The file collegetown contains data on 500 houses sold in Baton Rouge, LA during 2009-2013. Variable descriptions are in the file collegetown.def.

a. Estimate the log-linear model \(\ln (P R I C E)=\beta_{1}+\beta_{2} S Q F T+e\) for houses close to Louisiana State University [CLOSE = 1] and again for houses that are not close to Louisiana State University. How similar are the two sets of regression estimates. For each find the "corrected" predictor for a house with 2700 square feet of living area. What do you find?

b. Using the sample of homes that are not close to LSU \([C L O S E=0]\), find any observations on house sales that you would classify as unusual, based on the studentized residuals, LEVERAGE, DFBETAS, and DFFITS. Can you identify any house characteristics that might explain why they are unusual?

c. Estimate the log-linear model \(\ln (P R I C E)=\beta_{1}+\beta_{2} S Q F T+e\) for houses for which \(A G E<7\) and again for houses with \(A G E>9\). Note that \(A G E\) is not the actual age of the house, but a category. Examine the file collegetown.def for the specifics. How similar are the two sets of regression estimates. For each find the "corrected" predictor of a house with 2700 square feet of living area. What do you find?

d. Using the sample of homes with \(A G E>9\), find any observations on house sales that you would classify as unusual, based on the studentized residuals, LEVERAGE, DFBETAS, and DFFITS. Can you identify any house characteristics that might explain why they are unusual?