.055 -.002 -.045 .965

Stair -8.597 7.611 -.039 -1.130 .263

Concrete .054 .023 .086 2.360 .022

Steel_Grade -.501 1.721 -.012 -.291 .772

Transformer .065 .088 .031 .742 .461

Generator .000 .174 .000 .003 .998

Lift 6.702 2.625 .111 2.553 .013




4.32.2 Interpretation of the Model and Concluding Remarks By Enter Method

Enter Method considered 26 independent variables (IV) and entered with

Construction Cost as dependent variable (DV). All the variables were considered but

none was rejected. Referring to Table 4.56, the value of R2 and Adjusted R2 are 0.954

and 0.934 respectively. There is considerable change between R2 and Adjusted R2.

However, the model can explain 95.4% of the variability with the 26 variables. The

Standard Error (SE) is 62.433 which is very good considering the Model-1. Referring

to table 4.57 F(26, 60)=47.765 and level of significance=0.000, that means the overall

model is statistically significance below 5% level of significance which is a

compulsory condition. If we see table 4.58 we find that out of 26 variables only 5

variables (Paint, Mason, Area, Concrete and Lift is statistically significant at or below

5% level.


Model cannot be accepted because individual level of significance did not meet 5%

for many variables.

4.33 Backward Elimination Method-1(All Variables)

The model is done by Backward Elimination method using SPSS-17 considering all

the variables.



1 .977 .954 .934 62.433

2 .977 .954 .935 61.919

3 .977 .954 .936 61.419

4 .977 .954 .937 60.931

5 .977 .954 .938 60.488

6 .977 .954 .939 60.072

7 .977 .954 .940 59.681

8 .977 .954 .940 59.307

9 .976 .953 .941 58.945





10 .976 .953 .942 58.656

11 .976 .953 .942 58.453

12 .976 .952 .942 58.292

13 .976 .952 .942 58.259

14 .975 .951 .942 58.316

15 .975 .950 .942 58.406

16 .974 .949 .942 58.528

17 .974 .948 .942 58.743

18 .973 .947 .941 59.082

Table 4.60: ANOVA


1 Regression 4840671.653 26 186179.679 47.765 .000

Residual 233871.266 60 3897.854

Total 5074542.920 86

2 Regression 4840671.623 25 193626.865 50.503 .000

Residual 233871.297 61 3833.956

Total 5074542.920 86

3 Regression 4840663.640 24 201694.318 53.468 .000

Residual 233879.280 62 3772.246

Total 5074542.920 86

4 Regression 4840653.673 23 210463.203 56.690 .000

Residual 233889.247 63 3712.528

Total 5074542.920 86

5 Regression 4840377.107 22 220017.141 60.133 .000

Residual 234165.813 64 3658.841

Total 5074542.920 86

6 Regression 4839977.994 21 230475.143 63.867 .000

Residual 234564.926 65 3608.691

Total 5074542.920 86

7 Regression 4839460.060 20 241973.003 67.934 .000

Residual 235082.859 66 3561.862

Total 5074542.920 86





8 Regression 4838884.659 19 254678.140 72.408 .000

Residual 235658.260 67 3517.287

Total 5074542.920 86

9 Regression 4838274.848 18 268793.047 77.361 .000

Residual 236268.072 68 3474.530

Total 5074542.920 86

10 Regression 4837145.840 17 284537.991 82.702 .000

Residual 237397.080 69 3440.537

Total 5074542.920 86

11 Regression 4835373.640 16 302210.853 88.451 .000

Residual 239169.279 70 3416.704

Total 5074542.920 86

12 Regression 4833291.042 15 322219.403 94.829 .000

Residual 241251.878 71 3397.914

Total 5074542.920 86

13 Regression 4830169.508 14 345012.108 101.651 .000

Residual 244373.412 72 3394.075

Total 5074542.920 86

14 Regression 4826286.112 13 371252.778 109.167 .000

Residual 248256.808 73 3400.778

Total 5074542.920 86

15 Regression 4822106.212 12 401842.184 117.797 .000

Residual 252436.708 74 3411.307

Total 5074542.920 86

16 Regression 4817624.160 11 437965.833 127.851 .000

Residual 256918.759 75 3425.583

Total 5074542.920 86

17 Regression 4812286.945 10 481228.695 139.457 .000

Residual 262255.974 76 3450.737

Total 5074542.920 86

18 Regression 4805764.597 9 533973.844 152.974 .000

Residual 268778.322 77 3490.628

Total 5074542.920 86





Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -991.186 340.589 -2.910 .005

Steel .000 .002 -.022 -.515 .608

Cement .173 .369 .020 .468 .641

Brick -.060 .032 -.283 -1.889 .064

Sand .071 .137 .066 .519 .606

Paint 1.407 .442 .255 3.185 .002

Mason 5.793 2.170 .811 2.670 .010

Helper 1.542 1.574 .217 .980 .331

Carpenter -.223 .879 -.033 -.254 .801

Transport -.158 .081 -.105 -1.949 .056

Duration -4.034 2.357 -.104 -1.712 .092

Corner 12.710 28.964 .025 .439 .662

Rd_1 -.674 .709 -.038 -.950 .346

Rd_2 .362 .932 .025 .388 .699

Pile -.858 15.968 -.002 -.054 .957

Dual 18.410 22.615 .025 .814 .419

Area -20.912 9.301 -.289 -2.248 .028

Plinth .033 .017 .215 1.923 .059

Story 6.708 6.569 .045 1.021 .311

Lobby .045 .110 .016 .406 .686

Toilet -.092 2.055 -.002 -.045 .965

Stair -8.597 7.611 -.039 -1.130 .263

Concrete .054 .023 .086 2.360 .022

Steel_Grade -.501 1.721 -.012 -.291 .772

Transformer .065 .088 .031 .742 .461

Generator .000 .174 .000 .003 .998

Lift 6.702 2.625 .111 2.553 .013

2 (Constant) -991.306 335.087 -2.958 .004

Steel .000 .002 -.022 -.520 .605

Cement .173 .366 .020 .472 .639

Brick -.060 .031 -.283 -1.910 .061

Sand .071 .135 .066 .523 .603




Model

Unstandardized

Coefficients

Standardized

Coefficients


Paint 1.407 .431 .255 3.263 .002

Mason 5.794 2.123 .811 2.730 .008

Helper 1.541 1.537 .217 1.003 .320

Carpenter -.224 .839 -.033 -.267 .791

Transport -.158 .081 -.105 -1.966 .054

Duration -4.032 2.279 -.104 -1.769 .082

Corner 12.717 28.628 .025 .444 .658

Rd_1 -.674 .703 -.038 -.958 .342

Rd_2 .362 .920 .025 .393 .696

Pile -.857 15.835 -.002 -.054 .957

Dual 18.410 22.428 .025 .821 .415

Area -20.905 8.853 -.289 -2.361 .021

Plinth .033 .017 .215 1.981 .052

Story 6.709 6.513 .045 1.030 .307

Lobby .045 .107 .016 .418 .677

Toilet -.092 2.026 -.002 -.046 .964

Stair -8.601 7.413 -.040 -1.160 .250

Concrete .054 .022 .086 2.439 .018

Steel_Grade -.500 1.681 -.012 -.298 .767

Transformer .065 .087 .031 .751 .455

Lift 6.704 2.517 .111 2.663 .010

3 (Constant) -992.018 332.019 -2.988 .004

Steel .000 .002 -.022 -.522 .603

Cement .174 .363 .020 .478 .634

Brick -.061 .030 -.285 -2.025 .047

Sand .071 .134 .067 .534 .595

Paint 1.407 .428 .255 3.290 .002

Mason 5.784 2.093 .810 2.763 .008

Helper 1.562 1.455 .220 1.074 .287

Carpenter -.225 .832 -.033 -.271 .787

Transport -.158 .079 -.105 -1.999 .050

Duration -4.032 2.261 -.104 -1.784 .079

Corner 12.907 28.095 .025 .459 .648




Model

Unstandardized

Coefficients

Standardized

Coefficients


Rd_1 -.673 .698 -.038 -.965 .338

Rd_2 .360 .913 .025 .395 .694

Pile -.805 15.667 -.002 -.051 .959

Dual 18.451 22.229 .025 .830 .410

Area -21.016 8.444 -.290 -2.489 .016

Plinth .033 .017 .215 1.997 .050

Story 6.797 6.167 .045 1.102 .275

Lobby .045 .106 .016 .427 .671

Stair -8.612 7.349 -.040 -1.172 .246

Concrete .054 .021 .086 2.559 .013

Steel_Grade -.509 1.656 -.012 -.307 .760

Transformer .065 .086 .031 .763 .448

Lift 6.703 2.497 .111 2.685 .009

4 (Constant) -993.260 328.507 -3.024 .004

Steel .000 .002 -.022 -.525 .601

Cement .178 .349 .020 .511 .611

Brick -.061 .029 -.286 -2.081 .041

Sand .071 .133 .067 .537 .593

Paint 1.405 .423 .254 3.322 .001

Mason 5.783 2.077 .810 2.785 .007

Helper 1.571 1.434 .221 1.095 .278

Carpenter -.225 .825 -.033 -.273 .786

Transport -.157 .078 -.105 -2.030 .047

Duration -4.030 2.242 -.104 -1.797 .077

Corner 13.207 27.262 .026 .484 .630

Rd_1 -.664 .669 -.038 -.993 .325

Rd_2 .350 .882 .025 .396 .693

Dual 18.255 21.727 .025 .840 .404

Area -21.066 8.320 -.291 -2.532 .014

Plinth .033 .016 .215 2.024 .047

Story 6.859 5.999 .046 1.143 .257

Lobby .045 .105 .016 .428 .670

Stair -8.576 7.258 -.039 -1.182 .242




Model

Unstandardized

Coefficients

Standardized

Coefficients


Concrete .054 .021 .086 2.606 .011

Steel_Grade -.526 1.609 -.013 -.327 .745

Transformer .066 .085 .031 .772 .443

Lift 6.692 2.467 .111 2.713 .009

5 (Constant) -971.817 316.660 -3.069 .003

Steel .000 .002 -.023 -.550 .584

Cement .178 .346 .020 .514 .609

Brick -.064 .026 -.303 -2.498 .015

Sand .066 .130 .061 .504 .616

Paint 1.348 .364 .244 3.704 .000

Mason 5.680 2.027 .795 2.802 .007

Helper 1.672 1.376 .235 1.215 .229

Transport -.163 .074 -.108 -2.193 .032

Duration -4.429 1.688 -.114 -2.624 .011

Corner 12.896 27.041 .025 .477 .635

Rd_1 -.664 .664 -.038 -.999 .321

Rd_2 .359 .875 .025 .410 .683

Dual 18.218 21.569 .025 .845 .401

Area -20.904 8.238 -.289 -2.537 .014

Plinth .033 .016 .214 2.029 .047

Story 6.763 5.945 .045 1.137 .260

Lobby .044 .104 .016 .425 .672

Stair -8.588 7.205 -.039 -1.192 .238

Concrete .054 .021 .086 2.625 .011

Steel_Grade -.528 1.597 -.013 -.330 .742

Transformer .064 .084 .031 .764 .448

Lift 6.761 2.436 .112 2.775 .007

6 (Constant) -1014.442 287.178 -3.532 .001

Steel .000 .002 -.021 -.514 .609

Cement .176 .344 .020 .513 .610

Brick -.063 .025 -.297 -2.493 .015

Sand .060 .128 .056 .467 .642

Paint 1.379 .348 .250 3.958 .000




Model

Unstandardized

Coefficients

Standardized

Coefficients


Mason 5.641 2.010 .790 2.807 .007

Helper 1.668 1.366 .235 1.221 .227

Transport -.158 .072 -.105 -2.185 .033

Duration -4.427 1.676 -.114 -2.641 .010

Corner 12.458 26.823 .024 .464 .644

Rd_1 -.689 .655 -.039 -1.053 .296

Rd_2 .366 .869 .026 .421 .675

Dual 17.797 21.383 .024 .832 .408

Area -20.509 8.095 -.283 -2.534 .014

Plinth .033 .016 .215 2.053 .044

Story 6.387 5.795 .043 1.102 .274

Lobby .039 .102 .014 .379 .706

Stair -8.684 7.150 -.040 -1.215 .229

Concrete .053 .020 .084 2.626 .011

Transformer .050 .072 .024 .697 .488

Lift 6.693 2.411 .111 2.776 .007

7 (Constant) -1026.835 283.452 -3.623 .001

Steel .000 .002 -.020 -.492 .625

Cement .193 .339 .022 .570 .570

Brick -.063 .025 -.297 -2.507 .015

Sand .060 .127 .056 .474 .637

Paint 1.375 .346 .249 3.974 .000

Mason 5.662 1.996 .793 2.837 .006

Helper 1.608 1.348 .226 1.193 .237

Transport -.149 .068 -.099 -2.197 .032

Duration -4.307 1.636 -.111 -2.633 .011

Corner 13.717 26.443 .027 .519 .606

Rd_1 -.716 .647 -.041 -1.106 .273

Rd_2 .346 .862 .024 .402 .689

Dual 17.764 21.244 .024 .836 .406

Area -20.117 7.976 -.278 -2.522 .014

Plinth .034 .016 .217 2.089 .041

Story 6.509 5.749 .043 1.132 .262




Model

Unstandardized

Coefficients

Standardized

Coefficients


Stair -9.035 7.043 -.042 -1.283 .204

Concrete .053 .020 .084 2.635 .010

Transformer .051 .071 .024 .710 .480

Lift 6.710 2.395 .111 2.802 .007

8 (Constant) -1024.683 281.622 -3.638 .001

Steel .000 .002 -.024 -.617 .540

Cement .220 .330 .025 .667 .507

Brick -.064 .025 -.303 -2.593 .012

Sand .052 .125 .049 .416 .678

Paint 1.360 .342 .246 3.978 .000

Mason 5.779 1.962 .809 2.946 .004

Helper 1.567 1.336 .221 1.173 .245

Transport -.147 .067 -.098 -2.183 .033

Duration -4.249 1.619 -.109 -2.625 .011

Corner 22.310 15.463 .043 1.443 .154

Rd_1 -.566 .525 -.032 -1.078 .285

Dual 18.317 21.066 .025 .870 .388

Area -19.337 7.688 -.267 -2.515 .014

Plinth .032 .016 .208 2.063 .043

Story 6.424 5.709 .043 1.125 .264

Stair -9.475 6.914 -.044 -1.371 .175

Concrete .051 .019 .081 2.638 .010

Transformer .045 .070 .021 .645 .521

Lift 6.658 2.376 .110 2.802 .007

9 (Constant) -1111.571 187.967 -5.914 .000

Steel .000 .001 -.022 -.570 .571

Cement .252 .319 .029 .789 .433

Brick -.070 .021 -.329 -3.401 .001

Paint 1.394 .330 .252 4.224 .000

Mason 6.397 1.276 .896 5.013 .000

Helper 1.351 1.224 .190 1.104 .274

Transport -.143 .066 -.095 -2.159 .034

Duration -4.352 1.590 -.112 -2.737 .008




Model

Unstandardized

Coefficients

Standardized

Coefficients


Corner 22.979 15.286 .044 1.503 .137

Rd_1 -.531 .515 -.030 -1.031 .306

Dual 19.739 20.660 .027 .955 .343

Area -19.116 7.623 -.264 -2.508 .015

Plinth .032 .015 .208 2.082 .041

Story 6.576 5.662 .044 1.161 .250

Stair -9.536 6.870 -.044 -1.388 .170

Concrete .052 .019 .083 2.753 .008

Transformer .049 .068 .023 .724 .471

Lift 6.613 2.359 .109 2.803 .007

10 (Constant) -1138.162 181.194 -6.281 .000

Cement .234 .316 .026 .740 .462

Brick -.073 .020 -.342 -3.641 .001

Paint 1.393 .328 .252 4.241 .000

Mason 6.313 1.261 .884 5.005 .000

Helper 1.430 1.210 .201 1.181 .242

Transport -.140 .066 -.093 -2.131 .037

Duration -4.282 1.578 -.110 -2.714 .008

Corner 23.762 15.149 .046 1.569 .121

Rd_1 -.503 .510 -.029 -.986 .327

Dual 20.076 20.551 .028 .977 .332

Area -18.989 7.582 -.262 -2.504 .015

Plinth .033 .015 .212 2.129 .037

Story 7.146 5.546 .048 1.288 .202

Stair -9.233 6.816 -.042 -1.355 .180

Concrete .052 .019 .082 2.749 .008

Transformer .049 .068 .023 .718 .475

Lift 6.356 2.304 .105 2.758 .007

11 (Constant) -1166.719 176.158 -6.623 .000

Cement .245 .314 .028 .781 .438

Brick -.071 .020 -.332 -3.587 .001

Paint 1.383 .327 .250 4.230 .000

Mason 6.529 1.221 .914 5.349 .000




Model

Unstandardized

Coefficients

Standardized

Coefficients


Helper 1.165 1.149 .164 1.014 .314

Transport -.141 .065 -.094 -2.162 .034

Duration -4.150 1.562 -.107 -2.658 .010

Corner 24.201 15.084 .047 1.604 .113

Rd_1 -.461 .505 -.026 -.912 .365

Dual 21.996 20.305 .030 1.083 .282

Area -18.507 7.526 -.255 -2.459 .016

Plinth .033 .015 .216 2.183 .032

Story 6.900 5.516 .046 1.251 .215

Stair -9.364 6.790 -.043 -1.379 .172

Concrete .055 .018 .087 2.976 .004

Lift 6.302 2.295 .104 2.746 .008

12 (Constant) -1113.445 161.957 -6.875 .000

Brick -.071 .020 -.334 -3.621 .001

Paint 1.418 .323 .257 4.389 .000

Mason 6.563 1.216 .919 5.395 .000

Helper 1.261 1.139 .178 1.107 .272

Transport -.150 .064 -.100 -2.351 .021

Duration -4.272 1.550 -.110 -2.757 .007

Corner 24.749 15.026 .048 1.647 .104

Rd_1 -.482 .503 -.027 -.958 .341

Dual 21.853 20.248 .030 1.079 .284

Area -18.145 7.491 -.250 -2.422 .018

Plinth .033 .015 .214 2.171 .033

Story 6.932 5.501 .046 1.260 .212

Stair -10.503 6.613 -.048 -1.588 .117

Concrete .055 .018 .087 2.999 .004

Lift 6.266 2.288 .104 2.738 .008

13 (Constant) -1149.208 157.511 -7.296 .000

Brick -.069 .020 -.326 -3.547 .001

Paint 1.462 .319 .265 4.578 .000

Mason 6.511 1.215 .912 5.361 .000

Helper 1.276 1.138 .180 1.121 .266




Model

Unstandardized

Coefficients

Standardized

Coefficients


Transport -.158 .063 -.105 -2.496 .015

Duration -4.252 1.549 -.109 -2.746 .008

Corner 22.002 14.742 .043 1.492 .140

Dual 24.419 20.059 .034 1.217 .227

Area -17.678 7.471 -.244 -2.366 .021

Plinth .033 .015 .213 2.163 .034

Story 5.724 5.351 .038 1.070 .288

Stair -9.829 6.572 -.045 -1.496 .139

Concrete .056 .018 .089 3.081 .003

Lift 6.357 2.285 .105 2.782 .007

14 (Constant) -1155.419 157.560 -7.333 .000

Brick -.066 .019 -.311 -3.420 .001

Paint 1.492 .319 .270 4.684 .000

Mason 6.474 1.215 .907 5.327 .000

Helper 1.263 1.139 .178 1.109 .271

Transport -.156 .063 -.104 -2.460 .016

Duration -3.947 1.524 -.102 -2.591 .012

Corner 19.497 14.569 .038 1.338 .185

Dual 27.912 19.811 .038 1.409 .163

Area -16.436 7.388 -.227 -2.225 .029

Plinth .032 .015 .205 2.088 .040

Stair -9.853 6.578 -.045 -1.498 .139

Concrete .057 .018 .091 3.137 .002

Lift 6.772 2.254 .112 3.004 .004

15 (Constant) -1182.528 155.891 -7.586 .000

Brick -.054 .016 -.254 -3.381 .001

Paint 1.333 .285 .241 4.680 .000

Mason 7.566 .713 1.059 10.608 .000

Transport -.174 .061 -.116 -2.831 .006

Duration -3.493 1.470 -.090 -2.376 .020

Corner 16.419 14.324 .032 1.146 .255

Dual 26.337 19.791 .036 1.331 .187

Area -18.052 7.254 -.249 -2.489 .015




Model

Unstandardized

Coefficients

Standardized

Coefficients


Plinth .035 .015 .225 2.318 .023

Stair -8.768 6.515 -.040 -1.346 .182

Concrete .058 .018 .092 3.170 .002

Lift 7.072 2.241 .117 3.155 .002

16 (Constant) -1143.692 152.483 -7.500 .000

Brick -.056 .016 -.261 -3.492 .001

Paint 1.280 .282 .232 4.545 .000

Mason 7.680 .708 1.075 10.850 .000

Transport -.187 .060 -.125 -3.096 .003

Duration -3.414 1.471 -.088 -2.321 .023

Dual 26.804 19.828 .037 1.352 .180

Area -17.890 7.267 -.247 -2.462 .016

Plinth .033 .015 .213 2.207 .030

Stair -8.118 6.504 -.037 -1.248 .216

Concrete .057 .018 .090 3.104 .003

Lift 7.286 2.238 .121 3.255 .002

17 (Constant) -1172.446 151.285 -7.750 .000

Brick -.055 .016 -.260 -3.466 .001

Paint 1.198 .275 .217 4.358 .000

Mason 7.886 .691 1.104 11.417 .000

Transport -.198 .060 -.132 -3.299 .001

Duration -2.709 1.363 -.070 -1.987 .051

Dual 27.353 19.896 .038 1.375 .173

Area -19.804 7.130 -.273 -2.778 .007

Plinth .036 .015 .235 2.465 .016

Concrete .060 .018 .095 3.323 .001

Lift 7.055 2.239 .117 3.151 .002

18 (Constant) -1214.352 149.037 -8.148 .000

Brick -.055 .016 -.259 -3.425 .001

Paint 1.247 .274 .226 4.549 .000

Mason 7.844 .694 1.098 11.301 .000

Transport -.189 .060 -.125 -3.142 .002

Duration -2.759 1.371 -.071 -2.013 .048




Model

Unstandardized

Coefficients

Standardized

Coefficients


Area -19.772 7.171 -.273 -2.757 .007

Plinth .037 .015 .237 2.468 .016

Concrete .065 .018 .103 3.619 .001

Lift 6.468 2.210 .107 2.926 .005


Elimination Method-1

Backward Elimination Method considered 26 independent variables (IV) and entered

with Construction Cost as dependent variable (DV). The software has automatically

produced 16 models. In 1st model all the variables were considered and the variables

were removed each at one step and formulate a new model. Referring to Table: 4.59,

we see that the value of R2 lie between 0.954 and 0947; and Adjusted R2 from 0.934

and 0.934. There is considerable change between R2 and Adjusted R2 in first model

but decreases in the last model which is a good sign. However, the model can explain

95.4% to 94.7% of the variability with the 16 models. The Standard Error (SE)

ranges from 62.433 to 59.082 which are very good considering the Model-1.

Referring to Table 4.60, F varies from 47.765 to 152.974 at level of

significance=0.000, that means the all the model is overall statistically significant

below 5% level. If we see Table 4.61 we find that out of 16 models last one is valid as

all the variables are individually statistically significant (by "T" stat) at or below 5%

level. In this model total 9 IV were included where all are statistically significant

below 5% level. But the question comes in mind when only Paint and Mason has

shown practical significance others did not meet the condition.


None of the models can be accepted because they did not meet the basic requirement

of statistical significant and practical significant.




4.34 Forward Selection Method-1(All Variables)

The model is done by Forward Selection method using SPSS-17 considering all the

variables.



1 .935a .874 .873 86.611

2 .953b .908 .905 74.689

3 .959c .920 .917 70.070

4 .963d .928 .925 66.653

5 .967e .935 .931 63.935

6 .968f .938 .933 62.717

7 .970g .942 .936 61.216

Table 4.63: ANOVA


1 Regression 4436924.912 1 4436924.912 591.480 .000a

Residual 637618.007 85 7501.388

Total 5074542.920 86

2 Regression 4605955.827 2 2302977.913 412.837 .000b

Residual 468587.093 84 5578.418

Total 5074542.920 86

3 Regression 4667034.447 3 1555678.149 316.855 .000c

Residual 407508.473 83 4909.741

Total 5074542.920 86

4 Regression 4710253.141 4 1177563.285 265.064 .000d

Residual 364289.779 82 4442.558

Total 5074542.920 86

5 Regression 4743441.299 5 948688.260 232.085 .000e

Residual 331101.620 81 4087.674

Total 5074542.920 86

6 Regression 4759872.223 6 793312.037 201.687 .000f

Residual 314670.697 80 3933.384

Total 5074542.920 86





7 Regression 4778500.440 7 682642.920 182.166 .000g

Residual 296042.480 79 3747.373

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -357.338 76.820 -4.652 .000

Mason 6.678 .275 .935 24.320 .000

2 (Constant) -971.082 129.692 -7.488 .000

Mason 5.515 .317 .772 17.379 .000

Paint 1.351 .245 .245 5.505 .000

3 (Constant) -1004.041 122.029 -8.228 .000

Mason 7.693 .685 1.077 11.224 .000

Paint 1.021 .249 .185 4.110 .000

Brick -.062 .018 -.290 -3.527 .001

4 (Constant) -1241.238 138.771 -8.944 .000

Mason 8.144 .668 1.140 12.194 .000

Paint .972 .237 .176 4.102 .000

Brick -.072 .017 -.341 -4.262 .000

Concrete .060 .019 .095 3.119 .003

5 (Constant) -1241.484 133.113 -9.327 .000

Mason 8.426 .648 1.180 12.999 .000

Paint 1.110 .232 .201 4.775 .000

Brick -.065 .017 -.308 -3.964 .000

Concrete .058 .018 .092 3.136 .002

Transport -.180 .063 -.120 -2.849 .006

6 (Constant) -1232.431 130.652 -9.433 .000

Mason 7.703 .727 1.079 10.589 .000

Paint 1.443 .280 .261 5.148 .000

Brick -.055 .017 -.256 -3.201 .002

Concrete .059 .018 .093 3.250 .002

Transport -.199 .063 -.133 -3.173 .002

Duration -2.878 1.408 -.074 -2.044 .044




Model

Unstandardized

Coefficients

Standardized

Coefficients


7 (Constant) -1104.148 139.904 -7.892 .000

Mason 7.580 .712 1.061 10.644 .000

Paint 1.293 .282 .234 4.586 .000

Brick -.055 .017 -.258 -3.300 .001

Concrete .052 .018 .082 2.900 .005

Transport -.190 .061 -.126 -3.086 .003

Duration -3.424 1.396 -.088 -2.452 .016

Lift 4.423 1.984 .073 2.230 .029

4.34.1 Interpretation of the Model and Concluding Remarks by Forward

Selection Method-1

Forward Selection Method considered 26 independent variables (IV) and entered with

Construction Cost as dependent variable (DV). The software has automatically

produced 7 models. In 1st model a single variable Mason was considered and the

variables were entered each at one step and formulate a new model. Referring to

Table 4.62 we see that, the value of R2 ranges from 0.874 to 0942vand Adjusted R2

from 0.873 to 0.936. There is no considerable change between R2 and Adjusted R2

which is a good sign. However, the model can explain 87.4% to 94.2% of the

variability with the 7 models. The Standard Error (SE) ranges from 86.611 to 61.216

which are very good. Referring to Table 4.63, F varies from 591.480 to 182.166 at

level of significance=0.000, that means the all the model is overall statistically

significant below 5% level. If we see Table 4.64 we find that out all the 7 models are

valid as all the variables are individually statistically significant (by "T" stat) at or

below 5% level. But when the question comes of practical significance only Model 1

and 2 meet the requirement.

4.34.2 Concluding Remarks of the Model by Forward Selection Method-1

Model 2 is yield better result so we select Model-2 with R2= 0.908 and SE=74.689

with Paint and Mason.

The equation is:




Construction Cost= -971.082+5.515x (Mason) +1.351x (Paint)

Where;

Construction Cost unit is Taka/sft

Mason= Wage of a Mason (Taka/Day)

Paint= Price of Paint (Taka/Gallon)

4.35 Backward Elimination Method-1(All Variables)

The model is done by Backward Elimination method-2 using SPSS-17 considering

all the variables except Transport Cost.



1 .975 .951 .931 63.849

2 .975 .951 .932 63.332

3 .975 .951 .933 62.830

4 .975 .951 .934 62.344

5 .975 .951 .935 61.888

6 .975 .951 .936 61.454

7 .975 .951 .937 61.032

8 .975 .951 .938 60.618

9 .975 .951 .939 60.223

10 .975 .950 .939 60.058

11 .975 .950 .939 59.927

12 .974 .949 .939 59.825

13 .974 .948 .939 59.954

14 .973 .947 .938 60.278

15 .973 .946 .938 60.389

16 .972 .944 .937 61.040

17 .971 .942 .935 61.699

18 .970 .940 .934 62.352

19 .969 .938 .933 62.854




Table 4.66: ANOVA


1 Regression 4825866.614 25 193034.665 47.351 .000

Residual 248676.306 61 4076.661

Total 5074542.920 86

2 Regression 4825861.528 24 201077.564 50.132 .000

Residual 248681.392 62 4010.990

Total 5074542.920 86

3 Regression 4825846.805 23 209819.426 53.152 .000

Residual 248696.114 63 3947.557

Total 5074542.920 86

4 Regression 4825787.287 22 219353.968 56.436 .000

Residual 248755.632 64 3886.807

Total 5074542.920 86

5 Regression 4825583.301 21 229789.681 59.995 .000

Residual 248959.619 65 3830.148

Total 5074542.920 86

6 Regression 4825291.698 20 241264.585 63.885 .000

Residual 249251.221 66 3776.534

Total 5074542.920 86

7 Regression 4824975.635 19 253946.086 68.176 .000

Residual 249567.285 67 3724.885

Total 5074542.920 86

8 Regression 4824675.313 18 268037.517 72.945 .000

Residual 249867.606 68 3674.524

Total 5074542.920 86

9 Regression 4824289.303 17 283781.724 78.244 .000

Residual 250253.617 69 3626.864

Total 5074542.920 86

10 Regression 4822054.829 16 301378.427 83.554 .000

Residual 252488.091 70 3606.973

Total 5074542.920 86

11 Regression 4819561.595 15 321304.106 89.468 .000

Residual 254981.325 71 3591.286

Total 5074542.920 86

12 Regression 4816854.863 14 344061.062 96.133 .000





Residual 257688.057 72 3579.001

Total 5074542.920 86

13 Regression 4812145.432 13 370165.033 102.981 .000

Residual 262397.488 73 3594.486

Total 5074542.920 86

14 Regression 4805672.573 12 400472.714 110.220 .000

Residual 268870.347 74 3633.383

Total 5074542.920 86

15 Regression 4801027.355 11 436457.032 119.680 .000

Residual 273515.564 75 3646.874

Total 5074542.920 86

16 Regression 4791379.690 10 479137.969 128.599 .000

Residual 283163.230 76 3725.832

Total 5074542.920 86

17 Regression 4781422.394 9 531269.155 139.559 .000

Residual 293120.525 77 3806.760

Total 5074542.920 86

18 Regression 4771301.474 8 596412.684 153.410 .000

Residual 303241.445 78 3887.711

Total 5074542.920 86

19 Regression 4762444.499 7 680349.214 172.214 .000

Residual 312098.420 79 3950.613

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -1189.155 332.461 -3.577 .001

