Kyle Robson, an energy researcher for the U.S. Energy Information Administration, is trying to build a model for predicting annual electricity retail sales for states. Kyle has compiled a data set for the 50 states and the District of Columbia that contains average electricity retail price (Price in cents/kWh), per capita electricity generation (Generation), median household income (Income), and per capita electricity retail sales (Price in MWh). A portion of the data set is shown in the accompanying table. Build a default regression tree to predict per capita electricity retail sales (Sales). 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 default regression tree? 

b. Build a full-grown tree. Which cp value is associated with the lowest cross-validation error? How many leaf nodes 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 bestpruned 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? 

f. What is the predicted per capita electricity retail sales for a state with the following values: Price = 11, Generation = 25, and Income = 65,000?

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State Alabama 9.56 Alaska 17.93 ⠀ I 8.19 Price Generation 29.12 8.58 Wyoming ⠀ 81.32 Income Sales $44,765 18.05 $73,355 8.3 ⠀ $60,214 ⠀ 28.86