The data file \(b r 2\) contains data on 1080 house sales in Baton Rouge, Louisiana, during July and August 2005. The variables are: PRICE (\\($)\), SQFT (total square feet), BEDROOMS (number), BATHS (number), AGE (years), OWNER ( \(=1\) if occupied by owner; 0 if vacant or rented), TRADITIONAL (= 1 if traditional style; 0 if other style), FIREPLACE (= 1 if present), WATERFRONT (= 1 if on waterfront).

a. Compute the data summary statistics and comment. In particular, construct a histogram of PRICE. What do you observe?

b. Estimate a regression model explaining \(\ln (P R I C E / 1000)\) as a function of the remaining variables. Divide the variable \(S Q F T\) by 100 prior to estimation. Comment on how well the model fits the data. Discuss the signs and statistical significance of the estimated coefficients. Are the signs what you expect? Give an exact interpretation of the coefficient of WATERFRONT.

c. Create a variable that is the product of WATERFRONT and TRADITIONAL. Add this variable to the model and re-estimate. What is the effect of adding this variable? Interpret the coefficient of this interaction variable and discuss its sign and statistical significance.

d. It is arguable that the traditional style homes may have a different regression function from the diverse set of nontraditional styles. Carry out a Chow test of the equivalence of the regression models for traditional versus nontraditional styles. What do you conclude?

e. Predict the value of a traditional style house with 2500 square feet of area, that is 20 years old, which is owner occupied at the time of sale, with a fireplace, but no pool, and not on the waterfront.