Salmons Stores operates a national chain of women's apparel stores. Five thousand copies of an expensive four-color sales catalog have been printed, and each catalog includes a coupon that provides a $50 discount on purchases of $200 or more. Salmons would like to send the catalogs only to customers who have the highest probability of using the coupon. The le Salmons contains data from an earlier promotional campaign. For each of 1,000 Salmons customers, three variables are tracked: last year's total spending at Salmons, whether they have a Salmons store credit card, and whether they used the promotional coupon they were sent.

Create a standard partition of the data with all the tracked variables and 50% of observations in the training set, 30% in the validation set, and 20% in the test set. Use logistic regression to classify observations as a promotion-responder or not by using Spending and Card as input variables and Coupon as the output variable. Perform Variable Selection with the best subsets procedure with the number of best subsets equal to two.

a. Evaluate the logistic regression models based on their classification error.

Recommend a final model and express the model as a mathematical equation relating the output variable to the input variables.

b. For the model selected in part (a), interpret the meaning of the first-decile lift in the decile-wise lift chart on the test set.

c. What is the area under the ROC curve on the test set? To achieve a sensitivity of at least 0.80, how much Class 0 error rate must be tolerated?