The accompanying data set contains three predictor variables (x₁, x₂, and x₃) and the target variable (y). 

a. Bin predictor variables x₁, x₂, and x₃. For Analytic Solver, choose the Equal interval option and 2 bins for each of the three variables. For R, bin x₁ into [0, 125) and [125, 250); x₂ into [0, 30) and [30, 60); and x₃ into [0, 30) and [30, 60). What are the bin numbers for the variables of the first two observations? 

b. Partition the transformed data to develop a naïve Bayes classification model where “1” denotes the positive or success class for y. Report the accuracy, sensitivity, specificity, and precision rates for the validation data set. 

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

d. Change the cutoff value to 0.4. Report the accuracy, sensitivity, specificity, and precision rates for the validation data set.