Steel .000 .002 -.011 -.250 .804

Cement .356 .365 .040 .976 .333

Brick -.070 .032 -.328 -2.167 .034

Sand .044 .139 .041 .319 .751

Paint 1.520 .448 .275 3.393 .001




Model

Unstandardized

Coefficients

Standardized

Coefficients


Mason 5.719 2.219 .801 2.578 .012

Helper 1.779 1.604 .250 1.109 .272

Carpenter -.668 .868 -.099 -.770 .444

Duration -3.052 2.354 -.079 -1.296 .200

Corner 28.187 28.485 .055 .990 .326

Rd_1 -.709 .725 -.040 -.978 .332

Rd_2 .105 .944 .007 .111 .912

Pile 3.972 16.132 .008 .246 .806

Dual 14.418 23.033 .020 .626 .534

Area -20.151 9.504 -.278 -2.120 .038

Plinth .034 .018 .223 1.952 .056

Story 7.809 6.693 .052 1.167 .248

Lobby -.023 .107 -.009 -.219 .827

Toilet .520 2.077 .011 .250 .803

Stair -11.194 7.663 -.051 -1.461 .149

Concrete .054 .023 .086 2.323 .024

Steel_Grade -.062 1.745 -.001 -.035 .972

Transformer .059 .090 .028 .660 .512

Generator -.009 .178 -.002 -.053 .958

Lift 6.205 2.672 .103 2.322 .024

2 (Constant) -1193.362 307.883 -3.876 .000

Steel .000 .002 -.011 -.249 .804

Cement .355 .360 .040 .986 .328

Brick -.069 .031 -.326 -2.232 .029

Sand .044 .137 .041 .319 .751

Paint 1.524 .430 .276 3.545 .001

Mason 5.718 2.201 .801 2.598 .012

Helper 1.773 1.583 .250 1.120 .267

Carpenter -.669 .861 -.099 -.777 .440

Duration -3.051 2.335 -.078 -1.306 .196

Corner 28.057 28.017 .054 1.001 .321

Rd_1 -.713 .710 -.040 -1.004 .319

Rd_2 .107 .934 .008 .115 .909




Model

Unstandardized

Coefficients

Standardized

Coefficients


Pile 3.842 15.583 .008 .247 .806

Dual 14.404 22.843 .020 .631 .531

Area -20.076 9.188 -.277 -2.185 .033

Plinth .034 .017 .223 1.967 .054

Story 7.749 6.426 .052 1.206 .232

Lobby -.024 .105 -.009 -.229 .819

Toilet .508 2.036 .011 .250 .804

Stair -11.212 7.586 -.052 -1.478 .144

Concrete .054 .022 .086 2.413 .019

Transformer .058 .076 .027 .755 .453

Generator -.011 .174 -.002 -.061 .952

Lift 6.205 2.650 .103 2.341 .022

3 (Constant) -1192.121 304.762 -3.912 .000

Steel .000 .002 -.011 -.249 .804

Cement .356 .357 .040 .995 .323

Brick -.070 .031 -.327 -2.255 .028

Sand .044 .136 .041 .321 .749

Paint 1.520 .422 .275 3.598 .001

Mason 5.696 2.152 .797 2.647 .010

Helper 1.788 1.550 .252 1.154 .253

Carpenter -.655 .821 -.097 -.797 .429

Duration -3.082 2.259 -.079 -1.364 .177

Corner 27.884 27.650 .054 1.008 .317

Rd_1 -.715 .704 -.040 -1.015 .314

Rd_2 .113 .921 .008 .123 .903

Pile 3.796 15.440 .008 .246 .807

Dual 14.410 22.662 .020 .636 .527

Area -20.216 8.822 -.279 -2.292 .025

Plinth .035 .017 .224 2.039 .046

Story 7.721 6.359 .051 1.214 .229

Lobby -.023 .102 -.008 -.224 .824

Toilet .520 2.011 .011 .259 .797

Stair -11.130 7.405 -.051 -1.503 .138




Model

Unstandardized

Coefficients

Standardized

Coefficients


Concrete .054 .022 .086 2.486 .016

Transformer .058 .076 .027 .762 .449

Lift 6.162 2.536 .102 2.430 .018

4 (Constant) -1191.883 302.402 -3.941 .000

Steel .000 .002 -.012 -.290 .772

Cement .365 .346 .041 1.054 .296

Brick -.070 .030 -.329 -2.296 .025

Sand .041 .133 .038 .308 .759

Paint 1.515 .417 .274 3.631 .001

Mason 5.734 2.113 .803 2.714 .009

Helper 1.775 1.534 .250 1.157 .252

Carpenter -.654 .815 -.097 -.803 .425

Duration -3.062 2.236 -.079 -1.370 .176

Corner 30.640 16.029 .059 1.912 .060

Rd_1 -.663 .562 -.038 -1.181 .242

Pile 4.161 15.034 .009 .277 .783

Dual 14.516 22.470 .020 .646 .521

Area -19.991 8.563 -.276 -2.335 .023

Plinth .034 .017 .222 2.072 .042

Story 7.715 6.309 .051 1.223 .226

Lobby -.023 .101 -.008 -.229 .820

Toilet .518 1.995 .011 .260 .796

Stair -11.236 7.297 -.052 -1.540 .129

Concrete .054 .021 .085 2.548 .013

Transformer .056 .073 .026 .759 .451

Lift 6.142 2.511 .102 2.446 .017

5 (Constant) -1189.983 300.077 -3.966 .000

Steel .000 .002 -.012 -.302 .764

Cement .360 .343 .041 1.050 .298

Brick -.070 .030 -.331 -2.333 .023

Sand .040 .132 .038 .304 .762

Paint 1.523 .413 .276 3.687 .000

Mason 5.719 2.096 .801 2.728 .008




Model

Unstandardized

Coefficients

Standardized

Coefficients


Helper 1.826 1.507 .257 1.212 .230

Carpenter -.676 .804 -.100 -.841 .403

Duration -3.096 2.215 -.080 -1.398 .167

Corner 30.531 15.904 .059 1.920 .059

Rd_1 -.647 .553 -.037 -1.170 .246

Pile 4.118 14.923 .008 .276 .783

Dual 14.487 22.306 .020 .649 .518

Area -20.255 8.423 -.280 -2.405 .019

Plinth .034 .016 .220 2.078 .042

Story 7.703 6.263 .051 1.230 .223

Toilet .576 1.965 .012 .293 .771

Stair -11.119 7.226 -.051 -1.539 .129

Concrete .054 .021 .086 2.580 .012

Transformer .056 .073 .026 .763 .448

Lift 6.114 2.490 .101 2.455 .017

6 (Constant) -1179.577 295.606 -3.990 .000

Steel .000 .002 -.013 -.332 .741

Cement .344 .336 .039 1.025 .309

Brick -.069 .030 -.327 -2.333 .023

Sand .040 .131 .038 .309 .759

Paint 1.527 .410 .276 3.724 .000

Mason 5.750 2.078 .805 2.766 .007

Helper 1.775 1.485 .250 1.195 .236

Carpenter -.687 .797 -.102 -.862 .392

Duration -3.075 2.198 -.079 -1.399 .166

Corner 30.546 15.793 .059 1.934 .057

Rd_1 -.671 .542 -.038 -1.237 .220

Dual 15.564 21.807 .021 .714 .478

Area -19.907 8.270 -.275 -2.407 .019

Plinth .033 .016 .217 2.074 .042

Story 7.442 6.148 .050 1.211 .230

Toilet .564 1.951 .012 .289 .773

Stair -11.409 7.099 -.052 -1.607 .113




Model

Unstandardized

Coefficients

Standardized

Coefficients


Concrete .053 .021 .084 2.585 .012

Transformer .056 .072 .027 .782 .437

Lift 6.169 2.465 .102 2.503 .015

7 (Constant) -1175.073 293.171 -4.008 .000

Steel .000 .002 -.014 -.350 .727

Cement .345 .333 .039 1.036 .304

Brick -.067 .029 -.317 -2.350 .022

Sand .037 .130 .034 .284 .777

Paint 1.529 .407 .277 3.757 .000

Mason 5.814 2.052 .814 2.833 .006

Helper 1.659 1.420 .234 1.168 .247

Carpenter -.692 .791 -.102 -.874 .385

Duration -3.056 2.182 -.079 -1.401 .166

Corner 29.784 15.464 .058 1.926 .058

Rd_1 -.668 .538 -.038 -1.240 .219

Dual 15.188 21.619 .021 .703 .485

Area -19.292 7.937 -.266 -2.431 .018

Plinth .034 .016 .218 2.100 .040

Story 6.965 5.882 .046 1.184 .241

Stair -11.362 7.048 -.052 -1.612 .112

Concrete .052 .020 .082 2.609 .011

Transformer .056 .072 .027 .783 .437

Lift 6.158 2.448 .102 2.516 .014

8 (Constant) -1230.064 218.601 -5.627 .000

Steel .000 .002 -.013 -.324 .747

Cement .366 .323 .041 1.132 .261

Brick -.072 .024 -.338 -3.032 .003

Paint 1.541 .402 .279 3.834 .000

Mason 6.226 1.441 .872 4.321 .000

Helper 1.525 1.330 .215 1.147 .256

Carpenter -.647 .770 -.096 -.840 .404

Duration -3.207 2.102 -.083 -1.526 .132

Corner 30.140 15.309 .058 1.969 .053




Model

Unstandardized

Coefficients

Standardized

Coefficients


Rd_1 -.642 .527 -.036 -1.218 .228

Dual 16.210 21.172 .022 .766 .447

Area -19.110 7.858 -.264 -2.432 .018

Plinth .034 .016 .218 2.114 .038

Story 7.048 5.835 .047 1.208 .231

Stair -11.384 7.000 -.052 -1.626 .109

Concrete .053 .019 .083 2.701 .009

Transformer .059 .070 .028 .835 .407

Lift 6.143 2.430 .102 2.528 .014

9 (Constant) -1247.839 210.233 -5.936 .000

Cement .354 .319 .040 1.109 .271

Brick -.073 .023 -.343 -3.130 .003

Paint 1.546 .399 .280 3.874 .000

Mason 6.204 1.430 .869 4.339 .000

Helper 1.550 1.319 .218 1.175 .244

Carpenter -.666 .763 -.098 -.874 .385

Duration -3.133 2.076 -.081 -1.509 .136

Corner 30.495 15.170 .059 2.010 .048

Rd_1 -.623 .521 -.035 -1.198 .235

Dual 16.496 21.016 .023 .785 .435

Area -19.057 7.805 -.263 -2.442 .017

Plinth .034 .016 .220 2.151 .035

Story 7.389 5.702 .049 1.296 .199

Stair -11.172 6.924 -.051 -1.614 .111

Concrete .052 .019 .083 2.710 .008

Transformer .059 .070 .028 .836 .406

Lift 5.991 2.369 .099 2.529 .014

10 (Constant) -1258.250 209.238 -6.013 .000

Cement .345 .318 .039 1.085 .282

Brick -.073 .023 -.344 -3.147 .002

Paint 1.553 .398 .281 3.901 .000

Mason 6.207 1.426 .869 4.353 .000

Helper 1.526 1.315 .215 1.161 .250




Model

Unstandardized

Coefficients

Standardized

Coefficients


Carpenter -.631 .759 -.093 -.831 .409

Duration -3.270 2.063 -.084 -1.585 .117

Corner 30.855 15.122 .060 2.040 .045

Rd_1 -.679 .514 -.038 -1.320 .191

Area -19.358 7.774 -.267 -2.490 .015

Plinth .034 .016 .222 2.176 .033

Story 8.244 5.582 .055 1.477 .144

Stair -11.227 6.904 -.052 -1.626 .108

Concrete .054 .019 .086 2.839 .006

Transformer .065 .069 .031 .941 .350

Lift 5.637 2.320 .093 2.430 .018

11 (Constant) -1175.730 183.798 -6.397 .000

Cement .348 .317 .039 1.096 .277

Brick -.083 .020 -.392 -4.230 .000

Paint 1.374 .334 .249 4.108 .000

Mason 5.627 1.241 .788 4.535 .000

Helper 1.961 1.204 .276 1.629 .108

Duration -4.339 1.609 -.112 -2.697 .009

Corner 31.292 15.080 .061 2.075 .042

Rd_1 -.684 .513 -.039 -1.333 .187

Area -18.840 7.732 -.260 -2.437 .017

Plinth .034 .016 .218 2.148 .035

Story 7.939 5.558 .053 1.428 .158

Stair -11.471 6.883 -.053 -1.666 .100

Concrete .054 .019 .085 2.809 .006

Transformer .060 .069 .028 .868 .388

Lift 5.797 2.307 .096 2.513 .014

12 (Constant) -1213.758 178.196 -6.811 .000

Cement .363 .316 .041 1.147 .255

Brick -.081 .019 -.380 -4.155 .000

Paint 1.364 .334 .247 4.088 .000

Mason 5.891 1.201 .825 4.907 .000

Helper 1.632 1.141 .230 1.431 .157




Model

Unstandardized

Coefficients

Standardized

Coefficients


Duration -4.186 1.597 -.108 -2.622 .011

Corner 31.979 15.033 .062 2.127 .037

Rd_1 -.640 .510 -.036 -1.255 .214

Area -18.280 7.692 -.252 -2.376 .020

Plinth .035 .016 .224 2.211 .030

Story 7.756 5.544 .052 1.399 .166

Stair -11.669 6.868 -.054 -1.699 .094

Concrete .057 .019 .091 3.097 .003

Lift 5.676 2.298 .094 2.470 .016

13 (Constant) -1134.106 164.465 -6.896 .000

Brick -.083 .019 -.389 -4.253 .000

Paint 1.413 .332 .256 4.261 .000

Mason 5.870 1.203 .822 4.879 .000

Helper 1.839 1.129 .259 1.629 .108

Duration -4.366 1.592 -.112 -2.742 .008

Corner 33.546 15.003 .065 2.236 .028

Rd_1 -.684 .509 -.039 -1.342 .184

Area -17.664 7.690 -.244 -2.297 .024

Plinth .034 .016 .221 2.183 .032

Story 7.766 5.556 .052 1.398 .166

Stair -13.636 6.664 -.063 -2.046 .044

Concrete .058 .019 .092 3.109 .003

Lift 5.615 2.303 .093 2.438 .017

14 (Constant) -1190.650 159.834 -7.449 .000

Brick -.081 .019 -.380 -4.146 .000

Paint 1.480 .330 .268 4.489 .000

Mason 5.749 1.206 .805 4.766 .000

Helper 1.893 1.134 .266 1.669 .099

Duration -4.352 1.601 -.112 -2.718 .008

Corner 30.248 14.881 .059 2.033 .046

Area -16.979 7.714 -.234 -2.201 .031

Plinth .034 .016 .221 2.167 .033

Story 6.170 5.456 .041 1.131 .262




Model

Unstandardized

Coefficients

Standardized

Coefficients


Stair -12.893 6.677 -.059 -1.931 .057

Concrete .060 .019 .095 3.239 .002

Lift 5.650 2.315 .093 2.441 .017

15 (Constant) -1203.380 159.733 -7.534 .000

Brick -.077 .019 -.361 -4.000 .000

Paint 1.518 .329 .275 4.618 .000

Mason 5.735 1.208 .803 4.746 .000

Helper 1.847 1.135 .260 1.626 .108

Duration -4.026 1.578 -.104 -2.552 .013

Corner 27.378 14.690 .053 1.864 .066

Area -15.670 7.641 -.216 -2.051 .044

Plinth .033 .016 .213 2.090 .040

Stair -12.864 6.690 -.059 -1.923 .058

Concrete .062 .019 .098 3.335 .001

Lift 6.025 2.295 .100 2.625 .011

16 (Constant) -1242.690 159.594 -7.787 .000

Brick -.060 .016 -.283 -3.661 .000

Paint 1.260 .291 .228 4.329 .000

Mason 7.299 .740 1.022 9.869 .000

Duration -3.316 1.532 -.085 -2.164 .034

Corner 24.034 14.702 .046 1.635 .106

Area -18.050 7.580 -.249 -2.381 .020

Plinth .038 .016 .244 2.412 .018

Stair -11.710 6.723 -.054 -1.742 .086

Concrete .062 .019 .099 3.334 .001

Lift 6.514 2.300 .108 2.832 .006

17 (Constant) -1187.215 157.629 -7.532 .000

Brick -.064 .017 -.299 -3.852 .000

Paint 1.166 .288 .211 4.043 .000

Mason 7.444 .742 1.042 10.029 .000

Duration -3.168 1.546 -.082 -2.049 .044

Area -17.810 7.661 -.246 -2.325 .023

Plinth .035 .016 .229 2.248 .027




Model

Unstandardized

Coefficients

Standardized

Coefficients


Stair -11.062 6.784 -.051 -1.631 .107

Concrete .061 .019 .096 3.217 .002

Lift 6.824 2.317 .113 2.945 .004

18 (Constant) -1228.649 157.213 -7.815 .000

Brick -.064 .017 -.301 -3.835 .000

Paint 1.039 .281 .188 3.702 .000

Mason 7.714 .731 1.080 10.550 .000

Duration -2.163 1.433 -.056 -1.509 .135

Area -20.472 7.564 -.283 -2.706 .008

Plinth .040 .016 .260 2.579 .012

Concrete .066 .019 .104 3.489 .001

Lift 6.496 2.333 .107 2.785 .007

19 (Constant) -1265.436 156.563 -8.083 .000

Brick -.071 .016 -.334 -4.402 .000

Paint .831 .246 .150 3.373 .001

Mason 8.284 .631 1.160 13.128 .000

Area -22.513 7.502 -.311 -3.001 .004

Plinth .044 .015 .287 2.862 .005

Concrete .067 .019 .106 3.532 .001

Lift 6.085 2.335 .101 2.605 .011




with Construction Cost as dependent variable (DV). We excluded Transport Cost in

this analysis. The software has automatically produced 19 models. In 1st model all

the variables were considered and the variables were removed each at one step and

formulate a new model. Referring to Table 4.65, we see that, the value of R2 ranges

from 0.951 to 0.938 and Adjusted R2 from 0.931 and 0.933. There is considerable

change between R2 and Adjusted R2 in first model but decreases in the last model






which are very good. Referring to Table 4.66, F varies from 47.35 to 172.214 at 0.000

level of significance, that means the all the model is overall statistically significant

below 5% level. If we see Table 4.67 we find that out of 19 models last one is valid as

all the variables are individually statistically significant (by "T" stat) at or below 5%

level. In this model total 7 IV were included where all are statistically significant

below 5% level. But when the question of practical significance comes the condition

was not met in the best model.

4.35.2 Concluding Remarks of the Model by Backward Elimination Method-1



4.36 Forward Selection Method-2(All Variables except Transport)


variables except Transport.



1 .935a .874 .873 86.611

2 .953b .908 .905 74.689

3 .959c .920 .917 70.070

4 .963d .928 .925 66.653

5 .966e .932 .928 65.096

Table 4.69: ANOVA


1 Regression 4436924.912 1 4436924.912 591.480 .000a

Residual 637618.007 85 7501.388

Total 5074542.920 86

2 Regression 4605955.827 2 2302977.913 412.837 .000b

Residual 468587.093 84 5578.418

Total 5074542.920 86

3 Regression 4667034.447 3 1555678.149 316.855 .000c




Residual 407508.473 83 4909.741

Total 5074542.920 86

4 Regression 4710253.141 4 1177563.285 265.064 .000d

Residual 364289.779 82 4442.558

Total 5074542.920 86

5 Regression 4731301.589 5 946260.318 223.304 .000e

Residual 343241.330 81 4237.547

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -357.338 76.820 -4.652 .000

Mason 6.678 .275 .935 24.320 .000

2 (Constant) -971.082 129.692 -7.488 .000

Mason 5.515 .317 .772 17.379 .000

Paint 1.351 .245 .245 5.505 .000

3 (Constant) -1004.041 122.029 -8.228 .000

Mason 7.693 .685 1.077 11.224 .000

Paint 1.021 .249 .185 4.110 .000

Brick -.062 .018 -.290 -3.527 .001

4 (Constant) -1241.238 138.771 -8.944 .000

Mason 8.144 .668 1.140 12.194 .000

Paint .972 .237 .176 4.102 .000

Brick -.072 .017 -.341 -4.262 .000

Concrete .060 .019 .095 3.119 .003

5 (Constant) -1381.143 149.363 -9.247 .000

Mason 8.089 .653 1.133 12.392 .000

Paint 1.663 .387 .301 4.299 .000

Brick -.053 .019 -.247 -2.788 .007

Concrete .062 .019 .098 3.288 .001

Carpenter -1.310 .588 -.194 -2.229 .029





Selection Method-1





Table 4.68 we can see the value of R2 ranges from 0.874 to 0932 and Adjusted R2





0.000 level of significance, that means the all the model is overall statistically







with Paint and Mason.

The equation is same as expressed in paragraph 4.34.2.

4.37 Backward Elimination Method-3(All Variables except Transport and

Brick)


all the variables except Transport and Brick Cost.






1 .973 .947 .927 65.724

2 .973 .947 .928 65.207

3 .973 .947 .929 64.722

4 .973 .947 .930 64.254

5 .973 .947 .931 63.812

6 .973 .947 .932 63.379

7 .973 .947 .933 63.001

8 .973 .947 .934 62.629

9 .973 .946 .934 62.283

10 .973 .946 .935 61.934

11 .973 .946 .936 61.656

12 .972 .946 .936 61.442

13 .972 .945 .936 61.390

14 .972 .944 .936 61.469

15 .971 .943 .936 61.635

16 .970 .941 .935 62.163

17 .969 .940 .934 62.614

Table 4.72: ANOVA


1 Regression 4806721.291 24 200280.054 46.364 .000

Residual 267821.628 62 4319.704

Total 5074542.920 86

2 Regression 4806671.631 23 208985.723 49.151 .000

Residual 267871.289 63 4251.925

Total 5074542.920 86

3 Regression 4806452.658 22 218475.121 52.156 .000

Residual 268090.261 64 4188.910

Total 5074542.920 86

4 Regression 4806188.535 21 228866.121 55.435 .000

Residual 268354.384 65 4128.529

Total 5074542.920 86

5 Regression 4805792.343 20 240289.617 59.011 .000





Residual 268750.576 66 4071.978

Total 5074542.920 86

6 Regression 4805412.252 19 252916.434 62.963 .000

Residual 269130.667 67 4016.876

Total 5074542.920 86

7 Regression 4804645.075 18 266924.726 67.251 .000

Residual 269897.845 68 3969.086

Total 5074542.920 86

8 Regression 4803895.837 17 282582.108 72.043 .000

Residual 270647.082 69 3922.421

Total 5074542.920 86

9 Regression 4802999.097 16 300187.444 77.384 .000

Residual 271543.823 70 3879.197

Total 5074542.920 86

10 Regression 4802200.733 15 320146.716 83.463 .000

Residual 272342.186 71 3835.805

Total 5074542.920 86

11 Regression 4800838.288 14 342917.021 90.207 .000

Residual 273704.631 72 3801.453

Total 5074542.920 86

12 Regression 4798959.476 13 369150.729 97.785 .000

Residual 275583.444 73 3775.116

Total 5074542.920 86

13 Regression 4795658.890 12 399638.241 106.041 .000

Residual 278884.029 74 3768.703

Total 5074542.920 86

14 Regression 4791158.515 11 435559.865 115.274 .000

Residual 283384.405 75 3778.459

Total 5074542.920 86

15 Regression 4785824.253 10 478582.425 125.978 .000

Residual 288718.666 76 3798.930

Total 5074542.920 86

16 Regression 4776995.376 9 530777.264 137.356 .000

Residual 297547.543 77 3864.254

Total 5074542.920 86





17 Regression 4768744.617 8 596093.077 152.046 .000

Residual 305798.303 78 3920.491

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -1110.578 340.186 -3.265 .002

Steel .000 .002 -.024 -.532 .596

Cement .276 .374 .031 .738 .463

Sand .187 .126 .175 1.485 .143

Paint 1.784 .444 .323 4.022 .000

Mason 4.824 2.244 .675 2.150 .035

Helper .474 1.531 .067 .309 .758

Carpenter -1.582 .781 -.234 -2.025 .047

Duration -1.209 2.260 -.031 -.535 .595

Corner 18.167 28.933 .035 .628 .532

Rd_1 -.917 .740 -.052 -1.240 .220

Rd_2 .320 .966 .023 .331 .742

Pile -1.756 16.382 -.004 -.107 .915

Dual 10.206 23.625 .014 .432 .667

Area -19.832 9.782 -.274 -2.027 .047

Plinth .038 .018 .245 2.092 .041

Story 4.069 6.657 .027 .611 .543

Lobby -.047 .109 -.017 -.433 .666

Toilet -.732 2.054 -.016 -.356 .723

Stair -10.822 7.886 -.050 -1.372 .175

Concrete .044 .024 .070 1.870 .066

Steel_Grade .776 1.752 .019 .443 .659

Transformer .020 .090 .010 .224 .824

Generator -.041 .183 -.009 -.225 .823

Lift 6.555 2.746 .108 2.387 .020

2 (Constant) -1111.118 337.470 -3.292 .002




Model

Unstandardized

Coefficients

Standardized

Coefficients


Steel .000 .002 -.024 -.537 .593

Cement .285 .363 .032 .784 .436

Sand .188 .125 .176 1.510 .136

Paint 1.781 .439 .322 4.054 .000

Mason 4.813 2.224 .674 2.164 .034

Helper .483 1.516 .068 .319 .751

Carpenter -1.586 .774 -.234 -2.048 .045

Duration -1.195 2.239 -.031 -.534 .595

Corner 18.665 28.334 .036 .659 .512

Rd_1 -.898 .711 -.051 -1.262 .211

Rd_2 .300 .940 .021 .319 .751

Dual 9.767 23.086 .013 .423 .674

Area -19.969 9.621 -.276 -2.075 .042

Plinth .038 .018 .246 2.125 .037

Story 4.185 6.516 .028 .642 .523

Lobby -.047 .109 -.017 -.437 .663

Toilet -.732 2.038 -.016 -.359 .721

Stair -10.717 7.764 -.049 -1.380 .172

Concrete .044 .023 .070 1.906 .061

Steel_Grade .738 1.703 .018 .434 .666

Transformer .020 .090 .010 .227 .821

Generator -.041 .181 -.009 -.229 .820

Lift 6.537 2.719 .108 2.404 .019

3 (Constant) -1129.019 325.680 -3.467 .001

Steel .000 .002 -.023 -.534 .595

Cement .287 .360 .033 .798 .428

Sand .186 .123 .174 1.508 .137

Paint 1.780 .436 .322 4.081 .000

Mason 4.853 2.201 .679 2.205 .031

Helper .434 1.489 .061 .291 .772

Carpenter -1.559 .759 -.230 -2.053 .044

Duration -1.193 2.222 -.031 -.537 .593

Corner 19.578 27.838 .038 .703 .484




Model

Unstandardized

Coefficients

Standardized

Coefficients


Rd_1 -.877 .700 -.050 -1.253 .215

Rd_2 .262 .918 .018 .285 .777

Dual 10.230 22.824 .014 .448 .656

Area -19.500 9.327 -.269 -2.091 .041

Plinth .038 .018 .246 2.137 .036

Story 3.983 6.406 .027 .622 .536

Lobby -.049 .107 -.018 -.456 .650

Toilet -.751 2.021 -.016 -.372 .711

Stair -10.861 7.681 -.050 -1.414 .162

Concrete .044 .023 .070 1.920 .059

Steel_Grade .932 1.464 .023 .637 .527

Generator -.045 .179 -.010 -.251 .803

Lift 6.506 2.695 .108 2.414 .019

4 (Constant) -1119.468 321.112 -3.486 .001

Steel .000 .002 -.023 -.534 .595

Cement .291 .357 .033 .815 .418

Sand .187 .122 .175 1.530 .131

Paint 1.762 .427 .319 4.124 .000

Mason 4.753 2.149 .666 2.212 .031

Helper .489 1.462 .069 .335 .739

Carpenter -1.504 .722 -.222 -2.082 .041

Duration -1.307 2.159 -.034 -.606 .547

Corner 19.029 27.552 .037 .691 .492

Rd_1 -.879 .695 -.050 -1.265 .211

Rd_2 .281 .908 .020 .310 .758

Dual 10.251 22.659 .014 .452 .652

Area -20.143 8.905 -.278 -2.262 .027

Plinth .039 .017 .252 2.262 .027

Story 3.890 6.350 .026 .613 .542

Lobby -.044 .105 -.016 -.418 .677

Toilet -.702 1.997 -.015 -.352 .726

Stair -10.499 7.490 -.048 -1.402 .166

Concrete .046 .022 .072 2.035 .046




Model

Unstandardized

Coefficients

Standardized

Coefficients


Steel_Grade .879 1.438 .021 .611 .543

Lift 6.328 2.581 .105 2.452 .017

5 (Constant) -1109.711 317.367 -3.497 .001

Steel -.001 .002 -.027 -.655 .515

Cement .311 .349 .035 .890 .377

Sand .183 .121 .171 1.516 .134

Paint 1.753 .423 .317 4.141 .000

Mason 4.841 2.116 .678 2.288 .025

Helper .441 1.443 .062 .306 .761

Carpenter -1.525 .715 -.225 -2.134 .037

Duration -1.228 2.129 -.032 -.577 .566

Corner 25.865 16.382 .050 1.579 .119

Rd_1 -.757 .569 -.043 -1.330 .188

Dual 10.613 22.474 .015 .472 .638

Area -19.611 8.678 -.271 -2.260 .027

Plinth .038 .017 .244 2.263 .027

Story 3.843 6.304 .026 .610 .544

Lobby -.044 .104 -.016 -.427 .671

Toilet -.715 1.983 -.016 -.361 .719

Stair -10.801 7.375 -.050 -1.464 .148

Concrete .044 .021 .069 2.041 .045

Steel_Grade .818 1.415 .020 .578 .565

Lift 6.304 2.562 .104 2.460 .017

6 (Constant) -1158.761 271.906 -4.262 .000

Steel -.001 .002 -.027 -.650 .518

Cement .337 .336 .038 1.004 .319

Sand .160 .093 .150 1.712 .092

Paint 1.726 .412 .313 4.194 .000

Mason 5.447 .732 .763 7.446 .000

Carpenter -1.553 .704 -.229 -2.207 .031

Duration -1.075 2.055 -.028 -.523 .603

Corner 25.394 16.198 .049 1.568 .122

Rd_1 -.747 .565 -.042 -1.323 .190




Model

Unstandardized

Coefficients

Standardized

Coefficients


Dual 10.939 22.296 .015 .491 .625

Area -19.734 8.610 -.272 -2.292 .025

Plinth .039 .016 .250 2.358 .021

Story 3.893 6.259 .026 .622 .536

Lobby -.048 .102 -.018 -.472 .639

Toilet -.842 1.926 -.018 -.437 .664

Stair -10.591 7.293 -.049 -1.452 .151

Concrete .045 .021 .071 2.111 .038

Steel_Grade .783 1.400 .019 .559 .578

Lift 6.351 2.541 .105 2.500 .015

7 (Constant) -1169.490 269.180 -4.345 .000

Steel -.001 .002 -.027 -.653 .516

Cement .341 .334 .039 1.022 .311

Sand .168 .091 .157 1.840 .070

Paint 1.724 .409 .312 4.212 .000

Mason 5.475 .725 .767 7.556 .000

Carpenter -1.610 .687 -.238 -2.342 .022

Duration -.961 2.026 -.025 -.474 .637

Corner 26.312 15.965 .051 1.648 .104

Rd_1 -.745 .561 -.042 -1.328 .189

Dual 11.432 22.134 .016 .516 .607

Area -20.928 8.116 -.289 -2.578 .012

Plinth .039 .016 .251 2.383 .020

Story 4.565 6.031 .030 .757 .452

Lobby -.044 .101 -.016 -.434 .665

Stair -10.528 7.248 -.048 -1.452 .151

Concrete .047 .020 .075 2.320 .023

Steel_Grade .720 1.385 .017 .520 .605

Lift 6.393 2.524 .106 2.533 .014

8 (Constant) -1167.110 267.538 -4.362 .000

Steel -.001 .002 -.028 -.685 .496

Cement .337 .332 .038 1.015 .314

Sand .165 .090 .154 1.822 .073




Model

Unstandardized

Coefficients

Standardized

Coefficients


Paint 1.732 .406 .314 4.264 .000

Mason 5.540 .705 .776 7.861 .000

Carpenter -1.667 .671 -.246 -2.484 .015

Duration -.974 2.014 -.025 -.484 .630

Corner 25.953 15.850 .050 1.637 .106

Rd_1 -.709 .552 -.040 -1.285 .203

Dual 11.367 22.003 .016 .517 .607

Area -21.414 7.992 -.296 -2.680 .009

Plinth .039 .016 .249 2.386 .020

Story 4.496 5.993 .030 .750 .456

Stair -10.252 7.178 -.047 -1.428 .158

Concrete .047 .020 .075 2.362 .021

Steel_Grade .654 1.368 .016 .478 .634

Lift 6.351 2.507 .105 2.533 .014

9 (Constant) -1111.124 239.225 -4.645 .000

Steel -.001 .002 -.030 -.741 .461

Cement .342 .330 .039 1.037 .303

Sand .182 .083 .170 2.200 .031

Paint 1.692 .395 .306 4.281 .000

Mason 5.476 .688 .767 7.958 .000

Carpenter -1.671 .667 -.247 -2.505 .015

Duration -.906 1.998 -.023 -.454 .651

Corner 26.826 15.657 .052 1.713 .091

Rd_1 -.681 .545 -.039 -1.248 .216

Dual 12.179 21.817 .017 .558 .578

Area -21.661 7.931 -.299 -2.731 .008

Plinth .039 .016 .250 2.404 .019

Story 4.854 5.914 .032 .821 .414

Stair -10.326 7.137 -.047 -1.447 .152

Concrete .050 .019 .079 2.558 .013

Lift 6.406 2.490 .106 2.572 .012

10 (Constant) -1130.894 233.903 -4.835 .000

Steel -.001 .002 -.027 -.682 .497




Model

Unstandardized

Coefficients

Standardized

Coefficients


Cement .337 .328 .038 1.028 .307

Sand .192 .079 .180 2.441 .017

Paint 1.672 .391 .303 4.281 .000

Mason 5.643 .578 .790 9.756 .000

Carpenter -1.840 .550 -.272 -3.344 .001

Corner 26.190 15.507 .051 1.689 .096

Rd_1 -.679 .542 -.038 -1.253 .214

Dual 12.895 21.637 .018 .596 .553

Area -22.343 7.743 -.308 -2.886 .005

Plinth .040 .016 .258 2.528 .014

Story 4.688 5.869 .031 .799 .427

Stair -9.232 6.679 -.042 -1.382 .171

Concrete .051 .019 .080 2.624 .011

Lift 6.249 2.452 .103 2.548 .013

11 (Constant) -1128.616 232.822 -4.848 .000

Steel -.001 .002 -.028 -.703 .484

Cement .327 .326 .037 1.004 .319

Sand .201 .077 .188 2.612 .011

Paint 1.660 .388 .300 4.275 .000

Mason 5.601 .572 .784 9.799 .000

Carpenter -1.818 .547 -.269 -3.325 .001

Corner 26.337 15.436 .051 1.706 .092

Rd_1 -.728 .534 -.041 -1.363 .177

Area -22.631 7.693 -.312 -2.942 .004

Plinth .040 .016 .260 2.563 .012

Story 5.323 5.746 .035 .926 .357

Stair -9.198 6.649 -.042 -1.383 .171

Concrete .052 .019 .083 2.759 .007

Lift 5.968 2.396 .099 2.491 .015

12 (Constant) -1167.123 225.502 -5.176 .000

Cement .302 .323 .034 .935 .353

Sand .200 .077 .187 2.603 .011

Paint 1.693 .384 .307 4.410 .000




Model

Unstandardized

Coefficients

Standardized

Coefficients


Mason 5.510 .555 .772 9.929 .000

Carpenter -1.860 .541 -.275 -3.436 .001

Corner 27.259 15.326 .053 1.779 .079

Rd_1 -.686 .529 -.039 -1.297 .199

Area -22.425 7.661 -.310 -2.927 .005

Plinth .041 .016 .263 2.610 .011

Story 6.057 5.630 .040 1.076 .286

Stair -8.955 6.617 -.041 -1.353 .180

Concrete .051 .019 .082 2.732 .008

Lift 5.660 2.347 .094 2.411 .018

13 (Constant) -1099.536 213.422 -5.152 .000

Sand .206 .076 .193 2.699 .009

Paint 1.705 .383 .309 4.447 .000

Mason 5.640 .537 .790 10.506 .000

Carpenter -1.895 .540 -.280 -3.513 .001

Corner 28.081 15.288 .054 1.837 .070

Rd_1 -.733 .526 -.041 -1.394 .168

Area -22.190 7.650 -.306 -2.900 .005

Plinth .041 .016 .264 2.618 .011

Story 6.146 5.625 .041 1.093 .278

Stair -10.476 6.408 -.048 -1.635 .106

Concrete .052 .019 .082 2.755 .007

Lift 5.660 2.345 .094 2.413 .018

14 (Constant) -1118.243 213.009 -5.250 .000

Sand .196 .076 .184 2.586 .012

Paint 1.720 .384 .311 4.484 .000

Mason 5.645 .538 .790 10.503 .000

Carpenter -1.765 .527 -.261 -3.350 .001

Corner 24.868 15.022 .048 1.655 .102

Rd_1 -.611 .515 -.035 -1.188 .239

Area -20.572 7.516 -.284 -2.737 .008

Plinth .039 .016 .254 2.526 .014

Stair -10.573 6.416 -.049 -1.648 .104




Model

Unstandardized

Coefficients

Standardized

Coefficients


Concrete .054 .019 .086 2.890 .005

Lift 6.077 2.317 .101 2.623 .011

15 (Constant) -1191.139 204.535 -5.824 .000

Sand .183 .075 .171 2.428 .018

Paint 1.793 .380 .325 4.722 .000

Mason 5.717 .536 .800 10.675 .000

Carpenter -1.798 .528 -.266 -3.408 .001

Corner 22.810 14.962 .044 1.524 .132

Area -20.237 7.531 -.279 -2.687 .009

Plinth .040 .016 .256 2.540 .013

Stair -9.894 6.408 -.045 -1.544 .127

Concrete .056 .019 .089 3.020 .003

Lift 5.978 2.322 .099 2.575 .012

16 (Constant) -1103.433 197.957 -5.574 .000

Sand .203 .075 .190 2.718 .008

Paint 1.684 .376 .305 4.477 .000

Mason 5.616 .536 .786 10.478 .000

Carpenter -1.769 .532 -.261 -3.328 .001

Area -20.052 7.594 -.277 -2.640 .010

Plinth .037 .016 .241 2.383 .020

Stair -9.432 6.455 -.043 -1.461 .148

Concrete .054 .019 .086 2.875 .005

Lift 6.362 2.328 .105 2.733 .008

17 (Constant) -1106.346 199.382 -5.549 .000

Sand .202 .075 .189 2.689 .009

Paint 1.560 .369 .282 4.226 .000

Mason 5.618 .540 .787 10.407 .000

Carpenter -1.574 .518 -.233 -3.037 .003

Area -21.850 7.548 -.302 -2.895 .005

Plinth .041 .016 .263 2.605 .011

Concrete .057 .019 .091 3.066 .003

Lift 6.269 2.344 .104 2.674 .009







with Construction Cost as dependent variable (DV). We excluded Transport Cost and

Brick in this analysis. The software has automatically produced 17 models. In 1st

model all the variables were considered and the variables were removed each at one

step and formulate a new model. Referring to Table 4.71, the value of R2 ranges from

0.947 to 0.940 and Adjusted R2 from 0.927 and 0.934. There is considerable change

between R2 and Adjusted R2 in first model but decreases in the last model which is a

good sign. However, the model can explain 94.7% to 94% of the variability with the

17 models. The Standard Error (SE) ranges from 46.364 to 152.046 which are very

good. Referring to Table 4.72, F varies from 47.35 to 172.214 at 0.000 level of

significance, that means the all the model is overall statistically significant below 5%

level. If we see Table 4.73 we find that out of 17 models last one is valid as all the

variables are individually statistically significant (by "T" stat) at or below 5% level.

