The accompanying data set contains four predictor variables (x₁, x₂, x₃, and x₄) and the target variable (y). Partition the data in the Exercise_9.20_Data worksheet to develop a naïve Bayes classification model where “1” denotes the positive or success class for y. Score the five new observations on the Exercise_9.20_Score worksheet. 

a. Report the accuracy, sensitivity, and specificity rates for the validation data set. 

b. Generate the cumulative lift chart. Does the entire lift curve lie above the baseline? 

c. Generate the ROC curve. What is the area under the ROC curve (or the AUC value)? 

d. Report the scoring results for the five new observations. 

e. Develop the naïve Bayes model with only x₁, x₂, and y in the naïve Bayes model. Repeat parts a through c and compare the results.