Create a regression tree using the accompanying data set (predictor variables: x₁ to x₄; 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. According to the best-pruned tree, what is the predicted y for a new observation with the following values: x₁ = 20; x₂ = 40; x₃ = 36; x₄ = 8.3?