The data file collegetown contains observations on 500 single-family houses sold in Baton Rouge, Louisiana, during 2009-2013. The data include sale price (in thousands of dollars), PRICE, and total interior area of the house in hundreds of square feet, \(S Q F T\).

a. Create histograms for PRICE and \(\ln (\) PRICE). Are the distributions skewed or symmetrical?

b. Estimate the log-linear regression model \(\ln (P R I C E)=\gamma_{1}+\gamma_{2} S Q F T+e\). Interpret the OLS estimates, \(\hat{\gamma}_{1}\) and \(\hat{\gamma}_{2}\). Graph the fitted PRICE, \(\widehat{P R I C E}=\exp \left(\hat{\gamma}_{1}+\hat{\gamma}_{2} S Q F T\right)\), against \(S Q F T\), and sketch the tangent line to the curve for a house with 2000 square feet of living area. What is the slope of the tangent line?

c. Compute the least squares residuals from the model in (b) and plot them against SQFT. Do any of our assumptions appear violated?

d. Calculate summary statistics for PRICE and SQFT for homes close to Louisiana State University \((C L O S E=1)\) and for homes not close to the university \((C L O S E=0)\). What differences and/or similarities do you observe?

e. Estimate the log-linear regression model \(\ln (P R I C E)=\gamma_{1}+\gamma_{2} S Q F T+e\) for homes close to Louisiana State University \((C L O S E=1)\) and for homes not close to the university \((C L O S E=0)\). Interpret the estimated coefficient of SQFT in each sample's regression.

f. Are the regression results in part (b) valid if the differences you observe in part (e) are substantial? Think in particular about whether SR1 is satisfied.