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. For each of 1,000 Salmons customers, three variables were tracked from an earlier promotional campaign: last year’s total spending at Salmons (Spending), whether they have a Salmons store credit card (Card), and whether they used the promotional coupon they were sent (Coupon).

Apply logistic regression with lasso regularization to classify observations as a promotion-

responder or not by using Coupon as the target (or response) variable. Set aside 20% of the data as a test set and use 80% of the data for training and validation.

a. Determine the lasso regularization penalty that maximizes AUC in a validation procedure.

b. For the level of lasso regularization identified in part (a), what are the values of the intercept and variable coefficients in this final model? Interpret the coefficients.
Does the lasso regularization eliminate any variables?

c. For the final model selected in part (d), compute and interpret the lift measure on the top 10% of the test set observations most likely to use the promotional coupon.