Melissa Hill is a real estate agent in Berkeley, California. She wants to build a predictive model that can help her price a house more accurately. Melissa has compiled a data set in the House_Data worksheet that contains the information about the houses sold in the past year. The data set contains the following variables: number of bedrooms (BM), number of bathrooms (Bath), square footage of the property (SQFT), lot size (Lot_Size), type of property (Type), age of the property (Age), and price sold (Price). A portion of the data set is shown in the accompanying table. Build a default regression tree to predict house prices (Price). Display the regression tree.

a. What are the predictor variable and split value for the first split of the default regression tree? What are the rules that can be derived from the root node? 

b. Build a full-grown tree. Which cp value is associated with the lowest cross-validation error? How many splits are in the minimum-error tree? 

c. Is there a simpler tree with a cross-validation error that is within one standard error of the minimum error? If there is, then which cp value is associated with the best-pruned tree? 

d. Prune the full tree to the best-pruned tree or the minimum error tree if the answer to part c is “No.” Display the tree. How many leaf nodes are in the pruned tree? 

e. What are the ME, RMSE, MAE, MPE, and MAPE of the pruned tree on the validation data? On average, does the regression tree over- or under-predict prices of houses? Is the regression tree model effective in predicting prices of houses? 

f. Score the two new houses on the market in the Houses_ Score worksheet using the pruned tree. What are their predicted prices?

Transcribed Image Text:

BM Bath SQFT Lot_Size 4 2 1520 2 1251 E 4314 3 E 4 E 4 Type 4050 Single Family 3200 Single Family 1 B 7056 Single Family Age 110 112 1 78 Price 500000 775000 1 2635000