Using data on the "Ashcan School," we have an opportunity to study the market for art. What factors determine the value of a work of art? Use the data in the file ashcan_small. [Note: the file ashcan contains more variables.]

a. Define YEARS_OLD \(=\) DATE_AUCTN - CREATION, which is the age of the painting at the time of its sale. Use data on works that sold \((S O L D=1)\) to estimate the regression \(\ln (R H A M M E R)=\) \(\beta_{1}+\beta_{2}\) YEARS_OLD \(+e\). Construct a \(95 \%\) interval estimate for the percentage change in real hammer price given that a work of art is another year old at the time of sale. 

b. Test the null hypothesis that each additional year of age increases the "hammer price" by \(2 \%\), against the two-sided alternative. Use the \(5 \%\) level of significance.

c. The variable \(D R E C\) is an indicator variable taking the value one if a sale occurred during a recession and is zero otherwise. Use data on works that sold \((S O L D=1)\) to estimate the regression model \(\ln (\) RHAMMER \()=\alpha_{1}+\alpha_{2}\) DREC \(+e\). Construct a \(95 \%\) interval estimate of the percentage reduction in hammer price when selling in a recession. Explain your finding to a client who is considering selling during a recessionary period.

d. Test the conjecture that selling a work of art during a recession reduces the hammer price by \(2 \%\) or less, against the alternative that the reduction in hammer price is greater than \(2 \%\). Use the \(5 \%\) level of significance. Clearly state the test statistic used, the rejection region, and the test \(p\)-value. What is your conclusion?