In this exercise, we consider the auction market for art first introduced in Exercise 2.24. The variables in the data file ashcan_small that we will be concerned with are as follows: RHAMMER = the price at which a painting sold in thousands of dollars YEARS OLD- the time between completion of the painting and when it was sold INCHSQ = the size of the painting in square inches O Create a new variable INCHSQ10 INCHSQ/10 to express size in terms of tens of square inches. Only consider observations where the art was sold (SOLD = 1). a. Estimate the following log-linear equation and report the results: In(RHAMMER) =B₁ + B, YEARS OLD+B,INCHSQ10+e b. How much do paintings appreciate on a yearly basis? Find a 95% interval estimate for the expected percentage price increase per year. c. How much more valuable are large paintings? Using a 5% significance level, test the null hypothesis that painting an extra 10 square inches increases the value by 2% or less against the alternative that it increases the value by more than 2%. d. Add the variable INCHSQ10³ to the model and re-estimate. Report the results. Why would you consider adding this variable? e. Does adding this variable have much impact on the interval estimate in part (b)? f. Redo the hypothesis test in part (c) for art of the following sizes: (i) 50 square inches (sixth percentile). (ii) 250 square inches (approximately the median), and (iii) 900 square inches (97th percentile). What do you observe? g. Find a 95% interval estimate for the painting size that maximizes price. h. Find a 95% interval estimate for the expected price of a 75-year-old, 100-square-inch painting. (Use the estimator exp{E[In(RHAMMER YEARS OLD=75. INCHSQ10=10)]} and its stan- dard error.)