The accompanying data set in the Exercise_10.7_Data worksheet contains four predictor variables (x₁ to x₄) and one binary target variable (y). Select the best-pruned tree for scoring and display the full-grown, bestpruned, and minimum error trees.

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

b. Display the best-pruned tree. How many leaf nodes are in the best-pruned tree? How many leaf nodes are in the minimum error tree? 

c. What are the predictor variable and split value for the first split of the best-pruned tree? 

d. What are the classification accuracy rate, sensitivity, specificity, and precision of the best-pruned tree on the test data? 

e. Generate the decile-wise lift chart of the best-pruned tree on the test data. What is the lift value of the leftmost bar of the decile-wise lift chart? What does this value imply? 

f. Generate the ROC curve of the best-pruned tree on the test data. What is the area under the ROC curve (or AUC value)? 

g. Score the new observations in the Exercise_10.7_Score worksheet using the best-pruned tree. What is the predicted response value of the new observations? What is the Class 1 probability of the first observation? Round your answers to four decimal places.