26. Housing Price Bubble (random forest estimation). Refer to the scenario in Problem 24 regarding estimating house prices.

a. Consider the Pre-Crisis data. Apply a random forest of regression trees using Price as the target (or response) variable and all the other variables as input variables.

Experiment with the number of trees and the number of variables per tree to recommend a random forest model (based on predictive performance on a static validation set or a cross-validation procedure). Use this random forest to predict sale prices of houses in the test set.

b. Repeat part

(a) with the Post-Crisis data.

c. For each of the 2,000 houses in the test set, compare the predictions from part (a-ii)

based on the pre-crisis data to those from part (b-ii) based on the post-crisis data. Specifically, compute the percentage difference in predicted price between the pre-crisis and post-crisis models, where percentage difference = (post-crisis predicted price –

pre-crisis predicted price)/pre-crisis predicted price. What is the average percentage change in predicted price between the pre-crisis and post-crisis models? What does this suggest about the impact of the bursting of the housing bubble?