In this model total 8 IV were included where all are statistically significant below 5%

level. But when the question of practical significance comes the condition was not

met in case of Carpenter.




4.38 Forward Selection Method-3(All Variables except Transport)


variables except Transport.






1 .935a .874 .873 86.611

2 .953b .908 .905 74.689

3 .959c .919 .916 70.410

4 .962d .926 .922 67.732

5 .965e .930 .926 66.078

Table 4.75: ANOVA


1 Regression 4436924.912 1 4436924.912 591.480 .000a

Residual 637618.007 85 7501.388

Total 5074542.920 86

2 Regression 4605955.827 2 2302977.913 412.837 .000b

Residual 468587.093 84 5578.418

Total 5074542.920 86

3 Regression 4663062.523 3 1554354.174 313.530 .000c

Residual 411480.396 83 4957.595

Total 5074542.920 86

4 Regression 4698355.170 4 1174588.792 256.032 .000d

Residual 376187.750 82 4587.655

Total 5074542.920 86

5 Regression 4720867.548 5 944173.510 216.238 .000e

Residual 353675.372 81 4366.363

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -357.338 76.820 -4.652 .000

Mason 6.678 .275 .935 24.320 .000

2 (Constant) -971.082 129.692 -7.488 .000

Mason 5.515 .317 .772 17.379 .000




Model

Unstandardized

Coefficients

Standardized

Coefficients


Paint 1.351 .245 .245 5.505 .000

3 (Constant) -1177.267 136.524 -8.623 .000

Mason 6.441 .405 .902 15.908 .000

Paint 2.191 .339 .397 6.467 .000

Carpenter -1.883 .555 -.278 -3.394 .001

4 (Constant) -1406.269 155.128 -9.065 .000

Mason 6.606 .394 .925 16.766 .000

Paint 2.288 .328 .414 6.982 .000

Carpenter -2.086 .539 -.308 -3.872 .000

Concrete .053 .019 .085 2.774 .007

5 (Constant) -1159.754 186.254 -6.227 .000

Mason 5.685 .559 .796 10.172 .000

Paint 1.863 .370 .337 5.030 .000

Carpenter -1.804 .540 -.267 -3.342 .001

Concrete .051 .019 .081 2.695 .009

Sand .177 .078 .166 2.271 .026


Selection (Method-3)





Table 4.74 we can see the value of R2 ranges from 0.874 to 0930 and Adjusted R2













4.38.2 Concluding Remarks of the Model by Forward Selection-3


with Paint and Mason. The equation is same as expressed in paragraph 4.34.2.

4.39 Backward Elimination Method-4 (All Variables except Transport, Brick

and Carpenter)


all the variables except Transport, Brick Cost and Carpenter.



1 .971 .944 .923 67.322

2 .971 .944 .924 66.798

3 .971 .944 .925 66.303

4 .971 .944 .927 65.828

5 .971 .944 .928 65.372

6 .971 .943 .929 64.944

7 .971 .943 .929 64.579

8 .971 .943 .930 64.307

9 .971 .942 .930 64.126

10 .970 .942 .930 64.073

11 .970 .941 .931 64.022

12 .970 .940 .931 63.954

13 .969 .940 .931 63.899

14 .969 .938 .930 64.331

15 .967 .936 .928 65.036

16 .966 .934 .927 65.750

17 .966 .933 .927 65.791




Table 4.78: ANOVA


1 Regression 4789013.268 23 208217.968 45.942 .000

Residual 285529.651 63 4532.217

Total 5074542.920 86

2 Regression 4788974.807 22 217680.673 48.785 .000

Residual 285568.113 64 4462.002

Total 5074542.920 86

3 Regression 4788795.013 21 228037.858 51.873 .000

Residual 285747.906 65 4396.122

Total 5074542.920 86

4 Regression 4788545.971 20 239427.299 55.253 .000

Residual 285996.949 66 4333.287

Total 5074542.920 86

5 Regression 4788221.140 19 252011.639 58.971 .000

Residual 286321.779 67 4273.459

Total 5074542.920 86

6 Regression 4787739.669 18 265985.537 63.064 .000

Residual 286803.250 68 4217.695

Total 5074542.920 86

7 Regression 4786785.828 17 281575.637 67.518 .000

Residual 287757.091 69 4170.393

Total 5074542.920 86

8 Regression 4785061.819 16 299066.364 72.318 .000

Residual 289481.100 70 4135.444

Total 5074542.920 86

9 Regression 4782582.660 15 318838.844 77.536 .000

Residual 291960.260 71 4112.116

Total 5074542.920 86

10 Regression 4778955.787 14 341353.985 83.148 .000

Residual 295587.133 72 4105.377

Total 5074542.920 86

11 Regression 4775325.251 13 367332.712 89.618 .000

Residual 299217.669 73 4098.872

Total 5074542.920 86





12 Regression 4771877.481 12 397656.457 97.225 .000

Residual 302665.439 74 4090.073

Total 5074542.920 86

13 Regression 4768309.771 11 433482.706 106.165 .000

Residual 306233.149 75 4083.109

Total 5074542.920 86

14 Regression 4760020.957 10 476002.096 115.020 .000

Residual 314521.963 76 4138.447

Total 5074542.920 86

15 Regression 4748853.922 9 527650.436 124.748 .000

Residual 325688.998 77 4229.727

Total 5074542.920 86

16 Regression 4737339.262 8 592167.408 136.977 .000

Residual 337203.657 78 4323.124

Total 5074542.920 86

17 Regression 4732589.802 7 676084.257 156.193 .000

Residual 341953.117 79 4328.520

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -908.976 333.193 -2.728 .008

Steel -.001 .002 -.034 -.747 .458

Cement .300 .383 .034 .784 .436

Sand .202 .129 .189 1.565 .123

Paint 1.385 .407 .251 3.403 .001

Mason 3.158 2.138 .442 1.477 .145

Helper .918 1.552 .129 .591 .556

Duration -3.888 1.876 -.100 -2.072 .042

Corner 13.187 29.529 .026 .447 .657

Rd_1 -1.042 .755 -.059 -1.380 .172

Rd_2 .491 .986 .035 .498 .620




Model

Unstandardized

Coefficients

Standardized

Coefficients


Pile -3.363 16.760 -.007 -.201 .842

Dual 6.316 24.119 .009 .262 .794

Area -19.483 10.018 -.269 -1.945 .056

Plinth .041 .018 .264 2.210 .031

Story 1.254 6.668 .008 .188 .851

Lobby -.075 .111 -.027 -.670 .505

Toilet -1.233 2.089 -.027 -.591 .557

Stair -10.601 8.077 -.049 -1.313 .194

Concrete .042 .024 .066 1.724 .090

Steel_Grade 1.169 1.783 .028 .655 .515

Transformer -.008 .092 -.004 -.092 .927

Generator .058 .180 .012 .321 .749

Lift 6.744 2.811 .112 2.399 .019

2 (Constant) -899.897 315.810 -2.849 .006

Steel -.001 .002 -.034 -.758 .451

Cement .299 .380 .034 .788 .434

Sand .203 .127 .190 1.593 .116

Paint 1.383 .403 .250 3.430 .001

Mason 3.129 2.098 .438 1.491 .141

Helper .942 1.517 .133 .621 .537

Duration -3.909 1.848 -.101 -2.115 .038

Corner 12.768 28.950 .025 .441 .661

Rd_1 -1.052 .742 -.060 -1.417 .161

Rd_2 .508 .960 .036 .529 .599

Pile -3.355 16.630 -.007 -.202 .841

Dual 6.086 23.803 .008 .256 .799

Area -19.681 9.709 -.272 -2.027 .047

Plinth .041 .018 .265 2.233 .029

Story 1.320 6.578 .009 .201 .842

Lobby -.074 .110 -.027 -.672 .504

Toilet -1.229 2.072 -.027 -.593 .555

Stair -10.538 7.985 -.048 -1.320 .192

Concrete .042 .024 .066 1.737 .087




Model

Unstandardized

Coefficients

Standardized

Coefficients


Steel_Grade 1.089 1.548 .026 .704 .484

Generator .060 .177 .013 .339 .736

Lift 6.758 2.785 .112 2.427 .018

3 (Constant) -906.837 311.586 -2.910 .005

Steel -.001 .002 -.035 -.794 .430

Cement .299 .377 .034 .792 .431

Sand .199 .125 .186 1.593 .116

Paint 1.395 .396 .253 3.525 .001

Mason 3.166 2.075 .443 1.526 .132

Helper .939 1.506 .132 .624 .535

Duration -3.858 1.817 -.099 -2.123 .038

Corner 11.987 28.476 .023 .421 .675

Rd_1 -1.031 .730 -.058 -1.413 .162

Rd_2 .506 .953 .036 .531 .597

Pile -3.880 16.301 -.008 -.238 .813

Dual 7.051 23.140 .010 .305 .762

Area -19.214 9.357 -.265 -2.054 .044

Plinth .040 .018 .262 2.241 .028

Lobby -.073 .109 -.027 -.670 .505

Toilet -1.316 2.011 -.029 -.654 .515

Stair -10.567 7.925 -.049 -1.333 .187

Concrete .042 .024 .066 1.748 .085

Steel_Grade 1.138 1.517 .028 .750 .456

Generator .060 .176 .013 .343 .733

Lift 6.848 2.728 .113 2.510 .015

4 (Constant) -908.314 309.290 -2.937 .005

Steel -.001 .002 -.035 -.807 .422

Cement .318 .366 .036 .868 .389

Sand .200 .124 .187 1.621 .110

Paint 1.389 .392 .251 3.542 .001

Mason 3.139 2.057 .440 1.526 .132

Helper .963 1.492 .136 .645 .521

Duration -3.834 1.802 -.099 -2.128 .037




Model

Unstandardized

Coefficients

Standardized

Coefficients


Corner 12.947 27.987 .025 .463 .645

Rd_1 -.983 .696 -.056 -1.412 .163

Rd_2 .461 .927 .032 .497 .621

Dual 6.218 22.709 .009 .274 .785

Area -19.433 9.245 -.268 -2.102 .039

Plinth .041 .018 .264 2.281 .026

Lobby -.073 .109 -.027 -.676 .501

Toilet -1.334 1.995 -.029 -.668 .506

Stair -10.334 7.807 -.047 -1.324 .190

Concrete .042 .023 .067 1.794 .077

Steel_Grade 1.065 1.476 .026 .722 .473

Generator .060 .175 .013 .343 .733

Lift 6.825 2.707 .113 2.522 .014

5 (Constant) -911.955 306.863 -2.972 .004

Steel -.001 .002 -.036 -.821 .415

Cement .310 .362 .035 .856 .395

Sand .203 .122 .190 1.661 .101

Paint 1.396 .388 .253 3.594 .001

Mason 3.116 2.041 .436 1.527 .131

Helper .976 1.480 .137 .660 .512

Duration -3.841 1.789 -.099 -2.147 .035

Corner 12.603 27.765 .024 .454 .651

Rd_1 -1.006 .686 -.057 -1.465 .148

Rd_2 .469 .920 .033 .510 .612

Area -19.399 9.180 -.268 -2.113 .038

Plinth .041 .018 .264 2.295 .025

Lobby -.073 .108 -.026 -.674 .503

Toilet -1.370 1.977 -.030 -.693 .491

Stair -10.370 7.752 -.048 -1.338 .186

Concrete .043 .023 .068 1.849 .069

Steel_Grade 1.111 1.457 .027 .763 .448

Generator .058 .173 .012 .336 .738

Lift 6.707 2.653 .111 2.527 .014




Model

Unstandardized

Coefficients

Standardized

Coefficients


6 (Constant) -914.082 304.789 -2.999 .004

Steel -.001 .002 -.036 -.844 .401

Cement .307 .360 .035 .852 .397

Sand .202 .121 .189 1.665 .101

Paint 1.401 .386 .254 3.633 .001

Mason 3.172 2.021 .444 1.570 .121

Helper .923 1.462 .130 .632 .530

Duration -3.812 1.775 -.098 -2.147 .035

Corner 13.099 27.544 .025 .476 .636

Rd_1 -1.009 .682 -.057 -1.479 .144

Rd_2 .452 .913 .032 .495 .622

Area -18.513 8.735 -.256 -2.119 .038

Plinth .040 .017 .256 2.290 .025

Lobby -.081 .104 -.030 -.784 .436

Toilet -1.462 1.945 -.032 -.751 .455

Stair -10.852 7.568 -.050 -1.434 .156

Concrete .041 .022 .065 1.834 .071

Steel_Grade 1.188 1.429 .029 .832 .409

Lift 6.974 2.514 .115 2.774 .007

7 (Constant) -923.405 302.448 -3.053 .003

Steel -.001 .002 -.032 -.760 .450

Cement .290 .356 .033 .813 .419

Sand .207 .120 .194 1.719 .090

Paint 1.398 .383 .253 3.646 .001

Mason 3.139 2.008 .440 1.563 .123

Helper .935 1.454 .132 .643 .522

Duration -3.823 1.765 -.098 -2.166 .034

Rd_1 -1.140 .619 -.065 -1.841 .070

Rd_2 .803 .533 .057 1.507 .136

Area -19.143 8.586 -.264 -2.230 .029

Plinth .041 .017 .263 2.389 .020

Lobby -.079 .103 -.029 -.769 .445

Toilet -1.493 1.933 -.032 -.772 .443




Model

Unstandardized

Coefficients

Standardized

Coefficients


Stair -10.254 7.421 -.047 -1.382 .171

Concrete .043 .022 .068 1.962 .054

Steel_Grade 1.293 1.404 .031 .921 .360

Lift 7.069 2.492 .117 2.836 .006

8 (Constant) -1017.273 263.766 -3.857 .000

Steel -.001 .002 -.032 -.774 .441

Cement .351 .342 .040 1.027 .308

Sand .158 .092 .147 1.706 .093

Paint 1.324 .364 .240 3.635 .001

Mason 4.384 .534 .614 8.205 .000

Duration -3.588 1.720 -.092 -2.087 .041

Rd_1 -1.102 .614 -.062 -1.796 .077

Rd_2 .756 .526 .053 1.438 .155

Area -19.253 8.548 -.266 -2.252 .027

Plinth .042 .017 .273 2.517 .014

Lobby -.090 .101 -.033 -.883 .381

Toilet -1.797 1.867 -.039 -.962 .339

Stair -9.876 7.366 -.045 -1.341 .184

Concrete .044 .022 .070 2.035 .046

Steel_Grade 1.219 1.393 .030 .875 .384

Lift 7.183 2.476 .119 2.901 .005

9 (Constant) -1078.122 251.075 -4.294 .000

Cement .317 .338 .036 .939 .351

Sand .154 .092 .144 1.669 .099

Paint 1.354 .361 .245 3.749 .000

Mason 4.286 .518 .600 8.278 .000

Duration -3.492 1.710 -.090 -2.042 .045

Rd_1 -1.097 .612 -.062 -1.792 .077

Rd_2 .837 .513 .059 1.631 .107

Area -19.009 8.518 -.262 -2.232 .029

Plinth .044 .017 .282 2.618 .011

Lobby -.097 .101 -.035 -.959 .341

Toilet -1.866 1.860 -.041 -1.004 .319




Model

Unstandardized

Coefficients

Standardized

Coefficients


Stair -9.318 7.310 -.043 -1.275 .207

Concrete .044 .022 .069 2.016 .048

Steel_Grade 1.370 1.376 .033 .996 .323

Lift 6.852 2.432 .113 2.818 .006

10 (Constant) -1007.751 239.437 -4.209 .000

Sand .159 .092 .149 1.735 .087

Paint 1.359 .361 .246 3.767 .000

Mason 4.404 .502 .617 8.774 .000

Duration -3.551 1.708 -.091 -2.079 .041

Rd_1 -1.171 .606 -.066 -1.931 .057

Rd_2 .891 .510 .063 1.749 .085

Area -18.850 8.509 -.260 -2.215 .030

Plinth .044 .017 .285 2.647 .010

Lobby -.095 .101 -.034 -.940 .350

Toilet -1.919 1.857 -.042 -1.033 .305

Stair -10.821 7.127 -.050 -1.518 .133

Concrete .044 .022 .070 2.043 .045

Steel_Grade 1.397 1.374 .034 1.016 .313

Lift 6.865 2.430 .114 2.826 .006

11 (Constant) -994.257 238.817 -4.163 .000

Sand .153 .091 .143 1.672 .099

Paint 1.341 .360 .243 3.725 .000

Mason 4.442 .500 .622 8.886 .000

Duration -3.782 1.689 -.097 -2.240 .028

Rd_1 -1.092 .600 -.062 -1.819 .073

Rd_2 .891 .509 .063 1.749 .085

Area -20.115 8.396 -.278 -2.396 .019

Plinth .044 .017 .284 2.644 .010

Toilet -1.793 1.851 -.039 -.969 .336

Stair -10.146 7.085 -.047 -1.432 .156

Concrete .045 .022 .071 2.087 .040

Steel_Grade 1.251 1.364 .030 .917 .362

Lift 6.802 2.427 .113 2.803 .006




Model

Unstandardized

Coefficients

Standardized

Coefficients


12 (Constant) -892.078 211.011 -4.228 .000

Sand .187 .083 .175 2.248 .028

Paint 1.262 .349 .228 3.614 .001

Mason 4.310 .478 .603 9.016 .000

Duration -3.600 1.675 -.093 -2.149 .035

Rd_1 -1.023 .595 -.058 -1.720 .090

Rd_2 .903 .509 .064 1.776 .080

Area -20.503 8.376 -.283 -2.448 .017

Plinth .044 .017 .285 2.652 .010

Toilet -1.725 1.847 -.037 -.934 .353

Stair -10.183 7.078 -.047 -1.439 .154

Concrete .050 .021 .079 2.398 .019

Lift 6.909 2.421 .114 2.853 .006

13 (Constant) -916.969 209.143 -4.384 .000

Sand .200 .082 .187 2.442 .017

Paint 1.239 .348 .224 3.560 .001

Mason 4.314 .478 .604 9.034 .000

Duration -3.486 1.669 -.090 -2.088 .040

Rd_1 -1.027 .594 -.058 -1.729 .088

Rd_2 .941 .507 .066 1.857 .067

Area -22.598 8.063 -.312 -2.803 .006

Plinth .044 .017 .287 2.672 .009

Stair -10.074 7.071 -.046 -1.425 .158

Concrete .055 .020 .087 2.744 .008

Lift 7.112 2.410 .118 2.951 .004

14 (Constant) -947.802 209.425 -4.526 .000

Sand .210 .082 .196 2.546 .013

Paint 1.108 .338 .201 3.279 .002

Mason 4.512 .460 .632 9.805 .000

Duration -2.525 1.537 -.065 -1.643 .105

Rd_1 -.985 .598 -.056 -1.649 .103

Rd_2 .950 .510 .067 1.863 .066

Area -25.105 7.922 -.347 -3.169 .002




Model

Unstandardized

Coefficients

Standardized

Coefficients


Plinth .049 .016 .316 2.987 .004

Concrete .060 .020 .095 2.996 .004

Lift 6.833 2.418 .113 2.826 .006

15 (Constant) -897.676 209.462 -4.286 .000

Sand .260 .077 .243 3.363 .001

Paint .804 .286 .146 2.814 .006

Mason 4.659 .456 .652 10.214 .000

Rd_1 -1.023 .604 -.058 -1.695 .094

Rd_2 .844 .511 .059 1.650 .103

Area -27.660 7.853 -.382 -3.522 .001

Plinth .053 .016 .344 3.256 .002

Concrete .058 .020 .092 2.878 .005

Lift 6.512 2.436 .108 2.673 .009

16 (Constant) -802.264 203.532 -3.942 .000

Sand .266 .078 .249 3.410 .001

Paint .715 .284 .129 2.520 .014

Mason 4.604 .460 .645 10.010 .000

Rd_1 -.569 .543 -.032 -1.048 .298

Area -25.624 7.841 -.354 -3.268 .002

Plinth .048 .016 .308 2.949 .004

Concrete .049 .020 .078 2.515 .014

Lift 6.630 2.462 .110 2.693 .009

17 (Constant) -870.513 192.956 -4.511 .000

Sand .253 .077 .237 3.285 .002

Paint .777 .278 .141 2.800 .006

Mason 4.651 .458 .651 10.155 .000

Area -25.315 7.840 -.349 -3.229 .002

Plinth .048 .016 .312 2.980 .004

Concrete .051 .020 .082 2.624 .010

Lift 6.519 2.461 .108 2.649 .010










formulate a new model. Referring to Table 4.77 we see that, the value of R2 ranges

from 0.944 to 0.933 and Adjusted R2 from 0.923 and 0.927. The model can explain

94.4% to 93.3% of the variability with the 19 models. The Standard Error (SE)

ranges from 67.322 to 65.791 which are very good. Referring to Table 4.78, F varies

from 45.942 to 156.193 at 0.000 level of significance, that means the all the model is

overall statistically significant below 5% level. If we see Table 4.79 we find that out

of 19 models last one is valid as all the variables are individually statistically

significant (by "T" stat) at or below 5% level. In this model total 7 IV were included

where all are statistically significant below 5% level. But when the question of

practical significance comes the condition was not met in the best model.




4.40 Forward Selection-4



1 .935a .874 .873 86.611

2 .953b .908 .905 74.689

3 .957c .916 .913 71.487

4 .960d .921 .917 70.015




Table 4.81: ANOVA


1 Regression 4436924.912 1 4436924.912 591.480 .000a

Residual 637618.007 85 7501.388

Total 5074542.920 86

2 Regression 4605955.827 2 2302977.913 412.837 .000b

Residual 468587.093 84 5578.418

Total 5074542.920 86

3 Regression 4650383.655 3 1550127.885 303.331 .000c

Residual 424159.265 83 5110.353

Total 5074542.920 86

4 Regression 4672571.944 4 1168142.986 238.295 .000d

Residual 401970.975 82 4902.085

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -357.338 76.820 -4.652 .000

Mason 6.678 .275 .935 24.320 .000

2 (Constant) -971.082 129.692 -7.488 .000

Mason 5.515 .317 .772 17.379 .000

Paint 1.351 .245 .245 5.505 .000

3 (Constant) -690.457 156.419 -4.414 .000

Mason 4.450 .472 .623 9.426 .000

Paint .942 .273 .171 3.455 .001

Sand .242 .082 .226 2.949 .004

4 (Constant) -577.960 162.067 -3.566 .001

Mason 4.396 .463 .616 9.495 .000

Paint .729 .285 .132 2.554 .012

Sand .248 .080 .232 3.091 .003

Lift 4.641 2.182 .077 2.128 .036





Selection Method-4





Table 4.80 we can see the value of R2 ranges from 0.874 to 0.921 and Adjusted R2








below 5% level. This time the entire model has passed practical significance. Model

4 is the best and accepted.

4.40.2 Concluding Remarks of the Model by Forward Selection-4

Model 4 is yield better result so we select Model-4

The equation is as follows: (R2=0.921; SE=70.015)

Construction Cost=-577.960 +4.396 x Mason +0.729 x Paint + 0.248 x Sand +

4.641 x Lift

Where Construction is (Taka/sft)

Mason= Wage of Mason (Taka/ Day)


Sand= Price of sand (Taka/100 cft)

Lift= Capacity of Lift (Person/ building)

4.41 BACKWARD ELIMINATION METHOD-5 (All Variables except

Transport, Brick and Carpenter)






Table 4.83: Model Summary (Backward Elimination-5)


1 .969 .939 .919 69.336

2 .969 .939 .920 68.800

3 .969 .939 .921 68.279

4 .969 .939 .922 67.771

5 .969 .939 .923 67.282

6 .969 .939 .924 66.813

7 .969 .939 .925 66.383

8 .969 .939 .926 65.976

9 .969 .939 .927 65.824

10 .968 .938 .927 65.669

11 .968 .937 .927 65.549

12 .968 .936 .927 65.629

13 .967 .935 .927 65.673

14 .967 .935 .927 65.629

15 .966 .934 .927 65.751

16 .965 .931 .925 66.385

17 .964 .929 .924 66.991

Table 4.84: ANOVA (Backward Elimination-5)


1 Regression 4766867.602 22 216675.800 45.071 .000

Residual 307675.317 64 4807.427

Total 5074542.920 86

2 Regression 4766865.667 21 226993.603 47.955 .000

Residual 307677.253 65 4733.496

Total 5074542.920 86

3 Regression 4766852.681 20 238342.634 51.125 .000

Residual 307690.238 66 4661.973

Total 5074542.920 86

4 Regression 4766815.982 19 250885.052 54.624 .000

Residual 307726.938 67 4592.939





Total 5074542.920 86

5 Regression 4766715.509 18 264817.528 58.499 .000

Residual 307827.411 68 4526.874

Total 5074542.920 86

6 Regression 4766529.879 17 280384.111 62.811 .000

Residual 308013.041 69 4463.957

Total 5074542.920 86

7 Regression 4766073.172 16 297879.573 67.597 .000

Residual 308469.748 70 4406.711

Total 5074542.920 86

8 Regression 4765489.629 15 317699.309 72.986 .000

Residual 309053.290 71 4352.863

Total 5074542.920 86

9 Regression 4762584.578 14 340184.613 78.515 .000

Residual 311958.341 72 4332.755

Total 5074542.920 86

10 Regression 4759735.611 13 366133.509 84.902 .000

Residual 314807.308 73 4312.429

Total 5074542.920 86

11 Regression 4756593.214 12 396382.768 92.255 .000

Residual 317949.706 74 4296.618

Total 5074542.920 86

12 Regression 4751506.299 11 431955.118 100.288 .000

Residual 323036.620 75 4307.155

Total 5074542.920 86

13 Regression 4746758.758 10 474675.876 110.058 .000

Residual 327784.161 76 4312.949

Total 5074542.920 86

14 Regression 4742892.402 9 526988.045 122.352 .000

Residual 331650.518 77 4307.150

Total 5074542.920 86

15 Regression 4737336.739 8 592167.092 136.976 .000

Residual 337206.180 78 4323.156

Total 5074542.920 86

16 Regression 4726394.920 7 675199.274 153.213 .000





Residual 348147.999 79 4406.937

Total 5074542.920 86

17 Regression 4715516.822 6 785919.470 175.123 .000

Residual 359026.097 80 4487.826

Total 5074542.920 86

Table 4.85: Coefficients (Backward Elimination-5)

Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -701.746 329.297 -2.131 .037

