a. For each department's model, report the hit ratio in the corresponding department- specific test subset (e.g., for the Backcountry department, this will be the 1370 customers in the test subset for that department). Use a probability cutoff of 0.5 to calculate the Hit-Ratios (See the note and hints below). b. For each customer in the representative sample (215,000 customers in Pentathlon_Rep.csv), determine the department (Backcountry, Endurance, Strength, Team, or Winter) that is predicted to lead to the maximum probability of buying. Then, for each department, report the percentage of customers for whom that department's message maximizes their probability of buying (See the note and hints below). NOTE: As the oversampled training subset has no effect on the relative ranking of the predicted purchase probabilities across customers and/or messages, the probabilities do not have to be adjusted for question 2. HINTS: For question 2a, you should find that the logistic model for the Backcountry department has a hit ratio of 79.56% For question 2b, you should find that the Backcountry department's message maximizes the probability of buying only for 2.61% of the customers Q3. (4 points) For each customer in the representative sample, determine the department (Backcountry, Endurance, Strength, Team, or Winter) that is predicted to lead to the highest expected profit. Assume that the expected profit is a certain percentage of the order size, and that there is no cost for sending an e-mail. The percentage or the average profit margin is specific to the department sending the e-mail message