Create a regression tree using the accompanying data set in Exercise_10.28_Data worksheet (predictor variables: x₁ to x₅; target: y). Select the best-pruned tree for scoring and display the full-grown, best-pruned, and minimum error trees.

a. What is the minimum validation MSE in the prune log? How many decision nodes are associated with the minimum error?

b. How many leaf nodes are in the best-pruned and minimum error trees? 

c. Display the best-pruned tree. What are the predictor variable and split value for the first split (root node) of the best-pruned tree? What are the rules that can be derived from the root node?

d. What are the RMSE and MAD of the best-pruned tree on the test data?

e. Score the new observations in the Exericse_10.28_Score worksheet using the best-pruned tree. What is the predicted value of y for the first observation?

f. What are the minimum, maximum, and average values of predicted y?

For Analytic Solver, partition data sets into training, 30% validation, and 20% and use 12345 as the default random seed. For R, partition data sets into 70% and 30% validation. Use the statement set.seed(1) to specify the random seed of 1 for both data partitioning and cross-validation