Steel -.002 .002 -.048 -1.041 .302

Cement .293 .394 .033 .743 .460

Sand .209 .133 .195 1.573 .121

Paint 1.467 .418 .265 3.512 .001

Mason 2.443 2.177 .342 1.122 .266

Helper 1.256 1.590 .177 .790 .432

Duration -4.741 1.891 -.122 -2.507 .015

Corner 20.797 30.205 .040 .689 .494

Rd_1 -.897 .775 -.051 -1.157 .251

Rd_2 .053 .995 .004 .053 .958

Pile -6.722 17.190 -.014 -.391 .697

Dual 8.069 24.827 .011 .325 .746

Area -.100 4.989 -.001 -.020 .984

Story -.529 6.817 -.004 -.078 .938

Lobby -.079 .115 -.029 -.686 .495

Toilet -1.346 2.151 -.029 -.626 .534

Stair -15.160 8.043 -.070 -1.885 .064

Concrete .024 .023 .038 1.031 .306

Steel_Grade 1.398 1.833 .034 .762 .449

Transformer -.016 .094 -.007 -.166 .868

Generator -.023 .182 -.005 -.124 .902

Lift 6.683 2.895 .111 2.309 .024

2 (Constant) -704.589 294.964 -2.389 .020




Model

Unstandardized

Coefficients

Standardized

Coefficients


Steel -.002 .002 -.048 -1.067 .290

Cement .293 .391 .033 .749 .456

Sand .208 .121 .194 1.710 .092

Paint 1.469 .400 .266 3.672 .000

Mason 2.457 2.050 .344 1.199 .235

Helper 1.247 1.505 .176 .828 .411

Duration -4.738 1.872 -.122 -2.532 .014

Corner 20.839 29.902 .040 .697 .488

Rd_1 -.895 .764 -.051 -1.171 .246

Rd_2 .052 .984 .004 .052 .958

Pile -6.758 16.964 -.014 -.398 .692

Dual 8.112 24.543 .011 .331 .742

Story -.572 6.427 -.004 -.089 .929

Lobby -.079 .104 -.029 -.761 .450

Toilet -1.372 1.706 -.030 -.804 .424

Stair -15.185 7.887 -.070 -1.925 .059

Concrete .024 .023 .038 1.062 .292

Steel_Grade 1.411 1.696 .034 .832 .408

Transformer -.016 .086 -.008 -.189 .850

Generator -.023 .175 -.005 -.135 .893

Lift 6.670 2.803 .110 2.380 .020

3 (Constant) -703.896 292.432 -2.407 .019

Steel -.002 .002 -.048 -1.136 .260

Cement .297 .378 .034 .787 .434

Sand .207 .120 .194 1.725 .089

Paint 1.465 .391 .265 3.744 .000

Mason 2.472 2.014 .346 1.228 .224

Helper 1.237 1.482 .174 .835 .407

Duration -4.723 1.836 -.122 -2.573 .012

Corner 22.105 17.465 .043 1.266 .210

Rd_1 -.872 .616 -.049 -1.415 .162

Pile -6.560 16.410 -.013 -.400 .691

Dual 8.126 24.355 .011 .334 .740




Model

Unstandardized

Coefficients

Standardized

Coefficients


Story -.566 6.377 -.004 -.089 .930

Lobby -.080 .104 -.029 -.768 .445

Toilet -1.372 1.693 -.030 -.810 .421

Stair -15.213 7.808 -.070 -1.948 .056

Concrete .024 .022 .038 1.081 .284

Steel_Grade 1.403 1.677 .034 .837 .406

Transformer -.017 .085 -.008 -.203 .840

Generator -.024 .173 -.005 -.137 .892

Lift 6.669 2.781 .110 2.398 .019

4 (Constant) -702.577 289.883 -2.424 .018

Steel -.002 .002 -.048 -1.149 .255

Cement .297 .375 .034 .791 .432

Sand .208 .119 .195 1.748 .085

Paint 1.463 .388 .265 3.774 .000

Mason 2.467 1.998 .345 1.235 .221

Helper 1.230 1.469 .173 .837 .405

Duration -4.751 1.796 -.122 -2.645 .010

Corner 22.491 16.790 .044 1.340 .185

Rd_1 -.880 .604 -.050 -1.458 .150

Pile -6.384 16.169 -.013 -.395 .694

Dual 7.711 23.724 .011 .325 .746

Lobby -.081 .101 -.030 -.804 .424

Toilet -1.368 1.680 -.030 -.814 .418

Stair -15.251 7.739 -.070 -1.971 .053

Concrete .024 .022 .038 1.085 .282

Steel_Grade 1.392 1.659 .034 .839 .405

Transformer -.017 .084 -.008 -.206 .838

Generator -.025 .171 -.005 -.148 .883

Lift 6.609 2.678 .109 2.468 .016

5 (Constant) -701.500 287.700 -2.438 .017

Steel -.002 .002 -.047 -1.148 .255

Cement .297 .372 .034 .799 .427

Sand .207 .118 .193 1.755 .084




Model

Unstandardized

Coefficients

Standardized

Coefficients


Paint 1.465 .385 .265 3.808 .000

Mason 2.450 1.980 .343 1.237 .220

Helper 1.245 1.455 .175 .856 .395

Duration -4.780 1.772 -.123 -2.697 .009

Corner 22.499 16.668 .044 1.350 .182

Rd_1 -.875 .599 -.050 -1.462 .148

Pile -6.480 16.039 -.013 -.404 .687

Dual 7.834 23.539 .011 .333 .740

Lobby -.079 .099 -.029 -.796 .429

Toilet -1.372 1.668 -.030 -.823 .414

Stair -15.126 7.637 -.069 -1.981 .052

Concrete .024 .022 .038 1.118 .267

Steel_Grade 1.362 1.635 .033 .833 .408

Transformer -.017 .083 -.008 -.202 .840

Lift 6.452 2.441 .107 2.643 .010

6 (Constant) -689.966 280.039 -2.464 .016

Steel -.002 .002 -.047 -1.163 .249

Cement .296 .370 .034 .802 .426

Sand .205 .117 .192 1.757 .083

Paint 1.466 .382 .265 3.839 .000

Mason 2.444 1.966 .342 1.243 .218

Helper 1.259 1.443 .177 .873 .386

Duration -4.811 1.753 -.124 -2.745 .008

Corner 22.541 16.551 .044 1.362 .178

Rd_1 -.876 .594 -.050 -1.473 .145

Pile -6.478 15.927 -.013 -.407 .685

Dual 7.453 23.300 .010 .320 .750

Lobby -.082 .098 -.030 -.839 .404

Toilet -1.467 1.590 -.032 -.922 .360

Stair -15.115 7.584 -.069 -1.993 .050

Concrete .023 .021 .037 1.108 .272

Steel_Grade 1.221 1.469 .030 .831 .409

Lift 6.438 2.423 .107 2.657 .010




Model

Unstandardized

Coefficients

Standardized

Coefficients


7 (Constant) -694.043 277.949 -2.497 .015

Steel -.002 .002 -.048 -1.182 .241

Cement .292 .367 .033 .795 .429

Sand .209 .115 .195 1.808 .075

Paint 1.473 .379 .267 3.890 .000

Mason 2.408 1.951 .337 1.235 .221

Helper 1.283 1.432 .181 .896 .373

Duration -4.817 1.742 -.124 -2.766 .007

Corner 22.343 16.433 .043 1.360 .178

Rd_1 -.892 .588 -.050 -1.516 .134

Pile -5.689 15.634 -.012 -.364 .717

Lobby -.081 .097 -.029 -.832 .408

Toilet -1.510 1.574 -.033 -.959 .341

Stair -15.100 7.535 -.069 -2.004 .049

Concrete .024 .021 .039 1.176 .244

Steel_Grade 1.256 1.455 .030 .864 .391

Lift 6.284 2.359 .104 2.663 .010

8 (Constant) -697.270 276.105 -2.525 .014

Steel -.002 .002 -.047 -1.172 .245

Cement .315 .359 .036 .878 .383

Sand .211 .115 .197 1.838 .070

Paint 1.471 .376 .266 3.908 .000

Mason 2.353 1.933 .329 1.217 .228

Helper 1.325 1.418 .187 .935 .353

Duration -4.815 1.731 -.124 -2.782 .007

Corner 22.161 16.324 .043 1.358 .179

Rd_1 -.845 .571 -.048 -1.481 .143

Lobby -.082 .096 -.030 -.851 .398

Toilet -1.559 1.559 -.034 -1.000 .321

Stair -14.764 7.432 -.068 -1.987 .051

Concrete .025 .020 .040 1.227 .224

Steel_Grade 1.163 1.423 .028 .817 .417

Lift 6.238 2.341 .103 2.664 .010




Model

Unstandardized

Coefficients

Standardized

Coefficients


9 (Constant) -617.886 257.843 -2.396 .019

Steel -.002 .002 -.051 -1.267 .209

Cement .328 .358 .037 .915 .363

Sand .231 .112 .216 2.073 .042

Paint 1.402 .366 .254 3.831 .000

Mason 2.420 1.926 .339 1.256 .213

Helper 1.199 1.406 .169 .852 .397

Duration -4.688 1.720 -.121 -2.726 .008

Corner 23.405 16.216 .045 1.443 .153

Rd_1 -.773 .563 -.044 -1.375 .173

Lobby -.078 .096 -.028 -.811 .420

Toilet -1.637 1.552 -.036 -1.055 .295

Stair -14.903 7.413 -.068 -2.010 .048

Concrete .029 .020 .047 1.494 .140

Lift 6.253 2.336 .103 2.677 .009

10 (Constant) -616.824 257.234 -2.398 .019

Steel -.002 .002 -.050 -1.247 .216

Cement .304 .356 .034 .854 .396

Sand .219 .110 .205 1.989 .050

Paint 1.430 .363 .259 3.936 .000

Mason 2.386 1.921 .334 1.242 .218

Helper 1.273 1.400 .179 .909 .366

Duration -4.991 1.675 -.128 -2.979 .004

Corner 23.629 16.175 .046 1.461 .148

Rd_1 -.696 .553 -.039 -1.258 .212

Toilet -1.885 1.518 -.041 -1.242 .218

Stair -14.642 7.388 -.067 -1.982 .051

Concrete .028 .020 .045 1.435 .155

Lift 5.856 2.279 .097 2.570 .012

11 (Constant) -516.099 228.154 -2.262 .027

Steel -.002 .002 -.047 -1.183 .241

Sand .245 .106 .229 2.314 .023

Paint 1.447 .362 .262 3.996 .000




Model

Unstandardized

Coefficients

Standardized

Coefficients


Mason 2.040 1.875 .286 1.088 .280

Helper 1.598 1.345 .225 1.188 .239

Duration -5.052 1.671 -.130 -3.024 .003

Corner 24.668 16.100 .048 1.532 .130

Rd_1 -.746 .549 -.042 -1.359 .178

Toilet -1.766 1.509 -.038 -1.171 .246

Stair -16.067 7.184 -.074 -2.236 .028

Concrete .028 .020 .045 1.438 .155

Lift 5.876 2.275 .097 2.583 .012

12 (Constant) -393.011 198.378 -1.981 .051

Steel -.002 .002 -.041 -1.050 .297

Sand .329 .072 .308 4.548 .000

Paint 1.582 .341 .286 4.645 .000

Helper 3.009 .357 .424 8.431 .000

Duration -5.427 1.636 -.140 -3.316 .001

Corner 26.766 16.003 .052 1.673 .099

Rd_1 -.748 .550 -.042 -1.361 .178

Toilet -1.611 1.504 -.035 -1.071 .288

Stair -16.711 7.169 -.077 -2.331 .022

Concrete .025 .019 .040 1.291 .201

Lift 5.563 2.259 .092 2.462 .016

13 (Constant) -451.938 190.401 -2.374 .020

Sand .327 .072 .306 4.516 .000

Paint 1.557 .340 .282 4.579 .000

Helper 2.884 .337 .406 8.568 .000

Duration -5.176 1.620 -.133 -3.195 .002

Corner 26.483 16.012 .051 1.654 .102

Rd_1 -.679 .546 -.038 -1.244 .217

Toilet -1.414 1.493 -.031 -.947 .347

Stair -15.587 7.093 -.072 -2.198 .031

Concrete .025 .019 .040 1.295 .199

Lift 5.419 2.256 .090 2.401 .019

14 (Constant) -510.673 179.891 -2.839 .006




Model

Unstandardized

Coefficients

Standardized

Coefficients


Sand .325 .072 .304 4.487 .000

Paint 1.611 .335 .292 4.808 .000

Helper 2.929 .333 .412 8.795 .000

Duration -5.252 1.617 -.135 -3.248 .002

Corner 29.556 15.669 .057 1.886 .063

Rd_1 -.615 .542 -.035 -1.136 .260

Stair -16.048 7.072 -.074 -2.269 .026

Concrete .028 .019 .044 1.455 .150

Lift 4.849 2.173 .080 2.231 .029

15 (Constant) -565.358 173.649 -3.256 .002

Sand .315 .072 .295 4.379 .000

Paint 1.663 .333 .301 4.999 .000

Helper 2.945 .333 .415 8.837 .000

Duration -5.331 1.618 -.137 -3.294 .001

Corner 26.804 15.509 .052 1.728 .088

Stair -15.319 7.055 -.070 -2.171 .033

Concrete .030 .019 .048 1.591 .116

Lift 5.000 2.173 .083 2.301 .024

16 (Constant) -426.612 151.608 -2.814 .006

Sand .319 .073 .299 4.394 .000

Paint 1.604 .334 .290 4.806 .000

Helper 2.913 .336 .410 8.673 .000

Duration -5.205 1.632 -.134 -3.189 .002

Corner 24.494 15.590 .047 1.571 .120

Stair -16.286 7.097 -.075 -2.295 .024

Lift 5.629 2.157 .093 2.609 .011

17 (Constant) -375.692 149.456 -2.514 .014

Sand .338 .072 .316 4.673 .000

Paint 1.508 .331 .273 4.555 .000

Helper 2.884 .338 .406 8.521 .000

Duration -5.011 1.642 -.129 -3.052 .003

Stair -15.577 7.147 -.072 -2.179 .032

Lift 5.530 2.176 .091 2.541 .013










formulate a new model. Referring to Table 4.82, we observe that, the value of R2

ranges from 0.939 to 0.929 and Adjusted R2 from 0.919 and 0.924. There is

considerable change between R2 and Adjusted R2 in first model but decreases in the

last model which is a good sign. However, the model can explain 93.9% to 92,9% of

the variability with the 19 models. The Standard Error (SE) ranges from 639.336 to

66.991 which are very good. Referring to Table 4.83, F varies from 45.071 to 175.123

at 0.000 level of significance, which means all the models are overall statistically

significant below 5% level. If we see Table 4.84 we find that out of 17 models last

one is valid as all the variables are individually statistically significant (by "T" stat) at

or below 5% level. In this model total 7 IV were included where all are statistically

significant below 5% level. But when the question of practical significance comes the

condition was not met in the best model.





and Carpenter)






Table 4.86: Model Summary (Backward Elimination-6)


1 .965 .932 .912 72.229

2 .965 .932 .913 71.689

3 .965 .932 .914 71.178

4 .965 .932 .915 70.680

5 .965 .932 .916 70.220

6 .965 .932 .917 69.791

7 .965 .932 .918 69.371

8 .965 .932 .919 68.984

9 .965 .931 .920 68.603

10 .965 .931 .921 68.296

11 .965 .930 .921 68.213

12 .964 .929 .921 68.229

13 .963 .928 .921 68.341

14 .963 .927 .921 68.413

15 .962 .925 .920 68.767

16 .961 .924 .919 69.147

Table 4.87: ANOVA (Backward Elimination-6)


1 Regression 4730219.875 20 236510.994 45.335 .000

Residual 344323.045 66 5217.016

Total 5074542.920 86

2 Regression 4730204.724 19 248958.143 48.441 .000

Residual 344338.196 67 5139.376

Total 5074542.920 86

3 Regression 4730031.516 18 262779.529 51.868 .000

Residual 344511.404 68 5066.344

Total 5074542.920 86

4 Regression 4729846.673 17 278226.275 55.694 .000

Residual 344696.247 69 4995.598

Total 5074542.920 86

5 Regression 4729383.649 16 295586.478 59.946 .000





Residual 345159.270 70 4930.847

Total 5074542.920 86

6 Regression 4728719.782 15 315247.985 64.723 .000

Residual 345823.138 71 4870.748

Total 5074542.920 86

7 Regression 4728050.097 14 337717.864 70.177 .000

Residual 346492.823 72 4812.400

Total 5074542.920 86

8 Regression 4727154.215 13 363627.247 76.412 .000

Residual 347388.704 73 4758.749

Total 5074542.920 86

9 Regression 4726275.624 12 393856.302 83.687 .000

Residual 348267.296 74 4706.315

Total 5074542.920 86

10 Regression 4724721.158 11 429520.105 92.087 .000

Residual 349821.761 75 4664.290

Total 5074542.920 86

11 Regression 4720915.523 10 472091.552 101.460 .000

Residual 353627.397 76 4652.992

Total 5074542.920 86

12 Regression 4716095.843 9 524010.649 112.566 .000

Residual 358447.076 77 4655.157

Total 5074542.920 86

13 Regression 4710249.582 8 588781.198 126.066 .000

Residual 364293.338 78 4670.427

Total 5074542.920 86

14 Regression 4704791.019 7 672113.003 143.601 .000

Residual 369751.901 79 4680.404

Total 5074542.920 86

15 Regression 4696235.300 6 782705.883 165.517 .000

Residual 378307.620 80 4728.845

Total 5074542.920 86

16 Regression 4687251.821 5 937450.364 196.063 .000

Residual 387291.098 81 4781.372

Total 5074542.920 86




Table 4.88: Coefficients (Backward Elimination-6)

Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -755.342 341.832 -2.210 .031

Steel -.002 .002 -.041 -.853 .397

Cement .475 .401 .054 1.187 .240

Sand .248 .137 .232 1.811 .075

Paint .856 .363 .155 2.358 .021

Mason 3.692 2.196 .517 1.681 .097

Helper .547 1.617 .077 .338 .736

Corner 18.980 31.036 .037 .612 .543

Rd_1 -.704 .804 -.040 -.876 .384

Rd_2 -.183 1.014 -.013 -.180 .858

Pile -4.028 17.804 -.008 -.226 .822

Dual 10.634 25.820 .015 .412 .682

Area -.275 5.094 -.004 -.054 .957

Story -3.134 6.978 -.021 -.449 .655

Lobby -.108 .115 -.039 -.938 .352

Toilet -1.456 2.238 -.032 -.651 .517

Concrete .028 .024 .044 1.148 .255

Steel_Grade 1.260 1.906 .031 .661 .511

Transformer -.033 .096 -.015 -.337 .737

Generator -.031 .185 -.007 -.171 .865

Lift 5.930 2.990 .098 1.983 .052

2 (Constant) -763.693 302.408 -2.525 .014

Steel -.002 .002 -.040 -.869 .388

Cement .475 .397 .054 1.194 .237

Sand .245 .124 .230 1.976 .052

Paint .863 .338 .156 2.554 .013

Mason 3.728 2.075 .522 1.797 .077

Helper .522 1.538 .073 .339 .735

Corner 19.042 30.783 .037 .619 .538

Rd_1 -.699 .793 -.040 -.882 .381

Rd_2 -.185 1.005 -.013 -.184 .855




Model

Unstandardized

Coefficients

Standardized

Coefficients


Pile -4.113 17.602 -.008 -.234 .816

Dual 10.746 25.545 .015 .421 .675

Story -3.247 6.606 -.022 -.491 .625

Lobby -.110 .106 -.040 -1.037 .303

Toilet -1.529 1.769 -.033 -.864 .390

Concrete .027 .023 .044 1.169 .246

Steel_Grade 1.297 1.766 .031 .734 .465

Transformer -.034 .089 -.016 -.385 .702

Generator -.034 .179 -.007 -.188 .851

Lift 5.891 2.878 .097 2.047 .045

3 (Constant) -764.954 300.174 -2.548 .013

Steel -.001 .002 -.038 -.857 .394

Cement .457 .383 .052 1.194 .237

Sand .248 .122 .232 2.030 .046

Paint .869 .334 .157 2.604 .011

Mason 3.685 2.047 .516 1.800 .076

Helper .549 1.520 .077 .361 .719

Corner 14.473 17.984 .028 .805 .424

Rd_1 -.786 .633 -.044 -1.242 .218

Pile -4.879 16.978 -.010 -.287 .775

Dual 10.733 25.362 .015 .423 .673

Story -3.300 6.553 -.022 -.504 .616

Lobby -.110 .105 -.040 -1.047 .299

Toilet -1.524 1.756 -.033 -.868 .388

Concrete .028 .023 .045 1.233 .222

Steel_Grade 1.324 1.748 .032 .758 .451

Transformer -.032 .088 -.015 -.363 .717

Generator -.034 .178 -.007 -.191 .849

Lift 5.904 2.857 .098 2.067 .043

4 (Constant) -762.215 297.731 -2.560 .013

Steel -.001 .002 -.037 -.854 .396

Cement .456 .380 .052 1.200 .234

Sand .247 .121 .231 2.039 .045




Model

Unstandardized

Coefficients

Standardized

Coefficients


Paint .869 .331 .157 2.621 .011

Mason 3.669 2.031 .514 1.807 .075

Helper .567 1.506 .080 .376 .708

Corner 14.392 17.853 .028 .806 .423

Rd_1 -.780 .628 -.044 -1.244 .218

Pile -5.119 16.813 -.010 -.304 .762

Dual 11.025 25.139 .015 .439 .662

Story -3.453 6.458 -.023 -.535 .595

Lobby -.108 .104 -.039 -1.038 .303

Toilet -1.525 1.744 -.033 -.875 .385

Concrete .029 .023 .046 1.273 .207

Steel_Grade 1.286 1.724 .031 .746 .458

Transformer -.032 .087 -.015 -.362 .718

Lift 5.715 2.662 .095 2.147 .035

5 (Constant) -762.917 295.786 -2.579 .012

Steel -.001 .002 -.037 -.844 .402

Cement .472 .374 .054 1.263 .211

Sand .250 .120 .234 2.086 .041

Paint .866 .329 .157 2.631 .010

Mason 3.611 2.009 .506 1.798 .077

Helper .605 1.492 .085 .405 .686

Corner 14.397 17.736 .028 .812 .420

Rd_1 -.749 .615 -.042 -1.218 .227

Dual 9.717 24.608 .013 .395 .694

Story -3.232 6.375 -.022 -.507 .614

Lobby -.110 .103 -.040 -1.068 .289

Toilet -1.567 1.727 -.034 -.907 .368

Concrete .029 .022 .047 1.319 .192

Steel_Grade 1.202 1.691 .029 .711 .479

Transformer -.032 .087 -.015 -.367 .715

Lift 5.633 2.631 .093 2.141 .036

6 (Constant) -740.296 287.521 -2.575 .012

Steel -.001 .002 -.037 -.860 .392




Model

Unstandardized

Coefficients

Standardized

Coefficients


Cement .470 .371 .053 1.264 .210

Sand .248 .119 .232 2.082 .041

Paint .862 .327 .156 2.635 .010

Mason 3.612 1.997 .506 1.809 .075

Helper .624 1.482 .088 .421 .675

Corner 14.404 17.628 .028 .817 .417

Rd_1 -.751 .611 -.043 -1.229 .223

Dual 9.043 24.389 .012 .371 .712

Story -3.290 6.334 -.022 -.519 .605

Lobby -.116 .101 -.042 -1.148 .255

Toilet -1.744 1.649 -.038 -1.058 .294

Concrete .028 .022 .045 1.284 .203

Steel_Grade .932 1.513 .023 .616 .540

Lift 5.608 2.614 .093 2.145 .035

7 (Constant) -743.547 285.661 -2.603 .011

Steel -.001 .002 -.037 -.868 .388

Cement .460 .368 .052 1.250 .215

Sand .253 .118 .237 2.146 .035

Paint .865 .325 .157 2.664 .010

Mason 3.583 1.983 .502 1.807 .075

Helper .635 1.472 .089 .431 .667

Corner 14.444 17.522 .028 .824 .412

Rd_1 -.785 .601 -.044 -1.306 .196

Story -2.896 6.207 -.019 -.467 .642

Lobby -.116 .100 -.042 -1.152 .253

Toilet -1.784 1.635 -.039 -1.091 .279

Concrete .029 .022 .046 1.341 .184

Steel_Grade .980 1.498 .024 .654 .515

Lift 5.381 2.526 .089 2.130 .037

8 (Constant) -798.544 254.217 -3.141 .002

Steel -.002 .002 -.038 -.905 .369

Cement .503 .353 .057 1.428 .158

Sand .220 .089 .206 2.469 .016




Model

Unstandardized

Coefficients

Standardized

Coefficients


Paint .820 .306 .148 2.683 .009

Mason 4.402 .565 .616 7.797 .000

Corner 13.707 17.341 .027 .790 .432

Rd_1 -.779 .597 -.044 -1.304 .196

Story -2.640 6.144 -.018 -.430 .669

Lobby -.117 .100 -.043 -1.179 .242

Toilet -1.868 1.615 -.041 -1.157 .251

Concrete .030 .021 .048 1.416 .161

Steel_Grade .911 1.481 .022 .615 .541

Lift 5.562 2.477 .092 2.245 .028

9 (Constant) -784.381 250.678 -3.129 .003

Steel -.001 .002 -.035 -.836 .406

Cement .497 .350 .056 1.419 .160

Sand .226 .087 .212 2.599 .011

Paint .795 .298 .144 2.665 .009

Mason 4.341 .543 .608 7.991 .000

Corner 15.545 16.712 .030 .930 .355

Rd_1 -.821 .586 -.046 -1.401 .165

Lobby -.126 .097 -.046 -1.305 .196

Toilet -1.828 1.603 -.040 -1.140 .258

Concrete .029 .021 .046 1.375 .173

Steel_Grade .842 1.464 .020 .575 .567

Lift 5.237 2.345 .087 2.233 .029

10 (Constant) -720.789 223.930 -3.219 .002

Steel -.001 .002 -.037 -.903 .369

Cement .502 .349 .057 1.440 .154

Sand .244 .081 .229 3.016 .003

Paint .761 .291 .138 2.614 .011

Mason 4.267 .526 .598 8.120 .000

Corner 16.624 16.532 .032 1.006 .318

Rd_1 -.765 .575 -.043 -1.330 .187

Lobby -.122 .096 -.044 -1.266 .209

Toilet -1.877 1.593 -.041 -1.178 .242




Model

Unstandardized

Coefficients

Standardized

Coefficients


Concrete .032 .020 .051 1.581 .118

Lift 5.230 2.335 .087 2.240 .028

11 (Constant) -756.734 220.099 -3.438 .001

Cement .473 .347 .054 1.363 .177

Sand .247 .081 .231 3.054 .003

Paint .772 .291 .140 2.657 .010

Mason 4.096 .490 .574 8.367 .000

Corner 16.804 16.510 .033 1.018 .312

Rd_1 -.708 .571 -.040 -1.240 .219

Lobby -.118 .096 -.043 -1.232 .222

Toilet -1.683 1.577 -.037 -1.067 .289

Concrete .032 .020 .050 1.570 .121

Lift 5.142 2.330 .085 2.207 .030

12 (Constant) -712.607 215.836 -3.302 .001

Cement .480 .347 .054 1.384 .170

Sand .256 .080 .240 3.185 .002

Paint .722 .286 .131 2.521 .014

Mason 4.054 .488 .568 8.309 .000

Rd_1 -.635 .567 -.036 -1.121 .266

Lobby -.118 .096 -.043 -1.230 .223

Toilet -1.986 1.549 -.043 -1.282 .204

Concrete .029 .020 .047 1.470 .146

Lift 5.299 2.325 .088 2.279 .025

13 (Constant) -789.127 205.086 -3.848 .000

Cement .506 .346 .057 1.460 .148

Sand .243 .080 .227 3.049 .003

Paint .779 .282 .141 2.760 .007

Mason 4.095 .487 .573 8.401 .000

Lobby -.103 .095 -.037 -1.081 .283

Toilet -1.779 1.540 -.039 -1.155 .252

Concrete .032 .020 .051 1.604 .113

Lift 5.249 2.329 .087 2.254 .027

14 (Constant) -773.590 204.801 -3.777 .000




Model

Unstandardized

Coefficients

Standardized

Coefficients


Cement .466 .345 .053 1.352 .180

Sand .231 .079 .217 2.929 .004

Paint .756 .282 .137 2.683 .009

Mason 4.203 .477 .589 8.803 .000

Toilet -2.164 1.500 -.047 -1.443 .153

Concrete .030 .020 .047 1.488 .141

Lift 4.658 2.266 .077 2.055 .043

15 (Constant) -665.344 189.476 -3.511 .001

Sand .243 .079 .227 3.076 .003

Paint .736 .283 .133 2.601 .011

Mason 4.387 .460 .614 9.535 .000

Toilet -2.076 1.507 -.045 -1.378 .172

Concrete .031 .020 .050 1.578 .119

Lift 4.794 2.276 .079 2.107 .038

16 (Constant) -735.373 183.548 -4.006 .000

Sand .243 .079 .227 3.060 .003

Paint .774 .283 .140 2.736 .008

Mason 4.466 .459 .625 9.730 .000

Concrete .035 .020 .055 1.752 .084

Lift 3.907 2.195 .065 1.780 .079


Elimination Method-2 Backward Elimination Method considered 22 independent variables (IV) and entered




formulate a new model. Referring to Table 4.82, the value of R2 ranges from 0.939 to

0.929 and Adjusted R2 from 0.919 and 0.924. There is considerable change between

R2 and Adjusted R2 in first model but decreases in the last model which is a good sign.

However, the model can explain 93.9% to 92,9% of the variability with the 19

models. The Standard Error (SE) ranges from 639.336 to 66.991 which are very good.

Referring to Table 4.83, F varies from 45.071 to 175.123 at 0.000 level of




significance, which means all the models are overall statistically significant below 5%




level. But when the question of practical significance comes the condition was not

met in the best model.





and Carpenter)


20 variables.



1 .965 .931 .911 72.400

2 .965 .931 .912 71.883

3 .965 .931 .914 71.389

4 .965 .931 .915 70.922

5 .965 .931 .916 70.479

6 .965 .930 .917 70.059

7 .964 .930 .918 69.678

8 .964 .930 .919 69.317

9 .964 .930 .919 69.009

10 .964 .929 .920 68.812

11 .964 .929 .920 68.639

12 .963 .927 .920 68.734

13 .962 .926 .920 68.810

14 .962 .925 .919 68.931

15 .961 .923 .918 69.396

16 .960 .921 .917 70.015




Table 4.90: ANOVA


1 Regression 4723349.250 19 248597.329 47.427 .000

Residual 351193.669 67 5241.697

Total 5074542.920 86

2 Regression 4723178.782 18 262398.821 50.782 .000

Residual 351364.137 68 5167.120

Total 5074542.920 86

3 Regression 4722890.947 17 277817.115 54.512 .000

Residual 351651.973 69 5096.405

Total 5074542.920 86

4 Regression 4722449.468 16 295153.092 58.680 .000

Residual 352093.451 70 5029.906

Total 5074542.920 86

5 Regression 4721862.708 15 314790.847 63.372 .000

Residual 352680.212 71 4967.327

Total 5074542.920 86

6 Regression 4721144.078 14 337224.577 68.705 .000

Residual 353398.841 72 4908.317

Total 5074542.920 86

7 Regression 4720124.697 13 363086.515 74.785 .000

Residual 354418.223 73 4855.044

Total 5074542.920 86

8 Regression 4718986.518 12 393248.876 81.845 .000

Residual 355556.402 74 4804.816

Total 5074542.920 86

9 Regression 4717373.347 11 428852.122 90.052 .000

Residual 357169.572 75 4762.261

Total 5074542.920 86

10 Regression 4714680.047 10 471468.005 99.570 .000

Residual 359862.873 76 4735.038

Total 5074542.920 86

11 Regression 4711771.723 9 523530.191 111.122 .000

Residual 362771.196 77 4711.314

Total 5074542.920 86





12 Regression 4706042.381 8 588255.298 124.515 .000

Residual 368500.538 78 4724.366

Total 5074542.920 86

13 Regression 4700488.739 7 671498.391 141.820 .000

Residual 374054.181 79 4734.863

Total 5074542.920 86

14 Regression 4694428.849 6 782404.808 164.667 .000

Residual 380114.070 80 4751.426

Total 5074542.920 86

15 Regression 4684460.508 5 936892.102 194.544 .000

Residual 390082.411 81 4815.832

Total 5074542.920 86

16 Regression 4672571.944 4 1168142.986 238.295 .000

Residual 401970.975 82 4902.085

Total 5074542.920 86


Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -678.958 336.082 -2.020 .047

Steel -.001 .002 -.038 -.794 .430

Cement .489 .401 .055 1.217 .228

Sand .237 .137 .222 1.730 .088

Paint .855 .364 .155 2.347 .022

Mason 3.622 2.201 .507 1.646 .104

Helper .598 1.621 .084 .369 .713

Corner 23.037 30.907 .045 .745 .459

Rd_1 -.694 .806 -.039 -.861 .392

Rd_2 -.402 .998 -.028 -.402 .689

Pile -5.236 17.815 -.011 -.294 .770

Dual 14.098 25.703 .019 .548 .585

Area .902 5.002 .012 .180 .857

Story -2.770 6.987 -.018 -.396 .693

Lobby -.117 .115 -.042 -1.015 .314




Model

Unstandardized

Coefficients

Standardized

Coefficients


Toilet -2.062 2.180 -.045 -.946 .348

Steel_Grade 1.702 1.871 .041 .909 .366

Transformer -.028 .097 -.013 -.285 .777

Generator -.064 .183 -.014 -.349 .728

Lift 6.252 2.984 .103 2.095 .040

2 (Constant) -647.887 286.498 -2.261 .027

Steel -.002 .002 -.040 -.860 .393

Cement .491 .398 .056 1.234 .222

Sand .247 .124 .231 1.986 .051

Paint .831 .338 .150 2.461 .016

Mason 3.496 2.071 .489 1.688 .096

Helper .685 1.536 .096 .446 .657

Corner 22.955 30.683 .044 .748 .457

Rd_1 -.710 .795 -.040 -.894 .375

Rd_2 -.402 .991 -.028 -.406 .686

Pile -4.985 17.633 -.010 -.283 .778

Dual 13.829 25.477 .019 .543 .589

Story -2.372 6.582 -.016 -.360 .720

Lobby -.109 .107 -.040 -1.026 .309

Toilet -1.832 1.755 -.040 -1.044 .300

Steel_Grade 1.590 1.753 .039 .907 .368

Transformer -.021 .089 -.010 -.236 .814

Generator -.057 .178 -.012 -.322 .748

Lift 6.397 2.853 .106 2.242 .028

3 (Constant) -636.260 280.293 -2.270 .026

Steel -.002 .002 -.040 -.863 .391

Cement .486 .395 .055 1.230 .223

Sand .246 .124 .230 1.992 .050

Paint .831 .335 .150 2.476 .016

Mason 3.494 2.057 .489 1.698 .094

Helper .699 1.524 .098 .459 .648

Corner 21.945 30.174 .042 .727 .470

Rd_1 -.729 .786 -.041 -.927 .357




Model

Unstandardized

Coefficients

Standardized

Coefficients


Rd_2 -.360 .968 -.025 -.372 .711

Pile -5.150 17.499 -.011 -.294 .769

Dual 13.318 25.211 .018 .528 .599

Story -2.449 6.528 -.016 -.375 .709

Lobby -.113 .104 -.041 -1.083 .282

Toilet -1.939 1.684 -.042 -1.152 .253

Steel_Grade 1.410 1.568 .034 .899 .372

Generator -.056 .177 -.012 -.317 .752

Lift 6.366 2.831 .105 2.249 .028

4 (Constant) -634.948 278.423 -2.281 .026

Steel -.002 .002 -.040 -.873 .386

Cement .508 .385 .058 1.319 .191

Sand .248 .123 .232 2.024 .047

Paint .825 .333 .149 2.480 .016

Mason 3.454 2.039 .484 1.694 .095

Helper .725 1.512 .102 .480 .633

Corner 23.684 29.397 .046 .806 .423

Rd_1 -.668 .753 -.038 -.887 .378

Rd_2 -.430 .932 -.030 -.462 .646

Dual 12.058 24.682 .017 .489 .627

Story -2.196 6.429 -.015 -.342 .734

Lobby -.116 .103 -.042 -1.117 .268

Toilet -1.988 1.664 -.043 -1.195 .236

Steel_Grade 1.319 1.527 .032 .864 .391

Generator -.060 .175 -.013 -.342 .734

Lift 6.309 2.805 .104 2.249 .028

5 (Constant) -632.630 276.604 -2.287 .025

Steel -.001 .002 -.037 -.829 .410

Cement .504 .382 .057 1.318 .192

Sand .252 .121 .235 2.074 .042

Paint .803 .324 .145 2.476 .016

Mason 3.476 2.025 .487 1.716 .090

Helper .668 1.493 .094 .448 .656




Model

Unstandardized

Coefficients

Standardized

Coefficients


Corner 25.039 28.946 .048 .865 .390

Rd_1 -.707 .740 -.040 -.956 .343

Rd_2 -.424 .926 -.030 -.458 .648

Dual 10.472 24.090 .014 .435 .665

Lobby -.124 .100 -.045 -1.233 .222

Toilet -1.960 1.652 -.043 -1.187 .239

Steel_Grade 1.259 1.507 .031 .835 .406

Generator -.066 .173 -.014 -.380 .705

Lift 6.046 2.681 .100 2.255 .027

6 (Constant) -623.075 273.820 -2.275 .026

Steel -.001 .002 -.036 -.810 .421

Cement .505 .380 .057 1.327 .189

Sand .251 .121 .234 2.078 .041

Paint .797 .322 .144 2.476 .016

Mason 3.436 2.011 .481 1.709 .092

Helper .706 1.481 .099 .476 .635

Corner 25.471 28.751 .049 .886 .379

Rd_1 -.693 .734 -.039 -.943 .349

Rd_2 -.444 .919 -.031 -.483 .630

Dual 10.901 23.920 .015 .456 .650

Lobby -.119 .099 -.043 -1.203 .233

Toilet -1.969 1.642 -.043 -1.199 .234

Steel_Grade 1.186 1.486 .029 .798 .427

Lift 5.654 2.460 .094 2.298 .024

7 (Constant) -623.213 272.330 -2.288 .025

Steel -.001 .002 -.037 -.829 .410

Cement .494 .377 .056 1.309 .195

Sand .256 .119 .239 2.145 .035

Paint .807 .320 .146 2.524 .014

Mason 3.379 1.996 .473 1.693 .095

Helper .743 1.471 .105 .505 .615

Corner 25.051 28.580 .048 .877 .384

Rd_1 -.731 .725 -.041 -1.008 .317




Model

Unstandardized

Coefficients

Standardized

Coefficients


Rd_2 -.442 .914 -.031 -.484 .630

Lobby -.116 .098 -.042 -1.186 .239

Toilet -2.037 1.626 -.044 -1.253 .214

Steel_Grade 1.282 1.463 .031 .876 .384

Lift 5.457 2.409 .090 2.266 .026

8 (Constant) -620.703 270.868 -2.292 .025

Steel -.001 .002 -.030 -.722 .473

Cement .458 .368 .052 1.244 .218

Sand .265 .117 .248 2.261 .027

Paint .820 .317 .148 2.587 .012

Mason 3.223 1.960 .451 1.645 .104

Helper .840 1.449 .118 .579 .564

Corner 13.927 16.912 .027 .823 .413

Rd_1 -.936 .587 -.053 -1.594 .115

Lobby -.116 .098 -.042 -1.188 .239

Toilet -2.029 1.618 -.044 -1.254 .214

Steel_Grade 1.407 1.433 .034 .982 .329

Lift 5.500 2.394 .091 2.297 .024

9 (Constant) -689.454 242.417 -2.844 .006

Steel -.001 .002 -.032 -.777 .440

Cement .517 .352 .059 1.467 .146

Sand .220 .088 .206 2.515 .014

Paint .761 .299 .138 2.546 .013

Mason 4.313 .546 .604 7.899 .000

Corner 12.533 16.666 .024 .752 .454

Rd_1 -.929 .584 -.053 -1.590 .116

Lobby -.117 .097 -.042 -1.202 .233

Toilet -2.165 1.593 -.047 -1.359 .178

Steel_Grade 1.356 1.424 .033 .952 .344

Lift 5.816 2.321 .096 2.506 .014

10 (Constant) -672.420 240.666 -2.794 .007

Steel -.001 .002 -.032 -.784 .436

Cement .520 .351 .059 1.482 .143




Model

Unstandardized

Coefficients

Standardized

Coefficients


Sand .225 .087 .210 2.581 .012

Paint .731 .296 .132 2.475 .016

Mason 4.297 .544 .602 7.897 .000

Rd_1 -.875 .578 -.050 -1.514 .134

Lobby -.118 .097 -.043 -1.218 .227

Toilet -2.362 1.567 -.051 -1.507 .136

Steel_Grade 1.444 1.415 .035 1.020 .311

Lift 5.894 2.312 .098 2.549 .013

11 (Constant) -714.610 233.980 -3.054 .003

Cement .493 .348 .056 1.416 .161

Sand .225 .087 .210 2.587 .012

Paint .746 .294 .135 2.536 .013

Mason 4.158 .513 .582 8.100 .000

Rd_1 -.831 .574 -.047 -1.448 .152

Lobby -.116 .097 -.042 -1.200 .234

Toilet -2.180 1.546 -.047 -1.410 .163

Steel_Grade 1.550 1.405 .038 1.103 .274

Lift 5.806 2.303 .096 2.521 .014

12 (Constant) -570.641 194.440 -2.935 .004

Cement .505 .349 .057 1.446 .152

Sand .260 .081 .243 3.208 .002

Paint .670 .286 .121 2.340 .022

Mason 3.985 .489 .558 8.144 .000

Rd_1 -.729 .567 -.041 -1.286 .202

Lobby -.104 .096 -.038 -1.084 .282

Toilet -2.351 1.540 -.051 -1.526 .131

Lift 5.913 2.305 .098 2.566 .012

13 (Constant) -575.898 194.595 -2.959 .004

Cement .467 .347 .053 1.343 .183

Sand .246 .080 .230 3.074 .003

Paint .658 .286 .119 2.299 .024

Mason 4.104 .477 .575 8.600 .000

Rd_1 -.635 .561 -.036 -1.131 .261




Model

Unstandardized

Coefficients

Standardized

Coefficients


Toilet -2.682 1.511 -.058 -1.775 .080

Lift 5.269 2.229 .087 2.364 .021

14 (Constant) -641.705 186.022 -3.450 .001

Cement .502 .347 .057 1.448 .151

Sand .235 .080 .220 2.953 .004

Paint .715 .283 .129 2.529 .013

Mason 4.120 .478 .577 8.623 .000

Toilet -2.446 1.499 -.053 -1.631 .107

Lift 5.376 2.231 .089 2.409 .018

15 (Constant) -515.533 165.476 -3.115 .003

Sand .248 .080 .232 3.109 .003

Paint .690 .284 .125 2.429 .017

Mason 4.314 .462 .604 9.338 .000

Toilet -2.370 1.509 -.051 -1.571 .120

Lift 5.572 2.242 .092 2.485 .015

16 (Constant) -577.960 162.067 -3.566 .001

Sand .248 .080 .232 3.091 .003

Paint .729 .285 .132 2.554 .012

Mason 4.396 .463 .616 9.495 .000

Lift 4.641 2.182 .077 2.128 .036







formulate a new model. Referring to Table 4.88, the value of R2 ranges from 0.931 to

0.921 and Adjusted R2 from 0.911 and 0.917. There is considerable change between

R2 and Adjusted R2 in first model but decreases in the last model which is a good sign.

