Telecommunications companies providing cell-phone service are interested in customer retention. In particular, identifying customers who are about to churn (cancel their service) is potentially worth millions of dollars if the company can proactively address the reason that customer is considering cancellation and retain the customer. Data on past customers, some of whom churned and some who did not, have been collected. The variables in this data set are listed in the following table.

Apply logistic regression with lasso regularization to classify observations as churning or not by using Churn 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. Apply the final model selected in part

(a) to the test set. What are the values of the intercept and variable coefficients in this final model? Interpret the coefficients.

c. For the final model selected in part (a), compute and interpret the lift on the top 10% of test set observations most likely to churn.

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Variable AccountWeeks Description number of weeks customer has had active account ContractRenewal 1 if customer recently renewed contract, O if not DataPlan Data Usage CustServCalls DayMins DayCalls MonthlyCharge OverageFee Roam Mins Churn 1 if customer has data plan, 0 if not gigabytes of monthly data usage number of calls into customer service average daytime minutes per month average number of daytime calls average monthly bill largest overage fee in last 12 months average number of roaming minutes "Yes" if customer cancelled service, "No" if not