BEC 30325: MANAGERIAL ECONOMICS

Session 03

Dr. Sumudu Perera

DEMAND ESTIMATION (PART – II)

• Marketing Research Approaches

• Scatter Diagram

• Regression Analysis

• Simple Linear Regression Model

• Ordinary Least Squares (OLS)

Dr.Sumudu Perera 21/09/2017

2Session Outline

3Demand Estimation: Marketing

Research Approaches

Consumer Surveys

Observational Research

Consumer Clinics

Market Experiments

These approaches are usually covered extensively in marketing courses, however the most important

of these are consumer surveys and market experiments.

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Consumer surveys

These surveys require the questioning of a firm’s customers in anattempt to estimate the relationship between the demand for itsproducts and a variety of variables perceived to be for themarketing and profit planning functions.

These surveys can be conducted by simply stopping andquestioning people at shopping centre or by administeringsophisticated questionnaires to a carefully constructedrepresentative sample of consumers by trained interviewers.

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Consumer surveys continued…

Major advantages: they may provide the only information

available; they can be made as simple as possible; the

researcher can ask exactly the questions they want

Major disadvantages: consumers may be unable or

unwilling to provide reliable answers; careful and extensive

surveys can be very expensive.

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Market experiments

Market experiments include attempts made by the firm to estimate the demand for the

commodity by changing price and other determinants of the demand for the commodity in

the actual market place.

Major advantages: consumers are in a real market situation; they do not know that they

being observed; they can be conducted on a large scale to ensure the validity of results.

Major disadvantages: in order to keep cost down, the experiment may be too limited so

the outcome can be questionable; competitors could try to sabotage the experiment by

changing prices and other determinants of demand under their control; competitors can

monitor the experiment to gain very useful information about the firm would prefer not to

disclose.

7Scatter Diagram

It is two dimensional graph of plotted points in which thevertical axis represents values of the dependent variable andthe horizontal axis represents values of the independent orexplanatory variable.

The patterns of the intersecting points of variables cangraphically show relationship patterns.

Mostly, scatter diagram is used to prove or disprove cause-and-effect relationship. In the following example, it shows therelationship between advertising expenditure and its salesrevenues.

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Scatter Diagram-Example

Year X Y

1 10 44

2 9 40

3 11 42

4 12 46

5 11 48

6 12 52

7 13 54

8 13 58

9 14 56

10 15 60

Scatter Diagram

Scatter diagram shows a positive

relationship between the

relevant variables. The

relationship is approximately

linear.

This gives us a rough estimates of

the linear relationship between

the variables in the form of an

equation such as

Y= a+ b X

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Regression Analysis

Regression analysis: is a statistical technique for obtaining the

line that best fits the data points so that all researchers can

reach the same results.

Regression Line: Line of Best Fit

Regression Line: Minimizes the sum of the squared vertical

deviations (et) of each point from the regression line.

This is the method called Ordinary Least Squares (OLS).

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Purpose of Regression Analysis

Regression Analysis is Used Primarily to Model Causality and

Provide Prediction

Predict the values of a dependent (response) variable based on

values of at least one independent (explanatory) variable

Explain the effect of the independent variables on the dependent

variable

The relationship between X and Y can be shown on a scatter diagram

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Regression Analysis

In the table, Y1 refers actual or observed salesrevenue of $44 mn associated with theadvertising expenditure of $10 mn in the first yearfor which data collected.

In the following graph, Y^1 is the corresponding

sales revenue of the firm estimated from theregression line for the advertising expenditure of$10 mn in the first year.

The symbol e1 is the corresponding verticaldeviation or error of the actual sales revenueestimated from the regression line in the first year.

This can be expressed as e1= Y1- Y^1.

Year X Y

1 10 44

2 9 40

3 11 42

4 12 46

5 11 48

6 12 52

7 13 54

8 13 58

9 14 56

10 15 60

13Regression Analysis

In the graph, Y^1 is thecorresponding sales revenue of thefirm estimated from the regressionline for the advertising expenditureof $10 mn in the first year.

The symbol e1 is the correspondingvertical deviation or error of theactual sales revenue estimated fromthe regression line in the first year.This can be expressed as e1= Y1-Y^1.

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Regression Analysis

Since there are 10 observation points,we have obviously 10 verticaldeviations or error (i.e., e1 to e10). Theregression line obtained is the line thatbest fits the data points in the sensethat the sum of the squared (vertical)deviations from the line is minimum. Thismeans that each of the 10 e values is

first squared and then summed.

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Simple Regression Analysis

Now we are in a position to calculate the value of a ( the vertical intercept)

and the value of b (the slope coefficient) of the regression line.

Conduct tests of significance of parameter estimates.

Construct confidence interval for the true parameter.

Test for the overall explanatory power of the regression.

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Simple Linear Regression Model

Regression line is a straight line that describes the dependence of theaverage value of one variable on the other

ii iY X

Y Intercept SlopeCoefficient Random Error

Independent (Explanatory) Variable

Regression

Line

Dependent (Response) Variable

Ordinary Least Squares (OLS)

21/09/2017Dr.Sumudu Perera

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t t tY a bX e

ˆˆ ˆt tY a bX

ˆt t te Y Y

Model:

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Ordinary Least Squares (OLS)

Objective: Determine the slope and intercept

that minimize the sum of the squared errors.

2 2 2

1 1 1

ˆˆ ˆ( ) ( )n n n

t t t t t

t t t

e Y Y Y a bX

19Ordinary Least Squares (OLS)

Estimation Procedure