However, the model can explain 93.1% to 92.1% of the variability with the 16

models. The Standard Error (SE) ranges from 72.4 to 70.015 which are very good.

Referring to Table 4.89, F varies from 47.427071 to 238.295 at 0.000 level of




significance, which means all the models are overall statistically significant below 5%




level. This model show practical significance. This Model is accepted.


This model is same as stated in paragraph 4.40.2.

4.44 The Final Model

The final model is as follows:

The equation is as follows: (R2=0.921; SE=70.015)

Construction Cost=-577.960 +4.396 x Mason +0.729 x Paint + 0.248 x Sand +

4.641 x Lift

where Construction is (Taka/sft)

Mason= Wage of Mason (Taka/ Day)


Sand= Price of sand (Taka/100 cft)

Lift= Capacity of Lift (Person/ building)




CHAPTER FIVE

EMPERICAL RESULTS

AND DISCUSSIONS




CHAPTER FIVE

EMPERICAL RESULTS AND DISCUSSIONS

5.1 Introduction

This chapter presents the final results of the research work done. It deals with the

final form of the output gathered from three models and analysis of the data by

SPSS-17. I prepared three models to get a different flavour of the work and also to

compare the outputs from three different models. In previous chapter analysis results

were shown at each stages and steps. The statistical inferences were drawn in every

step for each table. This chapter will show descriptive statistics of the variables

finally selected in the models. Testing the assumptions and important hypothesis of

Multiple Linear Regression will also be shown in this chapter. Last but not the least

this chapter will perform validation and sensitivity analysis of the final results for

three models as to give feelings about the degree of precision of the result.

5.2 Boxplot and Identification of Outliers

Before working with the final data we need to check the data for any outliers.

Basically we will check the outliers of dependent variables. Boxplot is a unique

measure of finding outliers easily. In our last chapter we worked with 87 data set.

Figure 5.1: Boxplot of Construction Cost-87 Data




5.2.1 Box plot of 87 Data.

The box plot of dependent variable (Construction Cost) is prepared by SPSS taking 87

data as used in Chapter IV to check the state of outliers. Figure 5.1 above shows that

there are two outliers serial no 102 1nd 103.

Figure 5.2: Boxplot of Construction Cost-85 Data

5.2.1 Box plot of 85 Data

After removing data 102 and 103 we constructed the boxplot again in Figure 5.2. It is

clear from the figure that the data is free from outliers which is one of the basic

assumptions of multiple linear regression,

5.3 Histogram of DV

Figure 5.3 shows the Histogram of Construction Cost to check the normal distribution

of the data after removing the outliers. A histogram shows the frequency of values of

a variable. The size of the bins is determined by default when we create a histogram.

In this histogram, each bin contains two values. For example, the first bin contains

values 1000 and 166.67, the second bin contains 166.67 and 233.33 and so on. The

histogram is a graphical representation of the percentiles that were displayed with

percentiles as given below. The purpose of the histogram is to give an idea about the

distribution of the variable whether normal or not. In our case it is almost normal

distribution.




Figure 5.3: Histogram of Construction Cost

Table 5.1: Descriptive Statistics

N Range Minimum Maximum Mean

Std. Deviation Variance Skewness Kurtosis

Statistic Statistic Statistic Statistic Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error

Construction Cost

85 997 1003 2000 1481.67 222.947 49705.200 .249 .261 -.192 .517

Sand Price 85 926 724 1650 1225.45 220.710 48712.842 -.040 .261 -.195 .517

Paint Price 85 220 547 767 691.54 42.980 1847.241 -.284 .261 .102 .517

Mason Wage 85 147 200 347 276.07 32.655 1066.359 -.390 .261 .238 .517

Plinth Size 85 8300 1500 9800 3593.00 1580.830 2499022.5 1.592 .261 3.619 .517

No of Story 85 7 5 12 7.41 1.635 2.674 .897 .261 -.158 .517

Lift Capacity 85 21 0 21 9.00 3.873 15.000 1.372 .261 1.605 .517

Valid N (listwise)

85




5.4 Descriptive Statistics

Table 5.1 show the final forms of descriptive statistics of the selected variables. Each

of the state is described below:

a. Valid N (list wise): This is the number of non-missing values.

b. N: This is the number of valid observations for the variable. The total

number of observations is the sum of N and the number of missing

values. We do not have any missing value.

c. Minimum: This is the minimum, or smallest, value of the variable.

d. Maximum: This is the maximum, or largest, value of the variable.

e. Mean: This is the arithmetic mean across the observations. It is the most

widely used measure of central tendency. It is commonly called the average.

The mean is sensitive to extremely large or small values.

f. Standard Deviation (Std. Deviation): Standard deviation is the square root of

the variance. It measures the spread of set of observations. The larger the

standard deviation is, the more spread out the observations are.

g. Variance: The variance is a measure of variability. It is the sum of the

squared distances of data value from the mean divided by the variance divisor.

h. Skewness: Skewness measures the degree and direction of asymmetry. A

symmetric distribution such as a normal distribution has a skewness of 0, and

a distribution that is skewed to the left, e.g. when the mean is less than the

median, has a negative skewness.

i. Kurtos: Kurtosis is a measure of the heaviness of the tails of a distribution.

In a normal distribution has kurtosis 0. Extremely non-normal distributions

may have high positive or negative kurtosis values, while nearly normal

distributions will have kurtosis values close to 0. Kurtosis is positive if the

tails are "heavier" than for a normal distribution and negative if the tails are

"lighter" than for a normal distribution.




5.5 Explanation of Result from SPSS Output (Model-1)

This paragraph shows regression analysis with the output. Data was reduced to 85

from 87 for presence of outliers as explained in paragraph 5.2. Hence, the final model

was prepared on 85 Data collected from different developer of Dhaka city. In model-1

we considered the 9 independent variables (IV) which have direct cost impact. The

variables are materials cost of 5 construction materials (Steel, Cement, Sand, Brick

and Paint) and daily wage of 3 types of labour (Mason, Helper and Painter) and the

cost of Transportation. The dependent variable (DV)was Construction Cost per

square feet. The SPSS-17 was used as tools of analysis and SPSS automated output

give some tables and figures. This paragraph will explain these.

Table 5.2: Model Summary (Model-1)

Model

R R Square Adjusted R

Square Std. Error of the Estimate Durbin-Watson

1 .958 .917 .914 65.461 .659

5.5.1 Model Summary (Model-1).

The model summary table displays the followings:

i. Multiple Correlation Coefficient (Model-1)

R, the multiple correlation coefficient, is a measure of the strength of the

linear relationship between the response variable and the set of explanatory

variables. It is the highest possible simple correlation between the response

variable and any linear combination of the explanatory variables. For simple

linear regression where we have just two variables, this is the same as the

absolute value of the Pearson's correlation coefficient. However, in multiple

regression this allows us to measure the correlation involving the response

variable and more than one explanatory variable. We have R value 0.958 in

model-1which is very good as stated in Table 5.2.




ii. Proportion of Variation (Model-1)

R squared (R2) is the proportion of variation in the response variable explained

by the regression model. The values of R2 range from 0 to 1; small values

indicate that the model does not fit the data well and vice-versa. From the

above table (Table 5.2) we can see that the model fits the data reasonably well;

91.7% of the variation in the Construction Cost can be explained by the fitted

line together with the three IV (Sand, Mason and Paint) only. Other six data

did not response well with this model. R2 is also known as the coefficient of

determination. The R2 value can be over optimistic in its estimate of how well

a model fits the population; the adjusted R2 is attempts to correct for this. Here

we can see it has slightly reduced the estimated proportion. If we have a small

data set it may be worth reporting the adjusted R squared value. We have

Adjusted R2 value 0.914 which is almost near to R2.

. iii. Standard Error of the Estimate (Model-1)

The standard error of the estimate (SE) also called the root mean square error

is the estimate of the standard deviation of the error term of the model, ε and is

the square root of the Mean Square Residual (or Error).. This gives us an idea

of the expected variability of predictions and is used in calculation of

confidence intervals and significance tests.

iv. Durbin Watson Statistics (Model-1)

If the value of Durbin Watson is close to 0 (zero), it indicates strong positive

serial correlation and if same is close to 4 (four), it indicates strong negative

serial correlation. As a guideline statisticians use the value to be within the

range of 1.5 to 2.5, which means no autocorrelation exist. We have Durbin

Watson Statistics 0.659 which means our data have tendency of positive auto

correlation. But this value is not the absolute proof of auto correlation rather

we can depend on Normal P-P Plot of Standardized Residual Plot in Figure

5.5. This will be explained in this chapter separately.




Table 5.3: ANOVA (Model-1)

Model

Sum of


1 Regression 3828135.749 3 1276045.250 297.780 .000

Residual 347101.028 81 4285.198

Total 4175236.776 84

5.5.2 Analysis of Variance

The Analysis of Variance table is also known as the ANOVA table. It tells the story

of how regression equation accounts for variability in the response variable. Model of

SPSS allows us to specify multiple models in a single regression command. This tells

us the number of the model being reported. This multiple models were discussed in

previous chapter. This chapter will discuss only final results. Hence, in this chapter

we have shown only single (final) model. The significance of the value of Analysis of

Variance (ANOVA) is discussed below:

i. Sum of Square: This is the source of variance, Regression, Residual

and Total. The Total variance is partitioned into the variance which can be

explained by the independent variables (Regression) and the variance which is

not explained by the independent variables (Residual, sometimes called Error

Terms). Note that the Sums of Squares for the Regression and Residual add up

to the Total, reflecting the fact that the Total is partitioned into Regression and

Residual variance. Sum of Squares are the Sum of Squares associated with the

three sources of variance, Total, Model and Residual. These can be computed

in many ways.




ii. Degree of Freedom: Degree of Freedom (df) are the degrees of

freedom associated with the sources of variance. df1= k-1, k=numbers of

parameter (β0, β1…………..βn) ; df-2= N-(k+1)

(Since there were 3 independent variables in the model parameter will be 4;

k=4 and df1=k-1=4-1=3.[The intercept is automatically included in the model

(unless explicitly omit the intercept). Including the intercept, there are 4

predictors. The Residual degrees of freedom is the df2=85-4=81.

iii. Mean Squares: Mean Square are the Mean Squares, the Sum of

Squares divided by their respective df. For the Regression, Mean Square is

3828135.749/3=1276045.250 and for Residual, the value is

347101.028/81=4285.198

iv. F and Sig.: F and Sig.: The F value is the Mean Square Regression

(1276045.250) divided by the Mean Square Residual (4285.198), yielding

F=297.780. The p value associated with this F value is very small (0.0000).

These values are used to answer the question "Do the independent variables

reliably predict the dependent variable?" The "p" may be called probability

value is compared to type I error, i.e., level (typically 0.05) of significance

and, if smaller, we can conclude "Yes, the independent variables reliably

predict the dependent variable". We could say that the group of variables

Sand, Paint and Mason were used to reliably predict the Construction Cost of

the building (the dependent variable). If the p value were greater than 0.05, we

would say that the group of independent variables does not show a statistically

significant relationship with the dependent variable, or that the group of

independent variables does not reliably predict the dependent variable. Note

that this is an overall significance test assessing whether the group of

independent variables when used together reliably predict the dependent

variable, and does not address the ability of any of the particular independent

variables to predict the dependent variable. The ability of each individual




independent variable to predict the dependent variable is addressed in the table

below, the "Coefficient" where each of the individual variables is listed.

Table 5.4: Coefficients (Model-1)

Model

Unstandardized

Coefficients

Standardized

Coefficients Collinearity

Statistics

B

Std.

Error Beta t Sig. Tolerance VIF

1 (Constant) -574.830 145.814 -3.942 .000

Sand .251 .075 .248 3.340 .001 .186 5.387

Paint .864 .250 .167 3.451 .001 .440 2.272

Mason 4.170 .437 .611 9.537 .000 .250 3.997

5.5.3 Coefficients (Model-1)

This column shows the predictor variables (Constant, Sand, Mason and Paint). The

first variable (constant) represents the constant, also referred to in textbooks as the Y

intercept, the height of the regression line when it crosses the Y axis. In other words,

this is the predicted value of Construction Cost when all other variables are 0.

i. B is the value for the regression equation for predicting the dependent

variable from the independent variable. These are called unstandardized

coefficients because they are measured in their natural units. As such, the

coefficients cannot be compared with one another to determine which one is

more influential in the model, because they can be measured on different

scales. For example, how can you compare the values for Sand with the values

for Mason? The regression equation can be presented in many different ways,

for example:

Y predicted = β0 + β1*x1 + β2*x2 + β3*x3




The column of estimates (coefficients or parameter estimates, from here on

labeled coefficients) provides the values for β0, β1, β2, β3 for this equation.

Expressed in terms of the variables used in this example, the regression

equation is

Construction Cost = -574.830 + 0.251*Sand + 0.864*Paint + 4.170*Mason

These estimates tell us about the relationship between the independent

variables and the dependent variable. These estimates tell the amount of

increase in Construction Cost that would be predicted by a 1 unit increase in

the predictor. Note: For the independent variables which are not significant,

the coefficients are not significantly different from 0, which should be taken

into account when interpreting the coefficients. (See the columns with the "t"

value and "p" value about testing whether the coefficients are significant).

"Sand" The coefficient (parameter estimate) is 0.251. So, for every unit

increase in Sand, a 0.251unit increase in Construction Cost predicted, holding

all other variables constant. (It does not matter at what value we hold the other

variables constant, because it is a linear model.) Or, for every increase of one

point on the Sand, Construction Cost is predicted to be higher by 0.251points.

This is significantly different from 0.001

Similarly for every unit increase of Paint there is a 0.864 unit increase in the

predicted construction Cost. Similarly for every unit of increase of Mason

4.170 unit will increase in Construction Cost. All the variables are statistically

significant because the "p" value is less than 0.050.

ii. Std. Error are the standard errors associated with the coefficients. The

standard error is used for testing whether the parameter is significantly

different from 0 by dividing the parameter estimate by the standard error to

obtain a "t" value (see the column with "t" values and "p" values). The

standard errors can also be used to form a confidence interval for the

parameter, as shown in the last two columns of this table.

iii. Beta is the standardized coefficients. These are the coefficients that we

would obtain if we standardized all of the variables in the regression,

including the dependent and all of the independent variables, and ran the




regression. By standardizing the variables before running the regression, we

have put all of the variables on the same scale, and then we can compare the

magnitude of the coefficients to see which one has more of an effect. It is to be

noticed that the larger betas are associated with the larger "t" values.

iv. "t" and Sig. columns provide the "t" value and 2 tailed "p" value used

in testing the null hypothesis that the coefficient/parameter is 0. If we use a 2

tailed test, then we would compare each "p" value to our preselected value of

alpha. Coefficients having "p" values less than alpha are statistically

significant. For example, if we chose alpha to be 0.05, coefficients having a

"p" value of 0.05 or less would be statistically significant (i.e., we can reject

the null hypothesis and say that the coefficient is significantly different from

0). If we use a 1 tailed test (i.e., we predict that the parameter will go in a

particular direction), then we can divide the "p" value by 2 before comparing it

to our preselected alpha level. With a 2 tailed test and alpha of 0.05. In our

case all "p" value is less than 0.050. All the coefficients are statistically

significant because their "p" value of 0.000 is less than .05.

The equation of the model is

Construction Cost= - 574.83-0.251*Sand+0.864*Paint+4.17*Mason.

Where;

Construction Cost is in Taka/sft

Sand= Price of Sand (Taka/100 cft)

Paint=Price of Paint (Taka/Gallon) and





5.5.4 Collinearity Statistics

VIF and Tolerance are the two popular means of measuring Collinearity Statistics.

i. Tolerance Commonly used measure of collinearity and

multicollinearity. Tolerance values approaching zero indicate that the variable

is highly predicted (collinear) with the other predictor variables. Its limit is

0.1. If its value is less than 0.1 we can say that the variables are collinear. Our

all values are within limit.

ii. Variance inflation factor (VIF) measure of the effect of other

predictor variables on a regression coefficient. VIF is inversely related to the

tolerance value (VIF = 1 ÷ TOL). The VIF reflects the extent to which the

standard error of the regression coefficient is increased due to

multicollinearity. Large VIF values (a usual threshold is 10.0, which

corresponds to a tolerance of 0.10) indicate a high degree of collinearity or

multicollinearity among the independent variables, although sometimes values

of as high as four have been considered problematic. We have maximum value

5.387 which is less than 10. Our values are less than 10. There are less

possibilities of Multicollinearity.

Table 5.5: Residuals Statistics (Model-1)

Minimum Maximum Mean

Std. Deviation N

Predicted Value 916.45 1950.41 1481.67 213.478 85

Std. Predicted Value -2.648 2.196 .000 1.000 85

Standard Error of Predicted Value

9.977 26.084 13.790 3.410 85

Adjusted Predicted Value 900.20 1946.59 1481.27 214.235 85

Residual -120.871 191.959 .000 64.282 85

Std. Residual -1.846 2.932 .000 .982 85

Stud. Residual -1.874 3.011 .003 1.007 85

Deleted Residual -124.481 202.403 .400 67.629 85

Stud. Deleted Residual -1.904 3.175 .007 1.023 85

Mahal. Distance .963 12.348 2.965 2.173 85

Cook's Distance .000 0.123 .013 .024 85

Centered Leverage Value .011 0.147 .035 .026 85




5.5.5 Residual Statistics

This paragraph will explain the inference about the residual statistics. We will discuss

some more terms to assist in depth understanding of the terms given in Table 5.5.

i. Observed Value: The observed value for the dependent variable.

ii. Predicted Value: The predicted value given the current regression

equation.

iii. Standard Predicted Value: The standardized predicted value of the

dependent variable.

iv. Standard Error of Predicted Value: The standard error of the

unstandardized predicted value.

v. Residual Value: The observed value minus the predicted value.

vi. Standard Residual Value: The standardized residual value (observed

minus predicted divided by the square root of the residual mean square). . It is

usual practice to consider standardized residuals due to their ease of

interpretation. For instance outliers (observations that do not appear to fit the

model that well) can be identified as those observations with standardized

residual values above 3.3 (or less than -3.3). From the above we can see that

we do not appear to have any outliers.

vii. Studentized Residual: Most commonly used form of standardized

residual. It differs from other standardization methods in calculating the

standard deviation employed. To minimize the effect of a single outlier, the

standard deviation of residuals used to standardize the ith residual is computed

from regression estimates omitting the ith observation. This is done repeatedly

for each observation, each time omitting that observation from the

calculations. This approach is similar to the deleted residual, although in this

situation the observation is omitted from the calculation of the standard

deviation.




viii. Deleted Residual: The deleted residual is the residual value for the

respective case, had it not been included in the regression analysis, that is, if

one would exclude this case from all computations. If the deleted residual

differs greatly from the respective standardized residual value, then this case is

possibly an outlier because its exclusion changed the regression equation.

Process of calculating residuals in which the influence of each

observation is removed when calculating its residual. This is accomplished by

omitting the ith observation from the regression equation used to calculate its

predicted value.

ix. Studentized Deleted Residuals: As a further check that the fit is good,

note from the Residuals Statistics part of the regression output that all of the

studentized deleted residuals have a magnitude less than 1.9, which is an

indication that the error term distribution does not have heavy tails.

x. Cook's Distance: This is another measure of the impact of the

respective case on the regression equation. It indicates the difference

between the computed B values and the values one would have obtained, had

the respective case been excluded. All distances should be of about equal

magnitude; if not, then there is reason to believe that the respective case(s)

biased the estimation of the regression coefficients. Cook’s distance is

considered to be the single most representative measure of influence on

overall fit. It captures the impact of an observation from two sources: the size

of changes in the predicted values when the case is omitted (outlying

studentized residuals) as well as the observation’s distance from the other

observations (leverage). A rule of thumb is to identify observations with a

Cook’s distance of 1.0 or greater, although the threshold of 4/(n – k ‐ 1), where

n is the sample size and k is the number of independent variables, is suggested

as a more conservative measure in small samples or for use with larger data

sets. Even if no observation exceed this threshold, however, additional

attention is dictated if a small set of observations has substantially higher

values than the remaining observations. It is the summary measure of the

influence of a single case (observation) based on the total changes in all other

residuals when the case is deleted from the estimation process. Large values

(usually greater than 1) indicate substantial influence by the case in affecting




the estimated regression coefficients. For each of these, the usual "cutoff" is

1.0. Cases with values larger than 1.0 are "suspected of being outliers". The

Cook's distance statistic is a good way of identifying cases which may be

having an undue influence on the overall model. Cases where the Cook's

distance is greater than 1 may be problematic.

xi. Mahalanobis Distance: One can think of the independent variables (in t

he equation) as defining a multidimensional space in which each observation

can be plotted. Also, one can plot a point representing the means for all

independent variables. This "mean point" in the multidimensional space is also

called the centroid. The Mahalanobis distance is the distance of a case from

the centroid in the multidimensional space, defined by the correlated

independent variables (if the independent variables are uncorrelated, it is the

same as the simple Euclidean distance). Thus, this measure provides an

indication of whether or not an observation is an outlier with respect to the

independent variable values.

xii. Leverage Point: An observation that has substantial impact on the

regression results due to its differences from other observations on one or

more of the independent variables. The most common measure of a leverage

point is the hat value, contained in the hat matrix.

xiii. Note (Remedies for Outliers): The purpose of all of these statistics is to

identify outliers. Remember that particularly with small N (less than 100),

multiple regression estimates (the B coefficients) are not very stable. In other

words, single extreme observations can greatly influence the final estimates.

Therefore, it is advisable always to review these statistics (using these or the

following options), and to repeat crucial analyses after discarding any outliers.

Another alternative is to repeat crucial analysis using absolute deviations

rather than least squares regression, thereby "dampening" the effect of outliers.

You can use Nonlinear Estimation to estimate such models.




5.6 Histogram of Residuals (Model-1)

The above plot is a check on normality; the histogram should appear normal; a fitted

normal distribution aids us in our consideration. Serious departures would suggest that

normality assumption is not met. Here we have a slight suggestion of positive

skewness but considering we have only 85 data points we have no real cause for

concern.

Figure 5.4: Histogram of Residuals (Model-1)




Figure 5.5: Normal P-P Plot of Standardized Residual (Model-1)

5.7 Normal P-P Plot of Standardized Residual (Model-1)

The plot in Figure 5.5 is a check on normality; the plotted points should follow the

straight line. Serious departures would suggest that normality assumption is not met.

There is no major cause for concern. The residual should plot approximately diagonal

straight line on the plot. When sample size is small (we have only 85 sample) the line

may be jagged. The next plot shown below is a cumulative probability plot of

standardized residuals. If all the points lies on the diagonal, it means the residual are

normally distributed.




Figure 5.6: Scattered Plot of Standardized Residual vs. Standardized Predicted Value (Model-1)

5.8 Scatter Plot of Standardized Residuals (Model-1)

Plot in figure 5.6 is the scatter plot of standardized residuals against predicted values

should be a random pattern centered around the line of zero standard residual value.

The points should have the same dispersion about this line over the predicted value

range. From the above we can see no clear relationship between the residuals and the

predicted values which is consistent with the assumption of Homoscedasticity of

Variance. The dispersion of residuals over the predicted value range spreaded over the

graph, no systematic pattern is formed. There are a few points only to provide

evidence against a change in variability. So we can say, Residual are Homoscedastic,

not Heteroscedastic.




5.9 Validation of Model-1

The manner in which regression weights (parameter) are computed guarantee that

they will provide an optimal fit with respect to the least square criterion for the

existing set of data. If a statistician wishes to predict a different set of data, the

regression weights are no longer optimal. There will be substantial shrinkage in the

value of R2 if the weights estimated on one set of data are used on a second set of

data. The amount of shrinkage can be estimated using a cross validation procedure. In

cross validation, regression weights are estimated using one set of data and are tested

on a second set of data. If the regression weights estimated on the first set of data

predict the second set of data, the weights are said to be cross validated. If the new

data is successfully predicted using old regression weights, the regression procedure is

said to be cross validated. It is expected that the accuracy of prediction will not be as

good for the second set of data. This is because the regression procedure is subject to

variances in data from sample to sample, called "error". The greater the error in the

regression, the greater will be the shrinkage of the value of R2. The above procedure

is an idealized method of the use of multiple regression. In many real life applications

of the procedure, random samples may not be feasible. However, we carried out a

cross validation summary of tables and results are shown in Appendix H. As per

analysis of SPSS we got Standard Error of Estimate to be 65.461.

We took 20 data which were rejected for being incomplete in preliminary stage. But

the variables required for cross validation were present and we used those data for

cross validation. In our case the Standard Error of Residuals was 20.86629 which was

very good result for Model-1.

5.10 Sensitivity Analysis of Model-1

Sensitivity analysis is the study of how the uncertainty in the output of a mathematical

model or system (numerical or otherwise) can be apportioned to different sources

of uncertainty in its inputs. A related practice is uncertainty analysis, which has a

greater focus on uncertainty quantification and propagation of uncertainty. Ideally,

uncertainty and sensitivity analysis should be run together.

Sensitivity analysis can be useful for a range of purposes, including




Testing the robustness of the results of a model or system in the presence of

uncertainty.

Increased understanding of the relationships between input and output

variables in a system or model.

Uncertainty reduction: identifying model inputs that cause significant

uncertainty in the output and should therefore be the focus of attention if the

robustness is to be increased (perhaps by further research).

Searching for errors in the model (by encountering unexpected relationships

between inputs and outputs).

Model simplification – fixing model inputs that have no effect on the output,

or identifying and removing redundant parts of the model structure.

Enhancing communication from modelers to decision makers (e.g. by making

recommendations more credible, understandable, compelling or persuasive).

Finding regions in the space of input factors for which the model output is

either maximum or minimum or meets some optimum criterion.

In case of calibrating models with large number of parameters, a primary

sensitivity test can ease the calibration stage by focusing on the sensitive

parameters. Not knowing the sensitivity of parameters can result in time being

uselessly spent on non-sensitive ones.

Taking an example from economics, in any budgeting process there are always

variables that are uncertain. Sensitivity analysis answers the question, "if these

variables deviate from expectations, what will the effect be (on the business, model,

system, or whatever is being analyzed), and which variables are causing the largest

deviations?" The sensitivity of model-1 is shown in figure 5.7.




In this figure three lines are plotted. Each line shows the response of one variable. It is

the percentage of change in construction cost for percentage of change the value of IV

by one unit. Dashed (-----------) line shows the Wage of Mason which has the

maximum slope, Dotted (……..) line shows Price of Paint which has second slope and

continuous line (______) shows the Price of Sand which has the least slope. In reality

the construction cost increase most if Age of Mason increases and least if price of

sand increases. So our model can be accepted.





This paragraph shows regression analysis with the output of Model-2 with 85 Data

like Model-1. In model-2we considered the 19 independent variables (IV) which are

the design variables. The variables are Lift Capacity, Transformer Capacity,

Generator Capacity, No of Stair, No of Storey, No of Toilet per floor, Duration of

project, Lobby Size, Total Area of the Project, Total Plinth Area, Width of Road-1,

Width of Road-2, No of Basement, Structural Form, Pile or Not, Deep/Shallow

Foundation, Corner Plot or not, Concrete Strength and Steel Grade. The dependent

variable (DV) was Construction Cost per square feet. The SPSS-17 was used as tools

of analysis and SPSS automated output give some tables and figures which are

discuss below.


Model R R Square Adjusted R


1 .574a .329 .304 185.938 .608


Table 5.6 describes the model summary. The values are as follows:

R=0.576, R2 =0.329, Adj R2=0.304, SE= 185.938 and DW Stat=0.608

The output tells that the model can explain 32.9% of the variability by the 3 IV

expressed in Table 5.8. Value of SE is big and model is not that good in comparison

to Model-1.

Table 5.7: ANOVA (Model-2)


1 Regression 1374822.749 3 458274.250 13.255 .000a

Residual 2800414.028 81 34573.013

Total 4175236.776 84




5.11.2 Analysis of Variance (Model-2)

Table 5.7 expresses that F (3, 81) =13.255 which is statistically significance at 0.00

level which is less than 5%. So the overall model is significant. This model can be

accepted.

Table 5.8: Coefficients (Model-2)

Model


Standardized Coefficients

Collinearity Statistics

B Std. Error Beta t Sig. Toleran

ce VIF

1 (Constant) 1181.369 96.960 12.184 .000

Plinth -.047 .014 -.335 -3.398 .001 .851 1.176

Storey 31.168 14.580 .229 2.138 .036 .724 1.381

Lift 26.576 6.396 .462 4.155 .000 .671 1.491


Table 5.8 expresses the main equation of the model is

Construction Cost= 1181.369- 0.047*Plinth+31.168*Storey+26.576*Lift

Where;

Construction Cost in Taka/sft


Storey= No of Storey in the Building

Lift= Total Lift Capacity in the Building

The Unstandardized Coefficient (Std. Error is 96.96, 0,014, 14.58 and 6.396 for

Intercept, Plinth, Storey and Lift respectively.

Standardized Coefficient (Beta) is 0.335, 0.229 and 0.462 for Plinth, Storey and Lift

respectively.

"t" statistics are significant because all the "p" value is less than 0.050.




The threshold value of VIF and Tolerance are 10 and 0.01 respectively. In model-2 all

the values are within limit, that means there is less possibilities of Multicollinearity.



Std. Deviation N

Predicted Value 1084.67 1909.40 1481.67 127.933 85



22.327 94.153 37.537 14.850 85

Adjusted Predicted Value

1081.84 1911.18 1482.11 130.288 85

Residual -395.773 541.735 .000 182.588 85

Std. Residual -2.129 2.914 .000 .982 85

Stud. Residual -2.161 2.956 -.001 1.006 85

Deleted Residual -407.814 557.703 -.438 191.695 85


Mahal. Distance .223 20.550 2.965 3.704 85

Cook's Distance .000 .130 .013 .024 85

Centered Leverage Value

.003 .245 .035 .044 85


Table 5.9. Expresses the residual statistics. All values from "Predicted Value" to

Student Deleted Residuals are okay. Cook's distance is less than 1. So the residual

statistics gives reasonable output.

5.12 Histogram of Residuals

Figure 5.8 is the Histogram of Standardized Residuals. It is a check on normality; the

histogram should appear normal; a fitted normal distribution aids us in our

consideration. Serious departures would suggest that normality assumption is not met.

Here we have a approximately normal curve so we have no real cause for concern.




Figure 5.8: Histogram of Standardized Residuals (Model-2)







standardized residuals. If all the points lie on the diagonal, it means the residual are





Figure 5.9: Normal P-P Plot of Standardized Residuals (Model-2)






should be a random pattern centered on the line of zero standard residual value. The

points should have the same dispersion about this line over the predicted value range.

From the above we can see no clear relationship between the residuals and the


Variance. The dispersion of residuals over the predicted value range spread over the


evidence against a change in variability. So we can say Residual are Homoscedastic,


Figure 5.10: Scatter Plot of Standardized Residuals vs. Standardized Predicted Value (Model-2)





The amount of shrinkage can be estimated using a cross validation procedure. In cross

validation, regression weights are estimated using one set of data and are tested on a

second set of data. However, we carried out a cross validation summary of tables and

results are shown in Appendix H. As per analysis of SPSS we got Standard Error of

Estimate to be 67.2736. We took 20 data which were rejected for being incomplete in

preliminary stage. But the variables required for cross validation were present and we

used those data for cross validation. In our case the Standard Error of Residuals was

185.938 which was very good result for Model-1.


Sensitivity analysis answers the question, "if these variables deviate from

expectations, what will the effect be (on the business, model, system, or whatever is

being analyzed), and which variables are causing the largest deviations?" The

sensitivity of model-1 is shown in figure 5.7.





This paragraph shows regression analysis with the output of Model-3 with 85 Data

like Model-1 and 2. In model-3 we considered the 27 independent variables (IV).

These variables are basically total of variables used in Model-1 and 2. Similarly the

dependent variable (DV) was Construction Cost per square feet. The SPSS-17 was

used as tools of analysis and SPSS automated output give some tables and figures

which are discuss below.


R R Square Adjusted R


1 .960 .922 .918 63.762 .738

a. Predictors: (Constant), Lift, Mason, Paint, Sand


Table 5.10 describes the model summary. The values are as follows:

R=0.960, R2 =0.922, Adj R2=0.918, SE= 63.762 and DW Stat=0.738

The output tells that the model can explain 92.2% of the variability by the 5 IV

expressed in Table 5.12. Value of SE is small and model is very good in comparison

to Model-1.and 2.

Table 5.11: ANOVA (model-3)


1 Regression 3849985.833 4 962496.458 236.739 .000

Residual 325250.943 80 4065.637

Total 4175236.776 84

5.17.2 Analysis of Variance (Model-3)

Table 5.11 expresses that F (4, 80)=236.739 which is statistically significance at 0.00

level which is less than 5%. So the overall model is significant. This model can be

accepted.




Table 5.12: Coefficients (model-3)

Model


Standardized Coefficients


1 (Constant) -458.393 150.649 -3.043 .003

Sand .258 .073 .255 3.519 .001

Paint .642 .262 .124 2.450 .016

Mason 4.117 .427 .603 9.651 .000

Lift 4.843 2.089 .084 2.318 .023


Table 5.12 expresses the main equation of the model is

Construction Cost= -458.393+0.258*Sand+ 0.642*Paint+4.117*Mason+4.843*Lift

Where;

Construction Cost in Taka/sft



Mason= Wage of Mason (Taka/Day)


The Untandardized Coefficient (Std. Error is 150.649, 0.073, 0.262, 0.427 and 2.089

for Intercept, Sand, Paint, Mason and Lift respectively.

