Using the data in the file \(b r 5\), estimate the equation

where PRICE is the selling price in thousands of dollars for houses sold in Baton Rouge, Louisiana, in 2005, SQFT is the size of each house in hundreds of square feet and \(A G E\) is the age of each house in years.

a. Report the coefficient estimates and their standard errors.

b. Graph the estimate of \(E[\ln (P R I C E) \mid S Q F T=22, A G E]\) against \(A G E\). (In the sample the median and average values for \(S Q F T\) are 21.645 and 22.737, respectively.)

c. In part (b), you will have noticed that the higher-priced houses are the very new ones and the very old ones. Using a \(5 \%\) significance level test the joint null hypothesis that (i) two houses of the same size, a 5-year old house and an 80-year old house, have the same expected log-price, and (ii) a 5-year old house with 2000 square feet has the same expected log-price as a 30 -year old house with 2800 square feet.

d. Using a 5\% significance level, test the joint null hypothesis that (i) houses start becoming more expensive with age when they are 50 years old, and (ii) a 2200 square feet house that is 50 years old has an expected log-price that corresponds to \(\$ 100,000\).

e. Add the variables BATHS and SQFT \(\times\) BEDROOMS to the model with coefficients \(\beta_{5}\) and \(\beta_{6}\), respectively. Estimate this model and report the results.

f. Using a 5\% significance level, test whether adding these two variables has improved the predictive ability of the model.

g. You are building a new 2300 square-feet house \((A G E=0)\) with three bedrooms and two bathrooms. Adding one extra bedroom and bathroom will increase its size by 260 square feet. Estimate the increase in value of the house from the extra bedroom and bathroom. (Use the natural predictor.)

h. What do you estimate will be the extra value of the house in 20 years' time?

Transcribed Image Text:

In(PRICE) B + SQFT + AGE + BAGE + e