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 \(\ln (P R I C E)=\beta_{1}+\beta_{2} S Q F T+e\). Interpret the estimated model parameters. Calculate the slope and elasticity at the sample means, if necessary.

b. Estimate the log-log model \(\ln (P R I C E)=\alpha_{1}+\alpha_{2} \ln (S Q F T)+e\). Interpret the estimated parameters. Calculate the slope and elasticity at the sample means, if necessary.

c. Compare the \(R^{2}\) value from the linear model PRICE \(=\delta_{1}+\delta_{2} S Q F T+e\) to the "generalized" \(R^{2}\) measure for the models in (b) and (c).

d. Construct histograms of the least squares residuals from each of the models in (a)-(c) and obtain the Jarque-Bera statistics. Based on your observations, do you consider the distributions of the residuals to be compatible with an assumption of normality?

e. For each of the models in (a)-(c), plot the least squares residuals against \(S Q F T\). Do you observe any patterns?

f. For each model in (a)-(c), predict the value of a house with 2700 square feet.

g. For each model in (a)-(c), construct a \(95 \%\) prediction interval for the value of a house with 2700 square feet.

h. Based on your work in this problem, discuss the choice of functional form. Which functional form would you use? Explain.