Standardized Coefficient (Beta) is 0.255, 0.124, 0.603 and 0.89 for Sand, Paint,

Mason and Lift respectively.

"t" statistics are significant because all the "p" value is less than 0.050.

The threshold value of VIF and Tolerance are 10 and 0.01 respectively. In model-2 all

the values are within limit, that means there is less possibilities of Multicollinearity.






Std. Deviation N

Predicted Value 944.44 1966.63 1481.67 214.087 85



9.783 28.084 14.894 4.187 85

Adjusted Predicted Value

930.35 1963.59 1481.40 214.790 85

Residual -127.219 164.433 .000 62.226 85

Std. Residual -1.995 2.579 .000 .976 85

Stud. Residual -2.128 2.668 .002 1.012 85

Deleted Residual -144.740 175.988 .272 66.941 85


Mahal. Distance .989 15.307 3.953 2.999 85

Cook's Distance .000 .193 .016 .032 85

Centered Leverage Value

.012 .182 .047 .036 85


Table 5.13 expresses the residual statistics. All values from "Predicted Value" to

Student Deleted Residuals are okay. Cook's distance is less than 1. So the residual

statistics gives reasonable output.




Figure 5.12: Histogram of Standard Residuals (Model-3)

5.18 Histogram of Residuals (Model-3)

Figure 5.12 is the Histogram of Standardized Residuals. It is a check on normality

with slightly skewed toward left; the histogram should appear normal; a fitted normal

distribution aids us in our consideration. Serious departures would suggest that

normality assumption is not met. Here we have a approximately normal curve so we

have no real cause for concern.







standardized residuals. If all the points lie on the diagonal, it means the residual are





Figure 5.13: Normal P-P Plot of Standardized Residuals (Model-3)



should be a random pattern centered on the line of zero standard residual value. The

points should have the same dispersion about this line over the predicted value range.

From the above we can see no clear relationship between the residuals and the





Variance. The dispersion of residuals over the predicted value range spread over the


evidence against a change in variability. So we can say, Residual are Homoscedastic,


Figure 5.14: Scatter Plot of Standardized Residuals vs. Standardized Predicted Value (Model-3)





The amount of shrinkage can be estimated using a cross validation procedure. In cross

validation, regression weights are estimated using one set of data and are tested on a

second set of data. However, we carried out a cross validation summary of tables and

results are shown in Appendix H. As per analysis of SPSS we got Standard Error of

Estimate to be 20.96498. We took 20 data which were rejected for being incomplete

in preliminary stage. But the variables required for cross validation were present and

we used those data for cross validation. In our case the Standard Error of Residuals

was 185.938 which was very good result for Model-1.








sensitivity of model-1 is shown in figure 5.15.




5.23 Discussion on Empirical Result

A perfect model that is able to predict the exact value of the Construction

Cost is very hard to achieve – if not impossible – since it has to include all

aspects of what makes the information valuable. Trying to achieve such a

model would be very complex with variables that are difficult to measure

and may differ among people, country, location within the country, level of

quality assurance by the constructors, access to data, quality of data and many

more. Therefore we believe in having a simpler model that is easy to

understand and use, which at the same time predicts the value of the

construction cost reasonably well. In this section of the paper, I will discuss

about the three models I constructed as Construction Cost Functions. I will also

discuss the statistical tests I performed for the suitability of my models. My

discussion will be supplemented by checking of the assumptions as how I addressed

the issues. I will discuss some additional test away from statistics and Econometrics

as to validate my model. Finally I will conclude with the comments about the models.

5.23.1 The Data

The main aspect of the thesis was working with primary data. Initially data

was collected using structured questionnaires with open and close ended

questions. As people are not ready spend time for filling up the questions,

hence later on and Excel format was made to get the data. The data was

entered in Excel sheet and sorted out for errors and missing data. Data was

enhanced by few secondary data as these were not available primarily.

Initial data was 288 set but after sorting only 106 data was valid for this

research. Later removing the outliers only 85 data was available for final

model.

5.23.2 The Models

I developed three models as I expressed at the beginning. In all the cases

Construction Cost (Taka/sft) was the dependent variable. SPSS-17 was used in all

models as a tool of modeling and analysis. Four methods (Enter, Stepwise Regression,




Forward Selection and Backward Elimination) were used simultaneously as to get the

optimum result. Firstly, Model-1 was constructed considering nine independent

variables which were basically construction materials' costs and labour wages.

Secondly, Model-2 was constructed considering nineteen independent variables which

were basically design variables and finally in Model-3 all the variables were used.

Model-1 concluded with only three variables (Sand, Mason and Paint), Model-2 also

with three variables (Storey, Plinth and Lift) and finally Model-3 came out with all

the variables of Model-1 with additional variable (Lift) from Model-2. Thereby we

can conclude out of 27 variables these four variables are mostly describing the

variability of the data. The equations of the models as described in paragraph 5.5.3.,

5.11.3, and 5.18.3. are as follows:

Construction Cost= - 574.83-0.251*Sand+0.864*Paint+4.17*Mason………… (1)

Construction Cost= 1181.369- 0.047*Plinth+31.168*Storey+26.576*Lift …… (2)

Construction Cost= -458.393+0.258*Sand+ 0.642*Paint+4.117*Mason+4.843*Lift ... (3)

Where;

Construction Cost is in Taka/sft


Paint=Price of Paint (Taka/Gallon) and



Storey= No of Storey in the Building





Table 5.14: Comparison of the Models

Model Variables

Considered

Variable included

in the Model

Model Summary

R R2 Adj. R2 Std. Error

Durbin-Watson

Model-1

Materials' Cost and Labour Wage

Sand, Mason, Paint

.958 .917 .914 65.461 .659

Model-2 Design Variables

Storey, Plinth, Lift

.574a .329 .304 185.938 .608

Model-3

All variables

Sand, Mason, Paint, Lift

.960 .922 .918 63.762 .738

5.23.3 Comparison of the Models

If we compare three models we find that Model-3 is the combination of Model-1 and

2. Model-3 explain maximum variability (92.2%) with minimum residuals

(SE=63.762). Then comes Model-1 which explain 991.7% of variability with SE=

65.461. Model-2 explain very small portions of variability (32.9%) with huge

residuals (SE=185.938) almost 3 times of Model-3 and a bit more comparing to

Model-1. Inclusion of design variable explained a small amount of increased viability

only 0.5% (92.2-91.7). So, it may be concluded that inclusion of design related

variables do not yield much. It is better option to use Model-1 with only cost related

variables which are available in the market with less effort. Prediction cost calculating

MOdel-1 with an increase of 9% may serve the purpose of finding initial project cost

which would be used for decision making process.

5.23.4 Overall Significance

Referring to Table 5.3, 5,7 and 5.11 we can come in a conclusion that all the models

are overall significant at 0.00% level ("F" statistics significance or "p" value is 0.00

for all models. So, all the models are good and acceptable statistically.




5.23.5 Individual Significance

Referring to Table 5.4, 5,8 and 5.12 we can say that all the variables are individually

significant within the model ("t" statistics are significant below 5% level or "p" value

is less than 0.50.

5.23.6 Testing of Assumptions

Multiple Linear Regression has at least 10 assumptions to be tested to prove the

models significance. It is obvious some of the assumptions are not met in real data. In

this section we will show how all the assumptions are met in three models.

Assumption #1: Model is Linear in Parameter: The parameters are the

coefficients found by Table 5.4, 5.8 and 5.12 in three models are the

parameters and we can see these are the constant. So the models are linear in

parameter.

Assumption #2 Dependent Variables should be measured in continuous

(interval or ratio) scale. Our DV (Construction Cost) has numeric value

which may be told continuous scale.

Assumption #3: There have to be two or more independent variables. In our

models we considered multiple (more than 2) IV and all the models

concluded with minimum 3 variables.

Assumption #4: The data must not show multicollinearity. As we refer Table

5.4, 5.8 and 5.12 we find that, we have the value of VIF <10 and Tolerance

> 0.1. So apparently variables finally included in models are not perfectly

collinear to each other. Moreover, in case of prediction collinearity is not a

problem.

Assumption #5: The data needs to show homoscedasticity, i.e., the variance

must be equal (homo) spread. If we refer to Figure 5.6, 5.10 and 5.14 we

find the scatter plot are spread and no unique pattern are visible.

Assumption #6: There should be no significant outliers. We checked the data

by boxplot at Table 5.1 and 5.2 and removed the outliers before final model.

Assumption #7: Finally, you need to check that the residuals (errors) are not




serially correlated. From Table 5.2, 5.6 and 5.10 we find that Durbin-Watson

statistics are 0.659, 0.608 and 0.738 in consecutive 3 models. It is confirm

the value is neither 0 nor 4, so perfectly serial correlation of residuals do not

exist but this test indicates a inclination of positive correlation as value is

>1.5. We confirm further by Normal P-P Plot of Standardized Residuals in

three models (Figure 5.5, 5.9 and 5.13) that the lines are almost straight, that

means there is no perfect serial correlation.

Assumption #8: Number of observations must be greater than number of

parameter. We have maximum 5 parameter (one intercept and four

coefficients in model-3) and 85 observations. So, this assumption is met.

Assumption #9: The value of independent variables should be stochastic or

random. In our whole data set we had all IV randomly collected.

Assumption #10: The regression model is correctly specified. We have

prepared three models where all the variables are individually significant

below 5% and also each model is overall significant below 5% level. So, it

may be concluded that the the regression models are correctly specified.


In reference of Table 5.5, 5.9 and 5.13 the residual statistics are shown. I will discuss

only few. For instance outliers (observations that do not appear to fit the model that

well) can be identified as those observations with standardized residual values above

3.3 (or less than -3.3)

i. Cook’s distance is considered to be the single most representative

measure of influence on overall fit. It captures the impact of an observation

from two sources: the size of changes in the predicted values when the case is

omitted (outlying studentized residuals) as well as the observation’s distance

from the other observations (leverage). A rule of thumb is to identify

observations with a Cook’s distance of 1.0 or greater, although the threshold

of 4/(n – k ‐ 1), where n is the sample size and k is the number of independent

variables, is suggested as a more conservative measure in small samples or for

use with larger data sets. Even if no observation exceed this threshold,

however, additional attention is dictated if a small set of observations has

substantially higher values than the remaining observations. It is the summary




measure of the influence of a single case (observation) based on the total

changes in all other residuals when the case is deleted from the estimation

process. Large values (usually greater than 1) indicate substantial influence by

the case in affecting the estimated regression coefficients. For each of these,

the usual "cutoff" is 1.0. Cases with values larger than 1.0 are "suspected of

being outliers". The Cook's distance statistic is a good way of identifying cases

which may be having an undue influence on the overall model. Cases where

the Cook's distance is greater than 1 may be problematic.

5.23.8 Cross Validation of the Model.

The manner in which regression weights (parameter) are computed guarantee that

they will provide an optimal fit with respect to the least square criterion for the

existing set of data. If a statistician wishes to predict a different set of data, the

regression weights are no longer optimal. There will be substantial shrinkage in the

value of R2 if the weights estimated on one set of data are used on a second set of

data. The amount of shrinkage can be estimated using a cross validation procedure. In

cross validation, regression weights are estimated using one set of data and are tested

on a second set of data. If the regression weights estimated on the first set of data

predict the second set of data, the weights are said to be cross validated. If the new

data is successfully predicted using old regression weights, the regression procedure is

said to be cross validated. It is expected that the accuracy of prediction will not be as

good for the second set of data. This is because the regression procedure is subject to

variances in data from sample to sample, called "error". The greater the error in the

regression, the greater will be the shrinkage of the value of R2. The above procedure

is an idealized method of the use of multiple regression. In many real life applications

of the procedure, random samples may not be feasible. However, we carried out a

cross validation summary of tables and results are shown in Appendix H. As per

analysis of SPSS we got Standard Error of Estimate to be 65.461, 185.638 and 63.762

in three consecutive models. We took 20 data which were rejected for being

incomplete in preliminary stage. But the variables required for cross validation were

present and we used those data for cross validation. In our case the Standard Errors of

Residuals were 20.86629, 67.2736 and 20.96498 which were found to be an excellent




result. Standard Errors of Residuals so small by validation is a sudden output. In

maximum case it will cross the SE of the models.

5.23.9 Sensitivity Analysis

Sensitivity analysis is the study of how the uncertainty in the output of a mathematical

model or system (numerical or otherwise) can be apportioned to different sources

of uncertainty in its inputs. A related practice is uncertainty analysis, which has a

greater focus on uncertainty quantification and propagation of uncertainty. Ideally,

uncertainty and sensitivity analysis should be run together.

Sensitivity analysis can be useful for a range of purposes, including

Testing the robustness of the results of a model or system in the presence of

uncertainty.

Increased understanding of the relationships between input and output

variables in a system or model.

Uncertainty reduction: identifying model inputs that cause significant

uncertainty in the output and should therefore is the focus of attention if the

robustness is to be increased (perhaps by further research).

Searching for errors in the model (by encountering unexpected relationships

between inputs and outputs).

Model simplification – fixing model inputs that have no effect on the output,

or identifying and removing redundant parts of the model structure.

Enhancing communication from modelers to decision makers (e.g. by making

recommendations more credible, understandable, compelling or persuasive).

Finding regions in the space of input factors for which the model output is

either maximum or minimum or meets some optimum criterion.

In case of calibrating models with large number of parameters, a primary

sensitivity test can ease the calibration stage by focusing on the sensitive

parameters. Not knowing the sensitivity of parameters can result in time being

uselessly spent on non-sensitive ones.







sensitivity test results of models are shown in figure 5.7, 5.11 and 5.15. Interestingly

the result shows that the relationships between input and output variables in the

models are same as in real. To explain further in case of model-1 change in DV

(Construction Cost) with change in price by 1 unit of IV is correctly depicted in the

graph. All the lines have positive slope. Say, Wage of Mason is more sensitive (slope

is maximum) than Price of Paint (lesser slope) and Price of Paint is more sensitive or

elastic (in economics) than Price of Sand (least slope). Similar is the case in model-2

and 3. In model-2 slope is maximum for Storey and decreases for Lift and Plinth has a

negative slope (almost zero slope). In model-3 Lift is most sensitive and then come

the Mason, Sand is least sensitive and Paint is immediate above Sand.

5.23.10 Conclusion

Construction cost estimation is one of the most challenging responsibilities in order to

ensure proper allocation of funding resources among different phases and events of

construction. It plays a vital role in decision making process of various stakeholders

Thus the successful completion and extent of a construction project largely depend on

initial cost estimation. Previous researches emphasize on the accuracy of conceptual

cost estimation. Various approaches namely Regression Analysis, Neural Network,

Case Based Reasoning were adopted by different research groups to minimize the gap

between estimation and final project cost. A large number of variables related to

project thus introduced by the authors to incorporate maximum uncertainties and

deviation of the real project. Some of these variables are highly sensitive to location

of the project. This type of research work was not conducted at Bangladesh. The work

was done taking primary data. Moreover in Bangladesh the constructors or developers

do not keep the data after completion of work. Some developers do not want to share

their data as they think it be confidential. This study commences the first step of

working with Materials' Cost, Labour Wage and Design variables. The data collected

was massive but due to abnormal value and also missing value they had to reduce by

more than one third. From the above research we see that both design variables and

direct cost elements have influence on construction cost. Many variables like most




important materials' cost (steel, cement and brick) were not accepted by the models

and are not found statistically significant. But they contribute the maximum of

materials' cost. At the same time Sand and Paint is being inferior in cost contributing

in these models. Helper, Carpenter and Transport Cost contribute more than Sand but

these are not statistically significant in our models. Foundation system, Structural

form and Basement are more important cost contributor but these are not statically

significant in our case. Concrete Strength, Steel Grade should also contribute

inversely but during model building these variables did not show desired indication.

Last but not the least this is a just start and I hope to work on this in future.




CHAPTER SIX

CONCLUSIONS AND RECOMMENDATIONS

6.1 General

A building project can only be regarded as successful once it is delivered at the right

time, at the appropriate price and quality standards, and can provide the client with a

high level of satisfaction. One important influence on this is the authenticity of the

cost estimates prepared by the constructor during the various phases, especially during

the conception phase. Often the quality of the project design, along with the ability to

start construction and complete it on schedule, are dependent on the accuracy of cost

estimates made throughout the design phase of a project. Since cost has been

identified as one of the measures of function and performance of a building, it should

be capable of being “modeled” so that a tentative design can be evaluated. This will

assist in providing greater understanding and possibility of prediction of the cost

effect of changing the design variables by the firms.

The importance of precise estimates during the early stages of any projects has been

widely acknowledged for many years. Early project estimates represent a key

constituent in decision making and often become the basis for a project’s ultimate

planning and funding. However, an inconsiderate contrast arises when comparing the

importance of early estimates with the amount of information naturally available

during the preparation of an early estimate. Such inadequate scope often leads to

questionable estimate precision. Yet, very few quantitative methods are available that

enable estimators to objectively evaluate the accuracy of early cost estimates. The

primary objective of this study was to establish such a model. To achieve this

objective, quantitative data were collected from completed construction projects from

some developers of Dhaka city. The data were analyzed using multivariate regression

analysis on the 27 variables to determine a suitable model for predicting estimate

accurately. The resulting model would allow the stakeholders to make an estimate

with reasonable accuracy. The multivariate regression analysis was selected for

model development. Total three models were developed where construction cost was

the dependent variable for all three models. First model included construction




materials' cost and labour wage as independent variables and the second model

incorporated only design variables as independent variables. Finally the third model

took account of all the available variables as independent variables for analysis. Total

four methods were used to check which one works better and provides pragmatic

solution. Finally both forward selection and backward elimination methods were used

simultaneously to get best possible results. Basically materials' cost and wage of the

labour contributed the maximum. Design related variables exhibited insignificant

influence which is actually not workable to meet the purpose.

All the models had overall significance at 0% level and for individual significance

each accepted variable met the required level of significance. Model-1 comprises of

materials' cost variables and wage explained 91.4% of variability with standard error

65.461 and for model-2 comprises of design related variable explained only 32.9% of

variability with standard error 185.938. Although, mixed model yielded the optimum

result inclusion of design variable it explained an increased 0.5% of variability. All

assumption of multiple linear regression was tested and met almost full. Models were

also cross validated and found reliable output. Sensitivity analysis of variables for

each model was performed and passed. Hence it is concluded that model with

materials' cost and wage is better. Moreover design related variables are not readily

available before the design. On the other hand cost of materials and wage rate can be

very easily collected from market.

Primary data collection is a tedious job and takes huge effort in terms of time and

money. These data are not readily available to the developers. Few developers do not

share their business secret to public. It is also found that people are not interested to

provide the data considering waste of time and effort. If anyone interested to work

with primary data he should have enough time for data collection and sorting. Design

variables create different perception to different firms. So, even collected data from

many firms may not be homogeneous for these types of research. Time and space is

also a great concern to the cost which must not be forgotten.

6.2 Conclusions




The cost model may be considered satisfactory if the variation generates on

application is within the acceptable tolerant limit. The cost functions those were

identified in this research involve all possible cost and design variables and made a

generalized equation. Most interesting aspect of this model is that, the estimators had

options to change any variables at any stage and adjust the estimated cost without

much effort. At the same time, persons do not have adequate knowledge on building

design may estimate the cost at ease. The model is expected to be more versatile and

fits the residential buildings. It is also expected that the modeling technique will

unfold a new avenue for the researchers of Bangladesh for making further study.

Present study was carried out with only panel data. But this approach can be used for

both Time Series and Pooled data also. This model can be effectively planned for cost

function of other discipline also. It must be remembered that an estimated project

cost is not an exact number. Rather it is an opinion of probable cost, not an exact

calculation. The accuracy and reliability of an estimate is totally dependent project

scope and the time and effort expended in preparation the estimate. The type of

estimate to be made and its accuracy depends upon many factors including the

purpose of the estimates, knowledge of the project, and how much time and effort is

spent in preparing the estimate.

6.3 Limitations of the Study

The limitations of the study were as follows:

Main limitation of this study was primary data collection process. In

Bangladesh the constructors or developers do not keep the data after

completion of work. Some developers do not want to share their data as they

think it be confidential. The data supplied by the developers might be from

their memory and few old documents which might be flawed.

The year selected for the study (2006 to 2011) were exceptional than other

time as during these year the cost of materials had lots of ups and downs.

Price of construction materials especially steel had price jump in higher and

also in lower amount such that it did not follow any pattern. This

consideration could not be taken into account.

Within these years the numbers of developers increased a lot which allowed a




mixed workmanships and quality control of the construction often led to

generate wrong perceptions. Same building could be constructed with varied

price as it was not controlled by any authority in reality. Developers working

in Gulshan, Banani, Baridhra and D.O.H.S. area are considered to maintain a

high quality but during these years it did not happen rather both high and low

quality buildings were constructed. We did not have a measuring tool to

workmanship and quality of construction.

From the above research we see that both design variables and direct cost

elements have influence on construction cost. Many variables like most

important materials' cost (steel, cement and brick) were not accepted by the

models and are not found statistically significant. But they contribute the

maximum of materials' cost in reality.

Sand and Paint is being inferior in cost contributing in these models. Helper,

Carpenter and Transport Cost contribute more than Sand but these are not

statistically significant in our models.

Foundation system, Structural form and Basement are more important cost

contributor but these are not statically significant in our case.

Concrete Strength, Steel Grade should also contribute inversely but during

model building these variables did not show desired indication.

This model should not use blindly for preliminary cost estimation of a

building as the most cost contributing variables (steel, sand and brick) are not

in the function. A general idea may be taken as how much the cost might be.

This model requires some modification by taking a huge data and considering

spatial or location of the project.




6.4 Recommendation for Future Study

This section will discuss some recommendations for future study. The followings are the recommendations for future study.

It is obvious that the formats of regression model differed according to project

types, additional researches could be conducted to examine deeper into this

field through overcoming the limitations presented above. Moreover the

incorporation of the other factors such as technology, site-related problems,

and management-related problems would be promising in building a more

practical tool.

For working with primary data developers should be categorized as per their

quality of works. Then this method may be conducted again for analysis for

each category of developers.

Model can be done with fully secondary data.

More design variables may be included in future.

Project should be ranked as per workmanship and quality and only

then same modeling technique may be repeated taking data of a

single rank for each model.

More Materials' cost and labour wages may be included in future.

Few variables were collected per floor. It should have been better if all were

transformed in per sq. ft.

Other non linear models could be tried.

ANN model could be tried.

This technique can be used for office buildings and road sector.

Formatted: Space After: 10 pt, Line spacing: 1.5 lines, Widow/Orphan control, Allow hangingpunctuation, Adjust space between Latin andAsian text, Adjust space between Asian textand numbers




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APPENDICES




Survey on Residential Building-Dhaka

M.Sc Thesis Project, BUET

PART A (For Each Building)

Purpose of Survey: Developing a generalized cost function of residential building

construction-Dhaka

Respondents: Reliable Developers of Dhaka City

Project Location, Contract and Year

1. Financial year of the project contract:___________ ________(month/year) to

__________ ________(month/year).

2. Area Location of the Project (Dhanmondi/ Gulshan/ Banani etc):_________.

3. Plot No: ___________ Road No:____________.

4. Adjacent Road: Single Road of _______feet/Corner Plot of ______feet &

______ feet

5. Pin Point Location of the Building (Tick as applicable).

a. Centre of city / Residential Area/ New Housing Area/ Diplomatic Zone/

Commercial Zone/ Others (_________________)

b. Location of facilities in walking distance (Kacha Bazar/ Market/ School/

College/ University/Bus Stoppage/Govt Hospital/ Departmental Stores/

_________/ _________.

6. Financial Contracts between Owner & Developer:

a. Owner: _______Flat or _____%.

b. Developer: _______Flat or _______%.

c. Signing amount: ______________Tk.

Foundation

7. Foundation Depth: ( Deep / Shallow)

8. Footing Types :( Individual or Single/ Strip/ Combined/Raft/ Mat/

Pile/________ )

9. Basement Floor: (Yes/ No)

Frames , Floor & Shape

10. Structural Form (Tick one): Bearing Wall/ Framed/Shear Wall/ Wall-

Shear/Braced/ Tubular /__________

11. Floor System: (Tick one):One way slab/Two way slab/ Flat Slab/ Flat Plate/

_______.

A-1

APPENDIX-A




12. Building Shape: (Tick one): Rectangular/Square/Irregular/Others( )

Details of Flat

13. Total Area by property line____________ katha or _________decimal

or_________sft.

14. Total Plinth Area:________Katha or________decimal or __________sft.

15. Storey of Basement: Nil / 1 / 2 / 3/

16. No of Flat per Floor:_______

a. Size:_______ sft, Nos:_______.

b. Size:_______sft, Nos:________.

c. Size:_______sft, Nos:_______.

d. Size:_______sft, Nos:_______

17. Total No of Stories except Basement (Super structure):___________

18. Total No of Parking:_______: (Ground Floor_____. Basement______, Other

Floor:______)

19. Parking per flat: 1 /2 /3

20. Ground Floor contains (Tick as applicable): Security Room/ Machine Room/

Drivers waiting/ Toilet/ Parking/_________.

21. Size of Lobby at each Floor: ___________sft

22. Total Nos of Toilets per Floor: _________Nos. (Including servant’s one)

23. Toilet/ Bath room Facilities: Bath tub in Toilet/Shower enclose in

Toilet/Geyser / __________/__________

24. Fire Fighting: (Tick as applicable): Fire Extinguisher/ Fire Hose/ Fire pump.

25. Total No of Staircase: 1 / 2 / 3

26. Flat Contains (Tick as applicable): Separate Servant room/ servant toilet/

store room/ storing provision by false ceiling/reading room/study room.

27. Flat contains:

a. Wall Cabinet: (Yes/ No) & (Brand: _________________)

b. Kitchen Cabinet: (Yes/ No) & (Brand: _________________)

c. Furniture: (Yes/No); Brand: ___________________)

d. Air-condition :( Yes/No); Window/split/central; Brand:

__________;Total: ______KW.

e. Any other Facilities not mentioned:

f. Any other Facilities not mentioned:

Information about Materials

28. Concrete strength considered: __________Psi or __________MPa

29. Rod/ Reinforcement used: ______grade.

30. Sculpture in the Building: yes/ No

A-2




31. Internal/ Partition wall: Gas burn Brick/1st class Brick/ Hollow brick/Normal

Brick/Light weight Brick/ Others ( )

32. Main Door: Plane Teak/ Malaysian Readymade/ Hatil Oak Tree/Others( )

33. Inner Door: Flash Door/Solid Door/ Others ( ).

34. Other Door: Plastic/Flash Door/Solid Door/ Others ( ).

35. Floor Tiles: Brand_____________, Made in____________.

36. Bathroom Tiles: Brand_____________, Made in____________.

37. External Paint Type: Weather coat/ Snow cem/Others________, Brand_______.

38. Internal Paint Type: Plastic/ Distemper/ Colour wash/ white wash/

Others___________, Brand__________.

39. Window Frame: MS Steel/SS Steel/Thai Aluminum/ Wooden/ Others

40. Window Shutter: Local Glass/ Thai (Clear glass/tinted glass/Mercury)/

Wooden/Plane sheet

41. Community facilities in building (Tick as applicable): Swimming pool/ Gym/

Prayer Room/Laundry/ Community centre/ Conference Room/ School/Car

Washing Facilities/ Roof Garden/ Bar-B-Queue Space.

42. Community facilities in ground Floor (Tick as applicable): Driver’s Common

Room/ Waiting Room/Office Room/Reception/Guard Room/Guest’s

Toilet/CCTV/Intercom/

43. Common Utilities (Tick as applicable)

a. Sub Station (Transformer): Brand:___________, Made in:______,

KW_______

b. Generator: Brand___________ Made in__________, KVA________

c. Lift ( Total No_____, Capacity_____, Brand__________, Made

in_________)

d. Pump: (Yes/No)

e. __________

f. _________

44. Gas connection: yes/No

45. Electricity Connection: Yes/No

State Of Luxury:

46. Ultra Luxury/ Super Luxury/ Luxury/ Moderate/ Economic/ Low Cost

Cost Data

47. Only Construction cost per sft( cost at site): Tk.

A-3




48. Total Cost of Project: _______________Tk Total Cost/sft:_________Tk .[All

cost]

49. Project Delayed: Yes/ No.

a. Delayed by: _______months.

b. Additional Expenditure (Amount): _________taka and %________)

Any Other Information not asked that affect Cost of Construction

50._____________

51.______________

52.____________

A-4




Survey on Residential Building-Dhaka

M.Sc Thesis Project, BUET

PART B (For Each Building)

State Of Luxury:

1. Ultra Luxury/ Super Luxury/ Luxury/ Moderate/ Economic/ Low Cost

Only Cost/Expenditure Data(as % of Total Cost )

2. Total Cost per sft (Includes all cost except marketing and profit):

3. Only Construction Cost/sft: _________Tk .

4. Project Delayed: Yes/ No.

a. Delayed by: _______months.

b. Additional Expenditure (Amount): _________taka and %________)

5. Cost of Plan and Design:

a. Architectural Plan: Total Cost: Tk/ cost per sft_________ Tk

b. Structural Design: Total Cost: Tk/ cost per sft_________ Tk

c. Plumbing Design: Total Cost: Tk/ cost per sft_________ Tk

d. Electric Design: Total Cost: Tk/ cost per sft_________ Tk

6. Over head Cost:

a. Establishment Cost (Labour shed, Electrical connection, Water connection,

Stores and washing point etc): Tk/ cost per sft_________ Tk

b. Over Head HR ( Project Manager, Project/Site Engineer, Site Manager,

Security, curing man etc): Tk/ cost per sft_________ Tk

c.

7. Govt Cost:

a. Cost of Govt Plan pass, permission, tax etc.: Total :______ Tk Or Per

sft:____Tk. (City Corporation)

b. Cost of Govt Plan pass, permission, tax etc.: Total :______ Tk Or Per

sft:____Tk. (RAJUK)

c. Cost of Govt Plan pass, permission, tax etc.: Total :______ Tk Or Per

sft:____Tk. (if any)

d. Cost of Electric Connection: ____________Tk.

e. Cost of Gas connection:______________Tk

B-1

APPENDIX-B




8. Misc Cost: (% of Total Cost)

a. Structural construction: (Material _____________ Tk & Labour_________).

b. Plumbing: (Material: _____________ Tk & Labour: ____________).

c. Electrical: (Material: _____________ Tk & Labour:____________).

d. Interior Design and Finishing: (Material: _______ Tk & Labour: ________).

e. Painting : ( Brand:________; Type: ___________Quantity: ___________ltr;

Materials Cost____________ Tk & Labour Cost: ___________________Tk

f. Water and Sanitation Works: Materials: _______Tk & Labour: ________Tk.

g. Quantity of Steel Bar: _____________ton; Cost _______________Tk.

h. Quantity of Cement: _______Bag; Cost: __________________Tk.

i. Quantity of Sand: ______________cft; Cost_______________Tk.

j. Quantity of Stone Cheaps: ___________cft; Cost_____________Tk.

k. Quantity of Concrete ready mix (if used):___________cft;

Cost:________________Tk

l. Additional Steel for Earthquake Resistance: (Quantity: _________ton

or______ % of total steel and Cost: ________Tk or _______% of total steel.

m. Any other cost 1.

n. Any other cost 2.

o. Any other cost 3.

Any Other Information about materials and labour not asked that affect

Cost of Construction

9. _____________

10.______________

11.____________

12. ___________.

