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BA 275 Quantitative Business Methods

Please turn in Progress Report #2

Quiz # 5

Simple Linear Regression Introduction Case Study: Housing Prices

Agenda

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Midterm Examination #2

Monday, February 26, 2007 in class for 110 minutes. It covers materials assigned in Week 4 – 7. Need a calculator and a good night sleep. Close book/note/friends except for a 4” x 6” index

card. I will provide you 1. the normal probability table.2. Table D

A 4” x 6” index card is allowed. Write your name and section number on top and turn it in with your exam.

Office Hours: Friday, 2/23/2007, 3:10 – 5:00 p.m. Monday, 2/26/2007, 8:30 – 11:00 a.m.

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Regression Analysis

A technique to examine the relationship between an outcome variable (dependent variable, Y)

and an explanatory variable (independent variable, X) => Simple Regression Analysis

and a group of explanatory variables (independent variables, X1, X2, …). => Multiple Regression Analysis

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Case Study: Housing Prices

Case ID Area (1000 sq ft) Price ($000) Case ID Area (1000 sq ft) Price ($000)No. X Y No. X Y

1 2.100 150.00 13 3.000 205.002 1.455 114.90 14 1.400 79.403 1.630 106.50 15 2.750 200.004 2.600 195.00 16 2.900 215.105 1.210 75.50 17 2.500 180.806 1.857 126.60 18 1.535 120.907 2.000 135.40 19 1.333 70.008 2.400 178.65 20 2.455 165.209 2.256 145.10 21 3.010 185.0010 1.290 62.60 22 2.180 160.0011 2.332 168.20 23 1.870 119.9012 1.725 138.10 24 1.582 99.90

Does AREA affect PRICE?If so, how large is the effect?What is the expected price of a house = 2000 sf?

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Initial Analysis

Plot of Price vs Area

Area

Pric

e

1.2 1.6 2 2.4 2.8 3.260

100

140

180

220

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Correlation

(rho): Population correlation (its value most likely is unknown.)

r: Sample correlation (its value can be calculated from the sample.)

Correlation is a measure of the strength of linear relationship.

Correlation falls between –1 and 1. No linear relationship if correlation is close to

0.

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Correlation ( vs. r)

Is 0.9584 a or r?

Sample size

P-value for

H0: = 0Ha: ≠ 0

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Regression Report from SG

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Fitted Model: Least Squares Line

b1

b0

Least squares line: estimated_Price = –15.1245 + 76.1745 Area.

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Fitted Model: Least Squares Line

Plot of Fitted Model

Y_Price = -15.1245 + 76.1745*X_Area

1.2 1.6 2 2.4 2.8 3.2

X_Area

60

100

140

180

220

Y_P

rice