1 BA 275 Quantitative Business Methods Simple Linear Regression Introduction Case Study: Housing Prices Agenda

2 Midterm Examination #2

3 Linear Regression Analysis A technique to examine the relationship between an outcome variable (dependent variable, Y) and a group of explanatory variables (independent variables, X1, X2, …). The model allows us to understand (quantify) the effect of each X on Y. It also allows us to predict Y based on X1, X2, ….

4 Simple Linear Regression Model population sample True effect of X on Y Estimated effect of X on Y Key questions: 1. Does X have any effect on Y? 2. If yes, how large is the effect? 3. Given X, what is the estimated Y?

5 Case Study: Housing Prices Does AREA affect PRICE? If so, how large is the effect? What is the expected price of a house = 2000 sf?

6 Initial Analysis

7 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. Examples. Examples

8 Correlation (  vs. r) Is a  or r? Sample size P-value for H 0 :  = 0 H a :  ≠ 0

9 Fitted Model H 0 :  1 = 0 H a :  1 ≠ 0  1 or b 1 ?  0 or b 0 ? S b1 S b0 b1b1 b0b0

10 Fitted Model S b1 S b0 b1b1 b0b0 Degrees of freedom = n – k – 1 k = # of independent variable