13. __________

B-2




C-1

Serial

Co

nstructio

n C

ost p

er

sft (Tk)

Price

of Ste

el p

er to

n

(Tk)

Price

of 1

000

Bricks

Price

of 1

00 cft San

d

Price

of 1

Gallo

n P

aint

Wage

of M

ason

Wage

of H

elp

er

Wage

of C

arpe

nte

r

Transpo

rt Ch

arge 3 to

n

8 km

Date

Started

Date

end

ed

Du

ration

(Mo

nth

s)

Proje

ct Are

a

Total A

rea (K

antha)

Total P

linth

Are

a (sft)

74 900 37000 3252.00 735.00 521.00 200.00 153.33 200.00 528.00 25-Aug-02 10-May-06 45 Gulshan-1 28 14450

178 1003 47000 3252.00 735.00 547.00 200.00 153.33 200.00 528.00 2-Oct-02 27-Jan-05 28 Gulshan-2 15 7700

97 1062 42000 3168.00 735.00 647.78 204.25 119.25 287.00 571.02 21-Jul-04 10-Oct-08 51 Kazipara 5.5 2800

174 1089 42000 3192.00 724.00 521.00 201.83 112.25 200.00 747.45 1-Jan-05 1-Jun-06 17 Dhanmondi 6 3458

170 1091 45000 3192.00 724.00 612.00 201.83 112.25 250.00 747.45 12-Jan-05 15-Nov-07 34 Uttara 7.5 4320

90 1100 44000 3192.00 724.00 647.78 201.83 112.25 287.00 747.45 1-May-05 13-Aug-08 40 Banani 10 5760

23 1100 42000 3192.00 724.00 612.00 201.83 112.25 250.00 747.45 25-Jun-05 27-Jun-07 24 Banassri 5 6000

6 1120 47000 3192.00 724.00 652.00 201.83 112.25 328.00 747.45 30-Jun-05 2-Jan-10 54 Mirpur 20 40000

179 1148 46000 4014.00 1000.00 647.78 228.00 120.00 287.00 803.63 1-Feb-06 1-Jul-08 29 Mohammadpur 32 18433

7 1150 46000 4014.00 1000.00 652.00 228.00 120.00 328.00 1222.00 1-Feb-06 1-Dec-10 58 Adabar 29 16708

154 1160 61000 4014.00 1000.00 647.78 228.00 120.00 287.00 546.36 1-Feb-06 1-Sep-08 31 Dhaka Cantt 7.5 3590

176 1194 43000 4014.00 1000.00 685.00 228.00 120.00 300.00 1155.67 1-May-06 7-Aug-09 39 Uttara-11 5.5 2775

156 1198 50000 4014.00 1000.00 685.00 228.00 120.00 300.00 1155.67 15-Jun-06 2-Dec-09 42 Mirpur 29.90 18052

76 1200 55000 4014.00 1000.00 652.00 228.00 120.00 328.00 1222.00 1-Sep-06 4-Sep-10 48 Dhanmondi 21 9000

77 1200 55000 4014.00 1000.00 647.78 228.00 120.00 287.00 546.36 27-Sep-06 13-Sep-08 24 Balughat 4 2000

168 1218 55000 4014.00 1000.00 685.00 228.00 120.00 300.00 1155.67 12-Dec-06 7-Jun-09 30 Nakhalpara 5 2560

152 1230 63500 4300.00 1142.67 724.00 250.90 150.00 364.54 1142.67 1-Jan-07 21-Jul-11 55 Bongshal 3.5 1900

177 1234 46000 4300.00 1142.67 724.00 250.90 150.00 364.54 1142.67 1-Jan-07 12-Oct-11 57 Khilkhet 5 2550

167 1235 54500 4300.00 1142.67 685.00 250.90 150.00 300.00 1142.67 21-Jan-07 29-Jan-09 24 Azimpur 7 3482

86 1238 40000 4300.00 1142.67 652.00 250.90 150.00 328.00 1142.67 23-Jan-07 22-Feb-10 36 Dakskinkhan 19.85 8927

3 1250 55000 4300.00 1142.67 652.00 250.90 150.00 328.00 1142.67 4-Feb-07 10-Mar-10 37 Nikunjo 4 2100

166 1266 54000 4300.00 1142.67 685.00 250.90 150.00 300.00 1142.67 1-Mar-07 1-Jun-09 27 Baitul Aman 5 2880

157 1269 60000 4300.00 1142.67 652.00 250.90 150.00 328.00 1142.67 14-Mar-07 15-Feb-10 35 Mogbazar 5 1950

80 1272 40000 4300.00 1142.67 685.00 250.90 150.00 300.00 1142.67 1-Apr-07 1-Aug-09 28 Dhanmondi 6 2900

SPECIMEN OF SAMPLE DATA IN SPREADSHEET

APPENDIX-C

503




Serial

Co

rner P

lot

Ro

ad 1 (ft)

Ro

ad 2 (ft)

De

ep

Fou

nd

ation

Base

me

nt

Pile

Foo

ting

Du

al Structu

re

Floo

r /Slab System

Flat Slab

Final A

rea G

rou

p

Store

y

No

of P

arking

Lob

by Size (sft)

Toile

t per flo

or

No

of Stair case

Co

ncre

te Stren

gth (p

si)

Re

info

rce Ste

el G

rade

Transfo

rme

r (KV

A)

Ge

ne

rator (K

W)

Lift Capacity

74 1 100 30 1 1 1 1 Flat Plate 0 Gulshan-Bashundhara 7 100 200 8 2 4000 60 1250 1200 16

178 0 30 0 0 0 0 0 Two way 0 Gulshan-Bashundhara 6 20 100 12 1 4000 60 150 60 8

97 1 60 40 0 0 0 0 Two way 0 Mirpur-Md Pur 8 22 150 7 1 3500 72.5 250 70 6

174 0 50 0 0 0 0 0 Two way 0 Dhanmondi-Nilkhet 6 10 120 8 1 3500 60 80 40 8

170 1 30 40 1 0 1 0 Two way 0 Uttora-Ashkona-Balughat 6 10 80 8 1 4000 60 70 10 8



6 1 30 20 1 1 1 0 Two way 0 Mirpur-Md Pur 10 150 100 60 1 2500 60 350 70 12







77 1 20 15 1 0 1 0 Two way 0 Uttora-Ashkona-Balughat 6 6 120 7 1 3500 72.5 300 80 6

168 0 40 0 1 0 1 1 Two way 0 Nakalpara-Palton 7 6 130 6 1 3500 60 300 70 6





3 1 50 50 1 0 1 0 Two way 0 Gulshan-Bashundhara 7 6 150 6 1 3500 72.5 300 70 6



80 1 65 67 0 1 0 0 Two Way 0 Dhanmondi-Nilkhet 7 12 120 8 1 2500 60 150 32 6

C-2

504




505

DESCRIPTIVE STATISTICS Table D-1: Descriptive Statistics

N Range Minimum Maximum Mean

Statistic Statistic Statistic Statistic Statistic

Std. Error

Const_Cost 106 1300 900 2200 1494.88 26.583

Steel 106 26500 37000 63500 55503.77 657.417

Cement 106 185 225 410 355.75 3.298

Brick 106 3948 3168 7116 5500.08 116.315

Sand 106 1113 724 1837 1232.63 24.277

Paint 106 364 521 885 696.94 5.501

Mason 106 218 200 418 277.76 3.940

Helper 106 156 112 269 181.17 3.634

Carpenter 106 182 200 382 335.75 3.862

Transport 106 694 528 1222 1134.46 16.391

Duration 106 41 17 58 29.92 .833

Corner 106 1 0 1 .31 .045

Rd_1 106 53 12 65 32.91 1.396

Rd_2 106 67 0 67 9.01 1.647

Deep_Foundation 106 1 0 1 .44 .048

Basement 106 2 0 2 .25 .047

Pile 106 1 0 1 .46 .049

Dual 106 1 0 1 .15 .035

Area 106 20 3 23 8.08 .449

Plinth 106 9300 1500 10800 3951.58 206.687

Story 106 8 5 13 7.58 .176

Lobby 106 537 25 562 163.04 9.894

Toilet 106 57 3 60 9.24 .764

Stair 106 7 1 8 1.47 .114

Concrete 106 2000 2500 4500 3483.02 40.758

Steel_Grade 106 33 40 73 61.08 .541

Transformer 106 567 33 600 209.90 13.039

Generator 106 400 0 400 76.92 7.513

Lift 106 30 0 30 9.95 .517

Valid N (listwise) 106

D-1

APPENDIX-D




506

Std. Deviation Variance Skewness Kurtosis

Statistic Statistic Statistic Std. Error Statistic Std. Error

Const_Cost 273.688 74905.175 .596 .235 .308 .465

Steel 6768.526 4.581E7 -.992 .235 -.026 .465

Cement 33.957 1153.044 -1.524 .235 2.998 .465

Brick 1197.539 1434100.261 -.607 .235 -1.255 .465

Sand 249.951 62475.304 .099 .235 -.198 .465

Paint 56.640 3208.090 .014 .235 2.353 .465

Mason 40.561 1645.173 .461 .235 1.620 .465

Helper 37.409 1399.467 -.164 .235 -.473 .465

Carpenter 39.763 1581.117 -1.256 .235 2.032 .465

Transport 168.760 28479.918 -2.680 .235 6.079 .465

Duration 8.575 73.537 1.306 .235 1.738 .465

Corner .465 .216 .827 .235 -1.342 .465

Rd_1 14.377 206.696 .761 .235 -.631 .465

Rd_2 16.952 287.381 1.853 .235 2.397 .465

Deep_Foundation

.499 .249 .231 .235 -1.984 .465

Basement .479 .230 1.659 .235 1.879 .465

Pile .501 .251 .154 .235 -2.015 .465

Dual .360 .129 1.978 .235 1.950 .465

Area 4.628 21.416 1.741 .235 2.472 .465

Plinth 2127.972 4528266.856 1.617 .235 2.214 .465

Story 1.809 3.274 1.035 .235 .409 .465

Lobby 101.867 10376.894 1.941 .235 4.719 .465

Toilet 7.865 61.858 4.353 .235 22.043 .465

Stair 1.173 1.375 3.662 .235 15.004 .465

Concrete 419.631 176089.847 .170 .235 .129 .465

Steel_Grade 5.574 31.074 -.415 .235 5.588 .465

Transformer 134.241 18020.761 .890 .235 .360 .465

Generator 77.354 5983.615 3.141 .235 10.234 .465

Lift 5.319 28.293 1.547 .235 1.994 .465

D-2




507

PEARSON CORRELATIONS MATRIX

Table E-1: Pearson Correlation Matrix

Vari

able

Con

stru

ctio

n

Cost

Ste

el P

rice

Cem

ent

Price

Brick

Pri

ce

Sand P

rice

Pain

t P

rice

Maso

n W

age

1 Construction Cost (Tk per sft)

Correlation 1 .606** .632

** .807

** .919

** .661

** .942

**

Sig. (2-tailed) 0 0 0 0 0 0 N 106 106 106 106 106 106 106

2 Steel Price (Tk per Ton)

Correlation .606** 1 .631** .677** .579** .504** .646** Sig. (2-tailed) 0 0 0 0 0 0 N 106 106 106 106 106 106 106

3 Cement Price (Tk per Bag)

Correlation .632** .631** 1 .628** .596** .514** .622** Sig. (2-tailed) 0 0 0 0 0 0 N 106 106 106 106 106 106 106

4 Brick Price (Tk per 10000)

Correlation .807** .677** .628** 1 .712** .562** .887** Sig. (2-tailed) 0 0 0 0 0 0 N 106 106 106 106 106 106 106

5 Sand Price (Tk per 100 cft)

Correlation .919** .579** .596** .712** 1 .661** .899** Sig. (2-tailed) 0 0 0 0 0 0 N 106 106 106 106 106 106 106

6 Paint Price (Tk per gallon)

Correlation .661** .504** .514** .562** .661** 1 .632** Sig. (2-tailed) 0 0 0 0 0 0 N 106 106 106 106 106 106 106

7 Mason Wage (Tk per Day)

Correlation .942** .646** .622** .887** .899** .632** 1 Sig. (2-tailed) 0 0 0 0 0 0 N 106 106 106 106 106 106 106

8 Helper Wage (Tk per Day)

Correlation .887** .640** .620** .943** .797** .557** .954** Sig. (2-tailed) 0 0 0 0 0 0 0 N 106 106 106 106 106 106 106

9 Carpenter Wage (Tk per Day)

Correlation .761** .565

** .530

** .725

** .778

** .727

** .758

**

Sig. (2-tailed) 0 0 0 0 0 0 0 N 106 106 106 106 106 106 106

10 Transport Cost (Tk per 8 KM)

Correlation .613** .503** .409** .678** .667** .570** .663** Sig. (2-tailed) 0 0 0 0 0 0 0 N 106 106 106 106 106 106 106

11 Corner Plot (Yes/No)

Correlation -0.037 -0.034 -0.026 -0.04 -0.07 -0.08 -0.1 Sig. (2-tailed) 0.704 0.727 0.788 0.653 0.45 0.41 0.51 N 106 106 106 106 106 106 106

12 Road-1 Width (feet)


13 Road-2 Width (Feet)


14 Deep Foundation (Yes/No)

Correlation -0.114 -0.148 -0.133 -0.11 -0.1 0 -0.1 Sig. (2-tailed) 0.243 0.129 0.175 0.259 0.34 0.99 0.21 N 106 106 106 106 106 106 106

**. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed).

E-1

APPENDIX-E




508

Vari

able

Con

stru

ctio

n

Cost

Ste

el P

rice

Cem

ent

Pri

ce

Brick

P

rice

Sand P

rice

Pain

t P

rice

Maso

n

Wage

15 No of Basement Storey

Correlation 0.137 0.004 0.078 0.15 0.12 0.14 0.1 Sig. (2-tailed) 0.162 0.967 0.426 0.125 0.23 0.16 0.31 N 106 106 106 106 106 106 106

16 Pile Foundation (Yes/ No)

Correlation -0.071 -0.094 -0.122 -0.08 -0.04 0.05 -0.1 Sig. (2-tailed) 0.47 0.336 0.213 0.416 0.68 0.59 0.31 N 106 106 106 106 106 106 106

17 Dual Structural Form (Yes/ No)

Correlation -0.017 -0.053 -0.071 -0.02 0.03 0.08 -0 Sig. (2-tailed) 0.864 0.589 0.469 0.858 0.78 0.42 0.72 N 106 106 106 106 106 106 106

18 Total Project Area (Katha)

Correlation -0.156 -.255** -0.172 -0.17 -0.12 -0.1 -0.2 Sig. (2-tailed) 0.111 0.008 0.078 0.086 0.23 0.34 0.06 N 106 106 106 106 106 106 106

19 Total Plinth Area (sft)

Correlation -.225* -.317

** -.215

* -.252

** -.195

* -0.17 -.262

**

Sig. (2-tailed) 0.02 0.001 0.027 0.009 0.05 0.09 0.01 N 106 106 106 106 106 106 106

20 Total No of Storey

Correlation .313** 0.113 .212* .334** .286** .348** .273** Sig. (2-tailed) 0.001 0.248 0.029 0 0 0 0.01 N 106 106 106 106 106 106 106

21 Lobby Size per Floor (sft)

Correlation -0.015 -0.054 0.052 0 0.05 0.17 -0 Sig. (2-tailed) 0.875 0.585 0.598 0.996 0.63 0.08 0.7 N 106 106 106 106 106 106 106

22 No of Toilet per Floor

Correlation -.282** -.266** -.246* -.271** -.295** -0.14 -.302** Sig. (2-tailed) 0.003 0.006 0.011 0.005 0 0.14 0 N 106 106 106 106 106 106 106

23 No of Staircase


24 Design Concrete Strength (psi)

Correlation 0.1 -0.036 -0.015 0.047 0.07 -0.04 0.05 Sig. (2-tailed) 0.307 0.718 0.88 0.635 0.49 0.69 0.6 N 106 106 106 106 106 106 106

25 Steel Grade (Ksi)

Correlation 0.017 -0.092 0.026 -0.09 0.08 0.02 -0 Sig. (2-tailed) 0.861 0.347 0.793 0.347 0.41 0.86 0.7 N 106 106 106 106 106 106 106

26 Transformer Capacity (KVA)


27 Generator Capacity (KW)

Correlation 0.019 -0.076 -0.108 -0.02 0.05 0.08 -0 Sig. (2-tailed) 0.845 0.439 0.268 0.842 0.63 0.42 0.95 N 106 106 106 106 106 106 106

28 Total Lift Capacity (person)

Correlation .220* 0.11 0.1 0.148 .207* .240* 0.13 Sig. (2-tailed) 0.024 0.26 0.307 0.13 0.03 0.01 0.18 N 106 106 106 106 106 106 106


E-2




509

Vari

able

Help

er

Wage

Carp

ente

r W

age

Tra

nsp

ort

Cost

Corn

er

Plo

t

Road-1

W

idth

Road-2

Wid

th

Deep

Foundatio

n



** .613

** -0.04 -0.17 -0.085 -0.114

Sig. (2-tailed) 0 0 0 0.704 0.088 0.389 0.243 N 106 106 106 106 106 106 106



** .503

** -0.03 -0.16 -0.144 -0.148

Sig. (2-tailed) 0 0 0 0.727 0.114 0.141 0.129 N 106 106 106 106 106 106 106



** .409

** -0.03 -0.14 -0.014 -0.133

Sig. (2-tailed) 0 0 0 0.788 0.156 0.884 0.175 N 106 106 106 106 106 106 106


Correlation .943** .725** .678** -0.04 -0.12 -0.066 -0.111 Sig. (2-tailed) 0 0 0 0.653 0.237 0.499 0.259 N 106 106 106 106 106 106 106




Correlation .557** .727** .570** -0.08 -0.18 -0.112 0.002 Sig. (2-tailed) 0 0 0 0.413 0.064 0.253 0.985 N 106 106 106 106 106 106 106




Correlation 1 .692** .609** -0.03 -0.1 -0.037 -0.117 Sig. (2-tailed) 0 0 0.762 0.314 0.704 0.231 N 106 106 106 106 106 106 106


Correlation .692** 1 .732** -0.11 -0.1 -0.148 -0.036 Sig. (2-tailed) 0 0 0.272 0.316 0.13 0.714 N 106 106 106 106 106 106 106


Correlation .609** .732** 1 -.199* -0.07 -0.165 -0.17 Sig. (2-tailed) 0 0 0.04 0.48 0.091 0.081 N 106 106 106 106 106 106 106


Correlation -0.03 -0.108 -.199* 1 0.177 .794** -0.026 Sig. (2-tailed) 0.76 0.272 0.04 0.07 0 0.792 N 106 106 106 106 106 106 106


Correlation -0.1 -0.098 -0.07 0.177 1 .437** -0.08 Sig. (2-tailed) 0.31 0.316 0.48 0.07 0 0.413 N 106 106 106 106 106 106 106


Correlation -0.04 -0.148 -0.17 .794** .437** 1 -0.038 Sig. (2-tailed) 0.7 0.13 0.09 0 0 0.702 N 106 106 106 106 106 106 106


Correlation -0.12 -0.036 -0.17 -0.03 -0.08 -0.038 1 Sig. (2-tailed) 0.23 0.714 0.08 0.792 0.413 0.702 N 106 106 106 106 106 106 106


E-3




510

Variable

Help

er

Wage

Carp

ente

r W

age

Tra

nsp

ort

Cost

Corn

er

Plo

t

Road-1

W

idth

Roa

d-2

Wid

th

Deep

Foundatio

n


Correlation 0.15 0.173 0.04 0.068 0.103 0.065 .280** Sig. (2-tailed) 0.13 0.076 0.69 0.488 0.293 0.506 0.004 N 106 106 106 106 106 106 106


Correlation -0.1 0.034 -0.11 0.03 -0.04 0.066 .848** Sig. (2-tailed) 0.3 0.733 0.28 0.757 0.723 0.504 0 N 106 106 106 106 106 106 106


Correlation -0.02 0.02 0.03 -0.06 0.008 -0.091 .260**

Sig. (2-tailed) 0.86 0.842 0.76 0.57 0.933 0.354 0.007 N 106 106 106 106 106 106 106


Correlation -0.18 -0.065 -0.16 -0.08 -0 -0.092 0.157 Sig. (2-tailed) 0.07 0.505 0.11 0.427 0.985 0.35 0.109 N 106 106 106 106 106 106 106


Correlation -.251** -0.163 -.238* -0.08 0.012 -0.09 0.188 Sig. (2-tailed) 0.01 0.096 0.01 0.415 0.899 0.361 0.054 N 106 106 106 106 106 106 106


Correlation .293** .455** .244* -0.14 0.136 -0.103 -0.026 Sig. (2-tailed) 0 0 0.01 0.155 0.164 0.295 0.789 N 106 106 106 106 106 106 106


Correlation -0.06 0.144 0.12 -0.06 -0.05 -0.1 0.054 Sig. (2-tailed) 0.57 0.14 0.21 0.551 0.607 0.307 0.585 N 106 106 106 106 106 106 106


Correlation -.325** -0.132 -.266** -0.03 -0.14 -0.058 0.184 Sig. (2-tailed) 0 0.176 0.01 0.735 0.16 0.553 0.059 N 106 106 106 106 106 106 106


Correlation -0.18 -0.139 0.04 -0.01 -0.11 -0.09 -0.035 Sig. (2-tailed) 0.07 0.157 0.67 0.92 0.268 0.357 0.719 N 106 106 106 106 106 106 106


Correlation 0.04 0 -0 -0.13 -0.01 -.204* -0.032 Sig. (2-tailed) 0.69 1 0.97 0.172 0.901 0.036 0.745 N 106 106 106 106 106 106 106


Correlation -0.08 -0.057 -0.09 0.162 0.129 0.107 0.039 Sig. (2-tailed) 0.42 0.558 0.37 0.096 0.188 0.274 0.688 N 106 106 106 106 106 106 106


Correlation -0.18 0.024 -0.1 0.033 0.152 -0.051 .228* Sig. (2-tailed) 0.07 0.809 0.33 0.733 0.12 0.603 0.019 N 106 106 106 106 106 106 106


Correlation 0.02 0.067 -0.04 0.082 .242* 0.087 0.048 Sig. (2-tailed) 0.85 0.497 0.69 0.401 0.012 0.373 0.627 N 106 106 106 106 106 106 106


Correlation 0.14 .295** 0.17 -0.03 0.052 -0.063 0.065 Sig. (2-tailed) 0.16 0.002 0.08 0.741 0.597 0.518 0.506 N 106 106 106 106 106 106 106


E-4




511

Vari

able

No o

f B

asem

ent

Pile

F

oundatio

n

Dual S

truct

ura

l F

orm

Tota

l Pro

ject

A

rea

Plin

th A

rea

No of S

tory

Lobby S

ize


Correlation 0.137 -0.071 -0.017 -0.156 -.225* .313

** -0.015

Sig. (2-tailed) 0.162 0.47 0.864 0.111 0.02 0.001 0.875 N 106 106 106 106 106 106 106


Correlation 0.004 -0.094 -0.053 -.255** -.317

** 0.113 -0.054

Sig. (2-tailed) 0.967 0.336 0.589 0.008 0.001 0.248 0.585 N 106 106 106 106 106 106 106


Correlation 0.078 -0.122 -0.071 -0.172 -.215* .212

* 0.052

Sig. (2-tailed) 0.426 0.213 0.469 0.078 0.027 0.029 0.598 N 106 106 106 106 106 106 106


Correlation 0.15 -0.08 -0.018 -0.167 -.252** .334** 0 Sig. (2-tailed) 0.125 0.416 0.858 0.086 0.009 0 0.996 N 106 106 106 106 106 106 106


Correlation 0.118 -0.04 0.027 -0.118 -.195* .286** 0.047 Sig. (2-tailed) 0.228 0.684 0.784 0.227 0.045 0.003 0.634 N 106 106 106 106 106 106 106


Correlation 0.138 0.053 0.079 -0.095 -0.165 .348** 0.174 Sig. (2-tailed) 0.158 0.593 0.42 0.335 0.092 0 0.075 N 106 106 106 106 106 106 106


Correlation 0.1 -0.1 -0.035 -0.187 -.262** .273** -0.037 Sig. (2-tailed) 0.306 0.308 0.722 0.055 0.007 0.005 0.704 N 106 106 106 106 106 106 106


Correlation 0.147 -0.102 -0.018 -0.177 -.251** .293** -0.056 Sig. (2-tailed) 0.131 0.299 0.855 0.07 0.009 0.002 0.569 N 106 106 106 106 106 106 106


Correlation 0.173 0.034 0.02 -0.065 -0.163 .455** 0.144 Sig. (2-tailed) 0.076 0.733 0.842 0.505 0.096 0 0.14 N 106 106 106 106 106 106 106


Correlation 0.039 -0.105 0.03 -0.158 -.238* .244* 0.123 Sig. (2-tailed) 0.693 0.283 0.761 0.107 0.014 0.012 0.207 N 106 106 106 106 106 106 106


Correlation 0.068 0.03 -0.056 -0.078 -0.08 -0.139 -0.059 Sig. (2-tailed) 0.488 0.757 0.57 0.427 0.415 0.155 0.551 N 106 106 106 106 106 106 106


Correlation 0.103 -0.035 0.008 -0.002 0.012 0.136 -0.051 Sig. (2-tailed) 0.293 0.723 0.933 0.985 0.899 0.164 0.607 N 106 106 106 106 106 106 106


Correlation 0.065 0.066 -0.091 -0.092 -0.09 -0.103 -0.1 Sig. (2-tailed) 0.506 0.504 0.354 0.35 0.361 0.295 0.307 N 106 106 106 106 106 106 106


Correlation .280** .848** .260** 0.157 0.188 -0.026 0.054 Sig. (2-tailed) 0.004 0 0.007 0.109 0.054 0.789 0.585 N 106 106 106 106 106 106 106


E-5




512

Vari

able

No o

f B

asem

ent

Pile

F

oundatio

n

Dual S

truct

ura

l F

orm

Tota

l Pro

ject

A

rea

Plin

th A

rea

No of S

tory

Lobby S

ize


Correlation 1 .298** 0.051 .295

** .314

** .431

** .193

*

Sig. (2-tailed) 0.002 0.603 0.002 0.001 0 0.048 N 106 106 106 106 106 106 106


Correlation .298** 1 .243* 0.181 0.172 0.077 0.112 Sig. (2-tailed) 0.002 0.012 0.063 0.079 0.432 0.252 N 106 106 106 106 106 106 106


Correlation 0.051 .243* 1 -0.058 -0.064 0.024 -0.005 Sig. (2-tailed) 0.603 0.012 0.557 0.512 0.807 0.957 N 106 106 106 106 106 106 106


Correlation .295** 0.181 -0.058 1 .973

** .423

** .581

**

Sig. (2-tailed) 0.002 0.063 0.557 0 0 0 N 106 106 106 106 106 106 106


Correlation .314** 0.172 -0.064 .973** 1 .358** .554** Sig. (2-tailed) 0.001 0.079 0.512 0 0 0 N 106 106 106 106 106 106 106


Correlation .431** 0.077 0.024 .423** .358** 1 .385** Sig. (2-tailed) 0 0.432 0.807 0 0 0 N 106 106 106 106 106 106 106


Correlation .193* 0.112 -0.005 .581** .554** .385** 1 Sig. (2-tailed) 0.048 0.252 0.957 0 0 0 N 106 106 106 106 106 106 106


Correlation 0.108 0.144 -0.131 .599** .612** 0.065 .245* Sig. (2-tailed) 0.272 0.142 0.182 0 0 0.507 0.011 N 106 106 106 106 106 106 106


Correlation -0.029 -0.034 -0.012 .278** .265** -0.028 0.188 Sig. (2-tailed) 0.765 0.727 0.9 0.004 0.006 0.775 0.054 N 106 106 106 106 106 106 106


Correlation -0.026 -0.008 0.143 .216* 0.178 .211* 0.141 Sig. (2-tailed) 0.794 0.938 0.143 0.026 0.068 0.03 0.148 N 106 106 106 106 106 106 106


Correlation 0.029 0.117 0.155 -0.043 -0.046 0.04 0.077 Sig. (2-tailed) 0.766 0.232 0.113 0.663 0.636 0.681 0.432 N 106 106 106 106 106 106 106


Correlation .295** .234* 0.146 .610** .593** .329** .507** Sig. (2-tailed) 0.002 0.016 0.135 0 0 0.001 0 N 106 106 106 106 106 106 106


Correlation .309** 0.161 0.02 .561** .501** .424** .357** Sig. (2-tailed) 0.001 0.1 0.836 0 0 0 0 N 106 106 106 106 106 106 106


Correlation .457** 0.148 -0.146 .659** .591** .568** .507** Sig. (2-tailed) 0 0.131 0.136 0 0 0 0 N 106 106 106 106 106 106 106


E-6




513

Vari

able

Toile

t per

Flo

or

Sta

irca

se

Concr

ete

S

trength

Ste

el G

rade

Tra

nsf

orm

er

Capaci

ty

Genera

tor

C

apaci

ty

Lift C

apaci

ty


Correlation -.282** -0.14 0.1 0.017 -0.132 0.019 .220

*

Sig. (2-tailed) 0.003 0.154 0.307 0.861 0.179 0.845 0.024 N 106 106 106 106 106 106 106


Correlation -.266** -0.136 -0.036 -0.092 -0.166 -0.076 0.11

Sig. (2-tailed) 0.006 0.163 0.718 0.347 0.088 0.439 0.26 N 106 106 106 106 106 106 106


Correlation -.246* -0.177 -0.015 0.026 -0.121 -0.108 0.1

Sig. (2-tailed) 0.011 0.07 0.88 0.793 0.218 0.268 0.307 N 106 106 106 106 106 106 106


Correlation -.271** -0.169 0.047 -0.092 -0.13 -0.02 0.148 Sig. (2-tailed) 0.005 0.083 0.635 0.347 0.184 0.842 0.13 N 106 106 106 106 106 106 106


Correlation -.295** -0.082 0.068 0.082 -0.038 0.048 .207* Sig. (2-tailed) 0.002 0.401 0.491 0.405 0.698 0.628 0.033 N 106 106 106 106 106 106 106


Correlation -0.144 0.044 -0.039 0.017 0.032 0.08 .240* Sig. (2-tailed) 0.141 0.651 0.69 0.859 0.745 0.416 0.013 N 106 106 106 106 106 106 106


Correlation -.302** -0.146 0.051 -0.038 -0.171 -0.006 0.131 Sig. (2-tailed) 0.002 0.135 0.603 0.699 0.08 0.947 0.182 N 106 106 106 106 106 106 106


Correlation -.325** -0.18 0.039 -0.078 -0.176 0.019 0.136 Sig. (2-tailed) 0.001 0.065 0.691 0.424 0.071 0.85 0.163 N 106 106 106 106 106 106 106


Correlation -0.132 -0.139 0 -0.057 0.024 0.067 .295** Sig. (2-tailed) 0.176 0.157 1 0.558 0.809 0.497 0.002 N 106 106 106 106 106 106 106


Correlation -.266** 0.042 -0.004 -0.089 -0.096 -0.04 0.17 Sig. (2-tailed) 0.006 0.67 0.967 0.367 0.329 0.685 0.081 N 106 106 106 106 106 106 106


Correlation -0.033 -0.01 -0.134 0.162 0.033 0.082 -0.032 Sig. (2-tailed) 0.735 0.92 0.172 0.096 0.733 0.401 0.741 N 106 106 106 106 106 106 106


Correlation -0.137 -0.109 -0.012 0.129 0.152 .242* 0.052 Sig. (2-tailed) 0.16 0.268 0.901 0.188 0.12 0.012 0.597 N 106 106 106 106 106 106 106


Correlation -0.058 -0.09 -.204* 0.107 -0.051 0.087 -0.063 Sig. (2-tailed) 0.553 0.357 0.036 0.274 0.603 0.373 0.518 N 106 106 106 106 106 106 106


Correlation 0.184 -0.035 -0.032 0.039 .228* 0.048 0.065 Sig. (2-tailed) 0.059 0.719 0.745 0.688 0.019 0.627 0.506 N 106 106 106 106 106 106 106


E-7




514

Vari

able

Toile

t per

Flo

or

Sta

irca

se

Concr

ete

S

trength

Ste

el G

rade

Tra

nsf

orm

er

Capaci

ty

Genera

tor

C

apaci

ty

Lift C

apaci

ty


Correlation 0.108 -0.029 -0.026 0.029 .295** .309

** .457

**

Sig. (2-tailed) 0.272 0.765 0.794 0.766 0.002 0.001 0 N 106 106 106 106 106 106 106


Correlation 0.144 -0.034 -0.008 0.117 .234* 0.161 0.148

Sig. (2-tailed) 0.142 0.727 0.938 0.232 0.016 0.1 0.131 N 106 106 106 106 106 106 106


Correlation -0.131 -0.012 0.143 0.155 0.146 0.02 -0.146 Sig. (2-tailed) 0.182 0.9 0.143 0.113 0.135 0.836 0.136 N 106 106 106 106 106 106 106


Correlation .599** .278** .216* -0.043 .610** .561** .659** Sig. (2-tailed) 0 0.004 0.026 0.663 0 0 0 N 106 106 106 106 106 106 106


Correlation .612** .265** 0.178 -0.046 .593** .501** .591** Sig. (2-tailed) 0 0.006 0.068 0.636 0 0 0 N 106 106 106 106 106 106 106


Correlation 0.065 -0.028 .211* 0.04 .329** .424** .568** Sig. (2-tailed) 0.507 0.775 0.03 0.681 0.001 0 0 N 106 106 106 106 106 106 106


Correlation .245* 0.188 0.141 0.077 .507** .357** .507** Sig. (2-tailed) 0.011 0.054 0.148 0.432 0 0 0 N 106 106 106 106 106 106 106


Correlation 1 .229* -0.185 -0.066 .308** 0.051 .217* Sig. (2-tailed) 0.018 0.057 0.5 0.001 0.602 0.026 N 106 106 106 106 106 106 106


Correlation .229* 1 -0.042 -0.079 0.124 0.075 .220* Sig. (2-tailed) 0.018 0.672 0.421 0.206 0.444 0.023 N 106 106 106 106 106 106 106


Correlation -0.185 -0.042 1 .212* .246* 0.148 .205* Sig. (2-tailed) 0.057 0.672 0.03 0.011 0.129 0.035 N 106 106 106 106 106 106 106


Correlation -0.066 -0.079 .212* 1 .389** 0.035 -0.062 Sig. (2-tailed) 0.5 0.421 0.03 0 0.718 0.524 N 106 106 106 106 106 106 106


Correlation .308** 0.124 .246* .389** 1 .440** .439** Sig. (2-tailed) 0.001 0.206 0.011 0 0 0 N 106 106 106 106 106 106 106


Correlation 0.051 0.075 0.148 0.035 .440** 1 .624** Sig. (2-tailed) 0.602 0.444 0.129 0.718 0 0 N 106 106 106 106 106 106 106


Correlation .217* .220* .205* -0.062 .439** .624** 1 Sig. (2-tailed) 0.026 0.023 0.035 0.524 0 0 N 106 106 106 106 106 106 106


E-8




APPENDIX-F

BIVARIATE DATA ANALISIS AND CURVE FITTING

Table F-1: Curve Fit: The independent variable is Steel.

Model Summary and Parameter Estimates

Dependent Variable:Const_Cost

Equation

Model Summary Parameter Estimates

R Square F df1 df2 Sig. Constant Constant b1 b2 b3

Linear .367 60.362 1 104 .000 134.795 .025

Logarithmic .361 58.678 1 104 .000 -12134.908 1248.599

Inverse .351 56.157 1 104 .000 2633.087 -6.210E7

Quadratic .371 30.432 2 103 .000 1190.664 -.017 3.955E-7

Cubic .372 30.476 2 103 .000 888.533 .002 .000 2.681E-12

Compound .410 72.412 1 104 .000 569.728 1.000

Power .407 71.400 1 104 .000 .105 .875

S .400 69.230 1 104 .000 8.095 -43728.994

Growth .410 72.412 1 104 .000 6.345 1.709E-5

Exponential .410 72.412 1 104 .000 569.728 1.709E-5

Logistic .410 72.412 1 104 .000 .002 1.000

The independent variable is Steel.

F-1

515




F-2

Figure F-1: Construction Cost vs. Steel Price

516




Table F-2: Curve Fit: Independent Variable is Cement



Equation



Linear .399 69.078 1 104 .000 -316.597 5.092

Logarithmic .366 60.000 1 104 .000 -7768.503 1578.320

Inverse .327 50.600 1 104 .000 2830.660 -470036.740

Quadratic .483 48.105 2 103 .000 4329.669 -23.503 .043

Cubic .492 49.833 2 103 .000 2024.838 .000 -.035 8.397E-5

Compound .428 77.764 1 104 .000 426.882 1.003

Power .398 68.685 1 104 .000 2.516 1.085

S .361 58.869 1 104 .000 8.219 -325.809

Growth .428 77.764 1 104 .000 6.057 .003

Exponential .428 77.764 1 104 .000 426.882 .003

Logistic .428 77.764 1 104 .000 .002 .997

The independent variable is Cement.

F-3

517




F-4

Figure F-2: Construction Cost vs. Cement Price

518




Table F-3: Curve Fit: The independent variable is Brick.



Equation



Linear .651 194.356 1 104 .000 480.344 .184

Logarithmic .641 185.624 1 104 .000 -6326.512 910.977

Inverse .622 171.312 1 104 .000 2320.842 -4290853.798

Quadratic .658 99.113 2 103 .000 1104.013 -.073 2.504E-5

Cubic .662 100.949 2 103 .000 1113.035 .000 -5.621E-6 2.965E-9

Compound .713 258.574 1 104 .000 730.268 1.000

Power .713 258.501 1 104 .000 6.371 .634

S .704 247.438 1 104 .000 7.873 -3010.574

Growth .713 258.574 1 104 .000 6.593 .000

Exponential .713 258.574 1 104 .000 730.268 .000

Logistic .713 258.574 1 104 .000 .001 1.000

The independent variable is Brick.

F-5

519




F-6

Figure F-3: Construction Cost vs. Brick Price

520




Table F-4: Curve Fit: Independent variable is Sand.



