Sandhills Bank would like to increase the number of customers who use payroll direct deposit as part of the rollout of its new e-banking platform. Management has proposed offering an increased interest rate on a savings account if customers sign up for direct deposit into a checking account. To determine whether this proposal is a good idea, management would like to estimate how many of the 200 current customers who do not use direct deposit would accept the offer. In the Data worksheet of the le Sandhills, the IT company that handles Sandhills Bank's e-banking has provided anonymized data from one of its other client banks that made a similar promotion to increase direct deposit participation. For 1,000 customers, this data lists the average monthly checking account balance and whether the customer signed up for direct deposit. The Customer worksheet contains the average monthly balance data for Sandhill's 200 customers that would be the target of the direct-deposit promotion. Sandhills would like to estimate the likelihood of these customers signing up for direct deposit. Create a standard partition of the data in the Data worksheet with 60% of observations in the training set and 40% in the validation set. Classify the data using k-Nearest Neighbors with up to k = 20. Use Balance the as input variable and Direct as the output variable. In Step 2 of XLMiner's k-Nearest Neighbors Classification procedure, be sure to Normalize Input Data, Score on best k between 1 and specified value, and assign prior class probabilities According to relative occurrences in training data. In Step 3, specify the data in the Customer worksheet by selecting In Worksheet in the Score New Data area.

a. For the cutoff probability value 0.5, what value of k minimizes the overall error rate on the validation data?

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

c. Using the default cutoff value of 0.5, how many of Sandhills Bank's 200 customers does k-Nearest Neighbors classify as enrolling in direct deposit?