Using data on the "Ashcan School"14 we have an opportunity to study the market for art. What factors determine the value of a work of art? Use the data in ashcan_small.  For this exercise, use data only on works that sold \((S O L D=1)\).

a. Using data on works that sold, construct a histogram for RHAMMER and compute summary statistics. What are the mean and median prices for the artwork sold? What are the 25th and 75th percentiles?

b. Using data on works that sold, construct a histogram for \(\ln (R H A M M E R)\). Describe the shape of this histogram as compared to that in part (a).

c. Plot \(\ln (\) RHAMMER \()\) against the age of the painting at the time of its sale, YEARS_OLD = DATE_AUCTN - CREATION. Include in the plot the least squares fitted line. What patterns do you observe?

d. Use data on works that sold, estimate the regression \(\ln (R H A M M E R)=\beta_{1}+\beta_{2} Y E A R \_S O L D+e\). Interpret the estimated coefficient of YEARS_OLD.

e. \(D R E C\) is an indicator variable equaling 1 if the work was sold during a recession. Using data on works that sold, estimate the regression \(\ln (R H A M M E R)=\alpha_{1}+\alpha_{2} D R E C+e\). Interpret the estimated coefficient of DREC.