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

\(Y E A R S \_O L D=\) the time between completion of the painting and when it was sold \(I N C H S Q=\) the size of the painting in square inches Create a new variable \(I N C H S Q 10=I N C H S Q / 10\) to express size in terms of tens of square inches. Only consider observations where the art was sold \((S O L D=1)\).

a. Estimate the following equation and report the results:

b. How much do paintings appreciate on a yearly basis? Find a \(95 \%\) interval estimate for the expected yearly price increase.

c. How much more valuable are large paintings? Find a 95\% interval estimate for the expected extra value from an extra 10 square inches.

d. Add the variable \(I N C H S Q 10^{2}\) 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. Find \(95 \%\) interval estimates for the expected extra value from an extra 10 square inches 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). Comment on how the value of an extra 10 square inches changes as the painting becomes larger.

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.

i. How long would you have to keep a 100-square-inch painting for the expected price to become positive?

Transcribed Image Text:

RHAMMER B + BYEARS OLD + B3INCHSQ10+ e =