Equation



Linear .844 561.782 1 104 .000 255.072 1.006

Logarithmic .796 406.061 1 104 .000 -6699.290 1154.835

Inverse .714 259.834 1 104 .000 2517.171 -1205441.790

Quadratic .859 312.574 2 103 .000 856.990 -.002 .000

Cubic .861 210.892 3 102 .000 51.072 2.157 -.001 5.053E-7

Compound .852 596.735 1 104 .000 646.808 1.001

Power .830 508.121 1 104 .000 5.898 .778

S .771 349.946 1 104 .000 7.994 -826.089

Growth .852 596.735 1 104 .000 6.472 .001

Exponential .852 596.735 1 104 .000 646.808 .001

Logistic .852 596.735 1 104 .000 .002 .999

The independent variable is Sand.

F-7

521




F-8

Figure F-4: Construction Cost vs. Sand Price

522




Table F-5: Curve Fit: Independent Variable is Paint.



Equation



Linear .436 80.536 1 104 .000 -729.879 3.192

Logarithmic .447 84.080 1 104 .000 -13026.875 2219.307

Inverse .447 84.189 1 104 .000 3656.280 -1496240.602

Quadratic .462 44.278 2 103 .000 -3985.111 12.590 -.007

Cubic .469 45.428 2 103 .000 -3165.856 8.454 .000 -3.567E-6

Compound .468 91.549 1 104 .000 321.733 1.002

Power .485 97.955 1 104 .000 .068 1.525

S .492 100.533 1 104 .000 8.788 -1034.478

Growth .468 91.549 1 104 .000 5.774 .002

Exponential .468 91.549 1 104 .000 321.733 .002

Logistic .468 91.549 1 104 .000 .003 .998

The independent variable is Paint.

F-9

523




F-10

Figure F-5: Construction Cost vs. Paint Price

524




Table F-6: Curve Fit: Independent Variable is Mason.



Equation



Linear .887 812.612 1 104 .000 -269.797 6.353

Logarithmic .871 702.077 1 104 .000 -8309.555 1745.737

Inverse .831 512.662 1 104 .000 3168.415 -455074.758

Quadratic .887 402.622 2 103 .000 -325.272 6.748 .000

Cubic .887 403.705 2 103 .000 -357.388 6.819 .000 -1.834E-6

Compound .893 864.061 1 104 .000 457.448 1.004

Power .901 944.653 1 104 .000 2.048 1.171

S .882 779.593 1 104 .000 8.431 -309.227

Growth .893 864.061 1 104 .000 6.126 .004

Exponential .893 864.061 1 104 .000 457.448 .004

Logistic .893 864.061 1 104 .000 .002

The independent variable is Mason.

F-11

525




F-12

Figure F-6: Construction Cost vs. Mason Wage

526




Table F-7: Curve Fit: Independent Variable is Helper.



Equation



Linear .788 385.448 1 104 .000 318.675 6.492

Logarithmic .738 293.267 1 104 .000 -4055.794 1072.257

Inverse .677 218.204 1 104 .000 2460.452 -166807.939

Quadratic .822 238.595 2 103 .000 1239.181 -4.317 .030

Cubic .823 238.655 2 103 .000 987.908 .000 .007 4.188E-5

Compound .800 416.627 1 104 .000 672.852 1.004

Power .769 346.015 1 104 .000 35.060 .722

S .722 269.590 1 104 .000 7.951 -113.575

Growth .800 416.627 1 104 .000 6.512 .004

Exponential .800 416.627 1 104 .000 672.852 .004

Logistic .800 416.627 1 104 .000 .001 .996

The independent variable is Helper.

F-13

527




F-14

Figure F-7: Construction Cost vs. Helper Wage

528




Table F-8: Curve Fit: Independent Variable is Mason



Equation



Linear .887 812.612 1 104 .000 -269.797 6.353

Logarithmic .871 702.077 1 104 .000 -8309.555 1745.737

Inverse .831 512.662 1 104 .000 3168.415 -455074.758

Quadratic .887 402.622 2 103 .000 -325.272 6.748 .000

Cubic .887 403.705 2 103 .000 -357.388 6.819 .000 -1.834E-6

Compound .893 864.061 1 104 .000 457.448 1.004

Power .901 944.653 1 104 .000 2.048 1.171

S .882 779.593 1 104 .000 8.431 -309.227

Growth .893 864.061 1 104 .000 6.126 .004

Exponential .893 864.061 1 104 .000 457.448 .004

Logistic .893 864.061 1 104 .000 .002 .996

The independent variable is Mason.

F-15

529




F-16

Figure F-8: Construction Cost vs. Mason Wage

530




Table F-9: Curve Fit: Independent Variable is Carpenter



Equation



Linear .578 142.727 1 104 .000 -262.792 5.235

Logarithmic .537 120.544 1 104 .000 -7357.609 1524.079

Inverse .481 96.502 1 104 .000 2762.732 -418403.052

Quadratic .629 87.131 2 103 .000 2141.198 -10.565 .025

Cubic .633 88.704 2 103 .000 1208.039 .000 -.013 4.459E-5

Compound .635 180.944 1 104 .000 436.550 1.004

Power .602 157.228 1 104 .000 3.037 1.064

S .552 128.377 1 104 .000 8.190 -295.673

Growth .635 180.944 1 104 .000 6.079 .004

Exponential .635 180.944 1 104 .000 436.550 .004

Logistic .635 180.944 1 104 .000 .002 .996

The independent variable is Carpenter.

F-17

531




F-18

Figure F-9: Construction Cost vs. Carpenter Wage

532




Table F-10: Curve Fit: Independent Variable is Transport.



Equation



Linear .375 62.443 1 104 .000 367.978 .993

Logarithmic .334 52.264 1 104 .000 -4230.104 815.719

Inverse .295 43.555 1 104 .000 2071.249 -629416.865

Quadratic .560 65.599 2 103 .000 3962.217 -7.691 .005

Cubic .607 79.606 2 103 .000 1994.492 .000 -.005 3.689E-6

Compound .459 88.220 1 104 .000 646.427 1.001

Power .416 74.048 1 104 .000 21.819 .600

S .373 61.859 1 104 .000 7.721 -466.667

Growth .459 88.220 1 104 .000 6.471 .001

Exponential .459 88.220 1 104 .000 646.427 .001

Logistic .459 88.220 1 104 .000 .002 .999

The independent variable is Transport.

F-19

533




F-20

Figure F-10: Construction Cost vs. Transport Cost

534




Table F-11: Curve Fit: Independent Variable is Duration.



Equation



Linear .149 18.263 1 104 .000 1863.995 -12.335

Logarithmic .130 15.519 1 104 .000 2758.569 -375.781

Inverse .103 11.889 1 104 .001 1140.044 9917.468

Quadratic .157 9.618 2 103 .000 1587.810 4.656 -.240

Cubic .179 7.399 3 102 .000 123.576 140.606 -4.202 .036

Compound .163 20.291 1 104 .000 1897.166 .992

Power .140 16.886 1 104 .000 3491.646 -.257

S .108 12.641 1 104 .001 7.053 6.723

Growth .163 20.291 1 104 .000 7.548 -.009

Exponential .163 20.291 1 104 .000 1897.166 -.009

Logistic .163 20.291 1 104 .000 .001 1.009

The independent variable is Duration.

F-21

535




F-22

Figure F-11: Construction Cost vs. Project Duration

536




Table F-12: Curve Fit (Not Significant): Independent Variable is Rd-1



Equation



Linear .029 3.058 1 104 .083 1580.497 -2.502

Logarithmic .026 2.782 1 104 .098 1823.674 -96.146

Inverse .021 2.242 1 104 .137 1398.917 2665.660

Quadratic .029 1.538 2 103 .220 1599.200 -3.447 .009

Cubic .039 1.390 3 102 .250 1378.434 13.090 -.327 .002

Compound .032 3.408 1 104 .068 1561.031 .998

Power .028 3.025 1 104 .085 1843.575 -.066

S .023 2.397 1 104 .125 7.228 1.817

Growth .032 3.408 1 104 .068 7.353 -.002

Exponential .032 3.408 1 104 .068 1561.031 -.002

Logistic .032 3.408 1 104 .068 .001 1.002

The independent variable is Rd_1.

F-23

537




F-24

Figure F-12: Construction Cost vs. Road-1

538




Table F-13: Curve Fit (Not Significance): Independent Variable is Rd_2



Equation



Linear .007 .749 1 104 .389 1507.177 -1.365

Logarithmica . . . . . .000 .000

Inverseb . . . . . .000 .000

Quadratic .008 .422 2 103 .657 1509.531 -2.915 .032

Cubic .010 .334 3 102 .801 1511.311 -7.492 .260 -.003

Compound .010 1.082 1 104 .301 1485.226 .999

Powera . . . . . .000 .000

Sb . . . . . .000 .000

Growth .010 1.082 1 104 .301 7.303 -.001

Exponential .010 1.082 1 104 .301 1485.226 -.001

Logistic .010 1.082 1 104 .301 .001 1.001

The independent variable is Rd_2.

a. The independent variable (Rd_2) contains non-positive values. The minimum value is 0. The

Logarithmic and Power models cannot be calculated.

b. The independent variable (Rd_2) contains values of zero. The Inverse and S models cannot be

calculated.

F-25

539




F-26

Figure F-13: Construction Cost vs. Road-2

540




Table F-14: Curve Fit : Independent Variable is Area.



Equation



Linear .041 4.392 1 104 .039 1574.462 -9.404

Logarithmic .011 1.116 1 104 .293 1604.165 -55.154

Inverse .000 .029 1 104 .865 1483.699 72.753

Quadratic .112 6.499 2 103 .002 1333.868 38.495 -1.560

Cubic .133 5.234 3 102 .002 1085.314 112.663 -7.435 .125

Compound .055 6.007 1 104 .016 1563.259 .993

Power .017 1.820 1 104 .180 1612.191 -.046

S .002 .162 1 104 .688 7.276 .113

Growth .055 6.007 1 104 .016 7.355 -.007

Exponential .055 6.007 1 104 .016 1563.259 -.007

Logistic .055 6.007 1 104 .016 .001 1.007

The independent variable is Area.

F-27

541




F-28

Figure F-14: Construction Cost vs. Total Area

542




Table F-15: Curve Fit: Independent Variable is Plinth.



Equation



Linear .069 7.679 1 104 .007 1564.401 -.015

Logarithmic .046 4.979 1 104 .028 2339.769 -102.981

Inverse .017 1.804 1 104 .182 1412.567 265406.600

Quadratic .072 3.983 2 103 .022 1588.874 -.023 2.371E-7

Cubic .097 3.650 3 102 .015 1445.587 .038 -4.919E-6 9.400E-11

Compound .087 9.870 1 104 .002 1548.553 1.000

Power .061 6.721 1 104 .011 2796.097 -.078

S .024 2.584 1 104 .111 7.229 208.752

Growth .087 9.870 1 104 .002 7.345 -1.132E-5

Exponential .087 9.870 1 104 .002 1548.553 -1.132E-5

Logistic .087 9.870 1 104 .002 .001 1.000

The independent variable is Plinth.

F-29

543




F-30

Figure F-15: Construction Cost vs. Plinth Area

544




Table F-16: Curve Fit: Independent Variable is Storey.



Equation



Linear .097 10.996 1 102 .001 1137.032 47.222

Logarithmic .104 11.863 1 102 .001 699.342 397.870

Inverse .107 12.168 1 102 .001 1928.833 -3130.590

Quadratic .114 6.528 2 101 .002 476.286 212.074 -9.697

Cubic .116 6.605 2 101 .002 697.760 130.288 .000 -.369

Compound .105 11.920 1 102 .001 1151.099 1.033

Power .111 12.672 1 102 .001 856.428 .270

S .112 12.823 1 102 .001 7.586 -2.114

Growth .105 11.920 1 102 .001 7.048 .032

Exponential .105 11.920 1 102 .001 1151.099 .032

Logistic .105 11.920 1 102 .001 .001 .968

The independent variable is Story.

F-31

545




F-32

Figure F-16: Construction Cost vs. No of Storey

546




Table F-17: Curve Fit: Independent Variable is Lobby (Not Significance)



Equation



Linear .002 .202 1 104 .654 1511.707 -.101

Logarithmic .000 .031 1 104 .860 1534.082 -7.946

Inverse .000 .023 1 104 .881 1489.259 649.305

Quadratic .014 .720 2 103 .489 1449.544 .481 .000

Cubic .016 .559 3 102 .643 1491.127 -.114 .001 -1.643E-6

Compound .001 .108 1 104 .743 1482.849 1.000

Power .000 .003 1 104 .954 1483.380 -.002

S .000 .018 1 104 .893 7.290 .384

Growth .001 .108 1 104 .743 7.302 -4.888E-5

Exponential .001 .108 1 104 .743 1482.849 -4.888E-5

Logistic .001 .108 1 104 .743 .001 1.000

The independent variable is Lobby.

F-33

547




F-34

Figure F-17: Construction Cost vs. Lobby Size

548




Table F-18: Curve Fit: Independent Variable is Numbers of Toilet per floor.



Equation



Linear .080 8.983 1 104 .003 1585.498 -9.812

Logarithmic .114 13.333 1 104 .000 1875.076 -184.597

Inverse .139 16.790 1 104 .000 1252.540 1715.268

Quadratic .090 5.101 2 103 .008 1657.329 -21.000 .215

Cubic .097 3.663 3 102 .015 1737.406 -38.283 1.084 -.011

Compound .087 9.919 1 104 .002 1565.779 .993

Power .114 13.375 1 104 .000 1890.724 -.122

S .128 15.306 1 104 .000 7.140 1.087

Growth .087 9.919 1 104 .002 7.356 -.007

Exponential .087 9.919 1 104 .002 1565.779 -.007

Logistic .087 9.919 1 104 .002 .001 1.007

The independent variable is Toilet.

F-35

549




F-36

Figure F-18: Construction Cost vs. Toilet per Floor

550




Table F-19: Curve Fit: Independent Variable is total numbers of Stairs (Not Significance)



Equation

Model Summary

Parameter

Estimates


Linear .019 2.066 1 104 .154 1542.813 -32.572

Logarithmic .012 1.218 1 104 .272 1509.732 -63.007

Inverse .006 .664 1 104 .417 1423.730 83.132

Quadratic .025 1.343 2 103 .266 1482.645 28.905 -8.590

Cubic .026 .919 3 102 .435 1436.629 93.660 -30.712 1.925

Compound .019 1.965 1 104 .164 1516.917 .979

Power .011 1.132 1 104 .290 1484.801 -.040

S .006 .616 1 104 .434 7.248 .053

Growth .019 1.965 1 104 .164 7.324 -.021

Exponential .019 1.965 1 104 .164 1516.917 -.021

Logistic .019 1.965 1 104 .164 .001 1.021

The independent variable is Stair.

F-37

551




F-38

Figure F-19: Construction Cost vs. No of Stair

552




Table F-20: Curve Fit: Independent Variable is Concrete strength.



Equation



Linear .010 1.054 1 104 .307 1267.301 .065

Logarithmic .010 1.030 1 104 .312 -322.827 223.075

Inverse .010 1.042 1 104 .310 1715.474 -757185.710

Quadratic .011 .583 2 103 .560 1719.510 -.195 3.707E-5

Cubic .013 .661 2 103 .518 1593.030 .000 -4.260E-5 9.664E-9

Compound .007 .742 1 104 .391 1296.539 1.000

Power .007 .763 1 104 .385 523.619 .127

S .008 .821 1 104 .367 7.423 -443.847

Growth .007 .742 1 104 .391 7.167 3.621E-5

Exponential .007 .742 1 104 .391 1296.539 3.621E-5

Logistic .007 .742 1 104 .391 .001 1.000

The independent variable is Concrete.

F-39

553




F-40

Figure F-20: Construction Cost vs. Concrete Strength

554




Table F-21: Curve Fit: Independent Variable is Steel Grade (Not Significance)



Equation



Linear .000 .031 1 104 .861 1443.175 .846

Logarithmic .000 .029 1 104 .865 1300.327 47.360

Inverse .000 .026 1 104 .872 1535.658 -2468.107

Quadratic .000 .016 2 103 .984 1478.566 -.345 .010

Cubic .000 .016 2 103 .984 1472.347 .000 .004 3.575E-5

Compound .000 .021 1 104 .885 1430.195 1.000

Power .000 .013 1 104 .908 1347.973 .021

S .000 .007 1 104 .933 7.308 -.849

Growth .000 .021 1 104 .885 7.266 .000

Exponential .000 .021 1 104 .885 1430.195 .000

Logistic .000 .021 1 104 .885 .001 1.000

The independent variable is Steel_Grade.

F-41

555




F-42

Figure F-21: Construction Cost vs. Steel Grade

556




Table F-22: Curve Fit: Independent Variable is Transformer's KVA.



Equation

Model Summary

Parameter

Estimates


Linear .036 3.882 1 104 .051 1562.804 -.312

Logarithmic .035 3.765 1 104 .055 1853.443 -69.871

Inverse .044 4.817 1 104 .030 1426.123 8846.977

Quadratic .043 2.323 2 103 .103 1528.004 -.048 .000

Cubic .071 2.594 3 102 .057 1647.065 -1.584 .004 -2.511E-6

Compound .046 4.975 1 104 .028 1546.970 1.000

Power .035 3.753 1 104 .055 1862.566 -.046

S .039 4.266 1 104 .041 7.251 5.506

Growth .046 4.975 1 104 .028 7.344 .000

Exponential .046 4.975 1 104 .028 1546.970 .000

Logistic .046 4.975 1 104 .028 .001 1.000

The independent variable is Transformer.

F-43

557




F-44

Figure F-22: Construction Cost vs. Transformer

558




Table F-23: Curve Fit: Independent Variable is Generator's KW



Equation



Linear .012 1.265 1 104 .263 1513.109 -.204

Logarithmica . . . . . .000 .000

Inverseb . . . . . .000 .000

Quadratic .074 4.126 2 103 .019 1435.375 1.100 -.001

Cubic .081 2.992 3 102 .034 1399.849 1.872 -.004 1.450E-6

Compound .023 2.480 1 104 .118 1495.665 1.000

Powera . . . . . .000 .000

Sb . . . . . .000 .000

Growth .023 2.480 1 104 .118 7.310 .000

Exponential .023 2.480 1 104 .118 1495.665 .000

Logistic .023 2.480 1 104 .118 .001 1.000

The independent variable is Generator.

a. The independent variable (Generator) contains non-positive values. The minimum value is 0. The


b. The independent variable (Generator) contains values of zero. The Inverse and S models cannot

be calculated.

F-45

559




F-46

Figure F-23: Construction Cost vs. Generator

560




Table F-24: Curve Fit: Independent Variable is Capacity of Lift.



Equation

Model Summary

Parameter

Estimates


Linear .038 4.117 1 104 .045 1398.742 9.586

Logarithmica . . . . . .000 .000

Inverseb . . . . . .000 .000

Quadratic .079 4.435 2 103 .014 1183.614 48.028 -1.298

Cubic .086 3.192 3 102 .027 1331.361 9.824 1.437 -.056

Compound .034 3.669 1 104 .058 1385.203 1.006

Powera . . . . . .000 .000

Sb . . . . . .000 .000

Growth .034 3.669 1 104 .058 7.234 .006

Exponential .034 3.669 1 104 .058 1385.203 .006

Logistic .034 3.669 1 104 .058 .001 .994

The independent variable is Lift.

a. The independent variable (Lift) contains non-positive values. The minimum value is 0. The


b. The independent variable (Lift) contains values of zero. The Inverse and S models cannot be

calculated.

F-47

561




F-48

Figure F-24: Construction Cost vs. Lift Capacity

562




BOXPLOT AND HISTOGRAM Tabel G-1: Boxplot and Histogram: Steel Reinforcement Price (Tk per Ton)

Case Processing Summary

Cases

Valid Missing Total

N Percent N Percent N Percent

Const_Cost 106 100.0% 0 .0% 106 100.0%

Figure G-1: Boxplot and Histogram: Steel Reinforcement Price (Tk per Ton)

G-1

APPENDIX-G Formatted: Width: 8.27", Height: 11.69"




Tabel G-2: Boxplot and Histogram: Cement Price (Tk per Bag)


Cases

Valid Missing Total


Steel 106 100.0% 0 .0% 106 100.0% Figure G-2:Boxplot and Histogram: Cement Price (Tk per Bag)

G-2




Tabel G-3: Boxplot and Histogram: Brick Price (Tk per 1000)


Cases

Valid Missing Total


Cement 106 100.0% 0 .0% 106 100.0%

Figure G-3:Boxplot and Histogram: Brick Price (Tk per 1000)

G-3




Tabel G-4: Boxplot and Histogram: Sand Price (Tk per 100 cft)


Cases

Valid Missing Total


Brick 106 100.0% 0 .0% 106 100.0%

Figure G-4:Boxplot and Histogram: Sand Price (Tk per 100 cft)

G-4




Tabel G-5: Boxplot and Histogram: Paint Price (Tk per Gallon)


Cases

Valid Missing Total


Sand 106 100.0% 0 .0% 106 100.0%

Figure G-5:Boxplot and Histogram: Paint Price (Tk per Gallon)

G-5




Tabel G-6: Boxplot and Histogram: Masson Wage (Tk per Day)


Cases

Valid Missing Total


Paint 106 100.0% 0 .0% 106 100.0%

Figure G-6:Boxplot and Histogram: Masson Wage (Tk per Day)

G-6




Tabel G-7: Boxplot and Histogram: Helper Wage (Tk per Day)


Cases

Valid Missing Total


Mason 106 100.0% 0 .0% 106 100.0%

Figure G-7:Boxplot and Histogram: Helper Wage (Tk per Day)

G-7




Tabel G-8: Boxplot and Histogram: Carpenter Wage (Tk per Day) Case Processing Summary

8

Cases

Valid Missing Total


Helper 106 100.0% 0 .0% 106 100.0%

Figure G-8:Boxplot and Histogram: Carpenter Wage (Tk per Day)

G-8




Tabel G-9: Boxplot and Histogram: Transport Cost (Tk per 8 KM) Case Processing Summary

9

Cases

Valid Missing Total


Carpenter 106 100.0% 0 .0% 106 100.0%

Figure G-9:Boxplot and Histogram: Transport Cost (Tk per 8 KM)

G-9




Tabel G-10: Boxplot and Histogram: Project Duration (in Month)


Cases

Valid Missing Total


Transport 106 100.0% 0 .0% 106 100.0%

Figure G-10:Boxplot and Histogram: Project Duration (in Month)

G-10




Tabel G-11: Boxplot and Histogram: Corner Plot (Dichotomous) Case Processing Summary

11

Cases

Valid Missing Total


Duration 106 100.0% 0 .0% 106 100.0%

Figure G-11:Boxplot and Histogram: Corner Plot (Dichotomous)

G-11




Tabel G-12: Boxplot and Histogram: Road 1 (feet) Case Processing Summary

12

Cases

Valid Missing Total


Corner 106 100.0% 0 .0% 106 100.0%

Figure G-12:Boxplot and Histogram: Road 1 (feet)

G-12




Tabel G-13: Boxplot and Histogram: Road 2 (feet) Case Processing Summary

13

Cases

Valid Missing Total


Rd_1 106 100.0% 0 .0% 106 100.0%

Figure G-13:Boxplot and Histogram: Road 2 (feet)

G-13




Tabel G-14: Boxplot and Histogram: Deep Foundation (Dichotomous) Case Processing Summary

14

Cases

Valid Missing Total


Rd_2 106 100.0% 0 .0% 106 100.0%

Figure G-14:Boxplot and Histogram: Deep Foundation (Dichotomous)

G-14




Tabel G-15: Boxplot and Histogram: Basement (Dichotomous) Case Processing Summary

15

Cases

Valid Missing Total


Deep_Foundation 106 100.0% 0 .0% 106 100.0%

Figure G-15:Boxplot and Histogram: Basement (Dichotomous)

G-15




Tabel G-16: Boxplot and Histogram: Pile (Dichotomous) Case Processing Summary16

Cases

Valid Missing Total


Basement 106 100.0% 0 .0% 106 100.0%

Figure G-16:Boxplot and Histogram: Pile (Dichotomous)

G-16




Tabel G-17: Boxplot and Histogram: Dual Structure (Dichotomous) Case Processing Summary

17

Cases

Valid Missing Total


Pile 106 100.0% 0 .0% 106 100.0%

Figure G-17:Boxplot and Histogram: Dual Structure (Dichotomous)

G-17




Tabel G-18: Boxplot and Histogram: Total Area Case Processing Summary

18

Cases

Valid Missing Total


Dual 106 100.0% 0 .0% 106 100.0%

Figure G-18:Boxplot and Histogram: Total Area

G-18




Tabel G-19: Boxplot and Histogram: Plinth Area (sft) Case Processing Summary

19

Cases

Valid Missing Total


Area 106 100.0% 0 .0% 106 100.0%

Figure G-19:Boxplot and Histogram: Plinth Area (sft)

G-19




Tabel G-20: Boxplot and Histogram: No of Storey Case Processing Summary

20

Cases

Valid Missing Total


Plinth 106 100.0% 0 .0% 106 100.0%

Figure G-20:Boxplot and Histogram: No of Storey

G-20




Tabel G-21: Boxplot and Histogram: Lobby Size (sft) Case Processing Summary

21

Cases

Valid Missing Total


Storey 106 100.0% 0 .0% 106 100.0%

Figure G-21:Boxplot and Histogram: Lobby Size (sft)

G-21




Tabel G-22: Boxplot and Histogram: No of Toilet per Floor Case Processing Summary

22

Cases

Valid Missing Total


Lobby 106 100.0% 0 .0% 106 100.0%

Figure G-22:Boxplot and Histogram: No of Toilet per Floor

G-22




Tabel G-23: Boxplot and Histogram: No of Stairs Case Processing Summary

23

Cases

Valid Missing Total


Toilet 106 100.0% 0 .0% 106 100.0%

Figure G-23:Boxplot and Histogram: No of Stairs

G-23




Tabel G-24: Boxplot and Histogram: Concrete Strength (psi) Case Processing Summary 24

Cases

Valid Missing Total


Stair 106 100.0% 0 .0% 106 100.0%

Figure G-24:Boxplot and Histogram: Concrete Strength (psi)

G-24




Tabel G-25: Boxplot and Histogram: Steel Grade (Ksi) Case Processing Summary

25

Cases

Valid Missing Total


Concrete 106 100.0% 0 .0% 106 100.0%

Figure G-25:Boxplot and Histogram: Steel Grade (Ksi)

G-25




Tabel G-26: Boxplot and Histogram: Transformer (KVA) Case Processing Summary 26

Cases

Valid Missing Total


Steel_Grade 106 100.0% 0 .0% 106 100.0%

Figure G-26:Boxplot and Histogram: Transformer (KVA)

G-26




Tabel G-27: Boxplot and Histogram: Generator (KW) Case Processing Summary 27

Cases

Valid Missing Total


Transformer 106 100.0% 0 .0% 106 100.0%

Figure G-27:Boxplot and Histogram: Generator (KW)

G-27




Tabel G-28: Boxplot and Histogram: Lift Capacity (Person) Case Processing Summary

Cases

Valid Missing Total


Generator 106 100.0% 0 .0% 106 100.0%

Figure G-28:Boxplot and Histogram: Lift Capacity (Person)

G-28




Tabel G-29: Boxplot and Histogram: Lift Capacity (Person) Case Processing Summary

Cases

Valid Missing Total


Lift 106 100.0% 0 .0% 106 100.0%

Figure G-29:Boxplot and Histogram: Lift Capacity (Person)

G-29




VALIDATION OF MODELS

NEW DATA SET

Actual Serial

Constr Cost Sand Paint Mason Plinth Storey Lift

Observed Value

6 800 735.00 521.00 200.00 2500 6 6 800 9 1000 735.00 647.78 204.25 6500 6 8 1000

12 1000 724.00 647.78 210.83 4100 6 6 1000 15 1050 724.00 647.78 210.83 25900 6 8 1050 29 1300 1000.00 685.00 228.00 3376 9 8 1300 34 1150 1000.00 685.00 228.00 6200 6 6 1150 35 1200 1000.00 685.00 228.00 17280 6 8 1200 37 1150 1000.00 652.00 228.00 3000 6 6 1150 44 1194 958.33 652.00 250.92 2011 6 8 1194 46 1316 958.33 724.00 250.92 5328 6 8 1316 47 1300 958.33 724.00 250.92 5200 6 8 1300 50 1400 958.33 724.00 250.92 3600 6 8 1400 56 1230 958.33 652.00 250.92 4100 10 6 1230 58 1280 958.33 724.00 250.92 2500 5 6 1280 59 1250 958.33 652.00 250.92 2800 7 6 1250 60 1200 958.33 652.00 250.92 4000 5 6 1200 61 1350 958.33 767.00 250.92 2000 6 8 1350 63 1218 958.33 652.00 250.92 4255 8 8 1218 67 1280 958.33 724.00 250.92 3596 8 8 1280 69 1235 958.33 652.00 250.92 4254 8 16 1235 72 1266 958.33 652.00 250.92 6294 9 16 1266 76 1300 958.33 724.00 250.92 2523 10 8 1300 82 1300 1127.00 724.00 286.33 2725 8 8 1300 83 1500 1127.00 724.00 286.33 4050 8 16 1500 99 1500 1127.00 724.00 286.33 6000 10 8 1500

102 1600 1127.00 724.00 286.33 5500 8 16 1600 103 1580 1127.00 724.00 286.33 4200 10 12 1580 105 1450 1127.00 724.00 286.33 2800 7 8 1450 107 1450 1127.00 767.00 286.33 2700 6 12 1450 114 1700 1127.00 724.00 286.33 2000 6 10 1700 119 1460 1127.00 724.00 286.33 6200 8 16 1460 123 1550 1127.00 767.00 286.33 5000 8 8 1550 153 1700 1470.00 767.00 300.00 2200 6 8 1700

H-1

APPENDIX-H




MODEL-1

Actual Serial

Actual Value of

DV

Predicted Value

Residuals RSS

6 800 893.799 -93.799 8798.252

9 1000 1021.059 -21.0594 443.4992

12 1000 1045.737 -45.737 2091.875

15 1050 1045.737 4.26298 18.173

29 1300 1218.77 81.23 6598.313

34 1150 1218.77 -68.77 4729.313

35 1200 1218.77 -18.77 352.3129

37 1150 1190.258 -40.258 1620.707

44 1194 1275.375 -81.3752 6621.928

46 1316 1337.583 -21.5832 465.8358

47 1300 1337.583 -37.5832 1412.499

50 1400 1337.583 62.41677 3895.853

56 1230 1275.375 -45.3752 2058.911

58 1280 1337.583 -57.5832 3315.828

59 1250 1275.375 -25.3752 643.9023

60 1200 1275.375 -75.3752 5681.425

61 1350 1374.735 -24.7352 611.8316

63 1218 1275.375 -57.3752 3291.917

67 1280 1337.583 -57.5832 3315.828

69 1235 1275.375 -40.3752 1630.159

72 1266 1275.375 -9.37523 87.89494

76 1300 1337.583 -37.5832 1412.499

82 1300 1527.579 -227.579 51792.25

83 1500 1527.579 -27.5791 760.6068

99 1500 1527.579 -27.5791 760.6068

102 1600 1527.579 72.4209 5244.787

103 1580 1527.579 52.4209 2747.951

105 1450 1527.579 -77.5791 6018.517

107 1450 1564.731 -114.731 13163.23

114 1700 1527.579 172.4209 29728.97

119 1460 1527.579 -67.5791 4566.935

123 1550 1564.731 -14.7311 217.0053

153 1700 1707.828 -7.828 61.27758

-979.685 174160.9

MEAN= -48.9842 417.3259

SE= 20.86629

H-2




MODEL-2

Actual Serial

Actual Value of

DV

Predicted Value

Residuals RSS

6 800 1410.333 -516.534 266807.4

9 1000 1275.485 -254.426 64732.38

12 1000 1335.133 -289.396 83750.03

15 1050 363.685 682.052 465195

29 1300 1515.817 -297.047 88236.92

34 1150 1236.433 -17.663 311.9816

35 1200 768.825 449.945 202450.5

37 1150 1386.833 -196.575 38641.73

44 1194 1486.468 -211.093 44560.16

46 1316 1330.569 7.01423 49.19942

47 1300 1336.585 0.99823 0.996463

50 1400 1411.785 -74.2018 5505.903

56 1230 1459.805 -184.43 34014.34

58 1280 1379.165 -41.5818 1729.044

59 1250 1427.401 -152.026 23111.83

60 1200 1308.665 -33.2898 1108.209

61 1350 1486.985 -112.25 12600.01

63 1218 1443.336 -167.961 28210.82

67 1280 1474.309 -136.726 18693.94

69 1235 1655.991 -380.616 144868.4

72 1266 1591.279 -315.904 99795.19

76 1300 1587.076 -249.493 62246.64

82 1300 1515.246 12.3331 152.1054

83 1500 1665.579 -138 19043.97

99 1500 1423.657 103.9221 10799.8

102 1600 1597.429 -69.8499 4879.009

103 1580 1614.561 -86.9819 7565.851

105 1450 1480.553 47.0261 2211.454

107 1450 1560.389 4.3421 18.85383

114 1700 1540.137 -12.5579 157.7009

119 1460 1564.529 -36.9499 1365.295

123 1550 1408.321 156.4101 24464.12

153 1700 1477.585 230.243 53011.84 -2281.26 1810291 MEAN= -114.063 1345.47 SE= 67.27352

H-3




MODEL-3

Actual Serial

Actual Value of

DV

Predicted Value

Residuals RSS

6 800 918.201 -118.201 13971.48

9 1000 1026.785 -26.785 717.4368

12 1000 1041.343 -41.3429 1709.233

15 1050 1051.037 -1.03687 1.075099

29 1300 1216.829 83.171 6917.415

34 1150 1207.135 -57.135 3264.408

35 1200 1216.829 -16.829 283.2152

37 1150 1185.949 -35.949 1292.331

44 1194 1279.254 -85.2538 7268.207

46 1316 1325.478 -9.47778 89.82831

47 1300 1325.478 -25.4778 649.1173

50 1400 1325.478 74.52222 5553.561

56 1230 1269.56 -39.5598 1564.976

58 1280 1315.784 -35.7838 1280.479

59 1250 1269.56 -19.5598 382.585

60 1200 1269.56 -69.5598 4838.563

61 1350 1353.084 -3.08378 9.509699

63 1218 1279.254 -61.2538 3752.026

67 1280 1325.478 -45.4778 2068.228

69 1235 1318.03 -83.0298 6893.944

72 1266 1318.03 -52.0298 2707.098

76 1300 1325.478 -25.4778 649.1173

82 1300 1514.778 -214.778 46129.42

83 1500 1553.554 -53.5536 2867.989

99 1500 1514.778 -14.7776 218.3778

102 1600 1553.554 46.44639 2157.267

103 1580 1534.166 45.83439 2100.791

105 1450 1514.778 -64.7776 4196.139

107 1450 1561.772 -111.772 12492.89

114 1700 1524.472 175.5284 30810.22

119 1460 1553.554 -93.5536 8752.278

123 1550 1542.384 7.61639 58.0094

153 1700 1687.157 12.843 164.9426 -959.554 175812.2 MEAN= -47.9777 419.2996 SE= 20.96498

H-4




developing a construction cost function for …

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