The three most important words in real estate are "location, location, location!" We explore this question using 500, single-family home sales in Baton Rouge, LA from 2009 to 2013 in the data file collegetown. See collegetown.def for variable definitions.

a. Estimate the log-log model \(\ln (P R I C E)=\beta_{1}+\beta_{2} \ln (S Q F T)+\delta_{1} C L O S E+e\). Interpret the estimated coefficients of \(\ln (S Q F T)\) and CLOSE. Is the location variable CLOSE statistically significant at the \(5 \%\) level?

b. Estimate the log-log model \(\ln (P R I C E)=\beta_{1}+\beta_{2} \ln (S Q F T)+\delta_{2}[C L O S E \times \ln (S Q F T)]+e\). Interpret the estimated coefficients of \(\ln (S Q F T)\) and \([C L O S E \times \ln (S Q F T)]\). Is the location variable \([C L O S E \times \ln (S Q F T)]\) statistically significant at the \(5 \%\) level?

c. Estimate the log-log model

Are the location variables \(C L O S E\) and \([C L O S E \times \ln (S Q F T)]\) individually and jointly statistically significant at the \(5 \%\) level?

d. Using the model in (c), predict the prices of two houses with 2500 square feet, one close to the university and another that is not close. Use the corrected predictor.

e. Add FIREPLACE, TWOSTORY, and OCCUPIED to the model in (c). How do these features affect the price of a house?

f. Carry out a Chow test for the log-log model, comparing houses that are close to the university to those that are not close, using explanatory variables \(\ln\) (SQFT), FIREPLACE, TWOSTORY, and OCCUPIED. What is the \(p\)-value of the test?

Transcribed Image Text:

= In(PRICE) + B2 In(SQFT) +8, CLOSE + 82[CLOSE x In(SQFT)] + e