Chapter 15.9, Problem 46E

Community Bank would like to increase the number of customers who use payroll direct deposit. Management is considering a new sales campaign that will require each branch manager to call each customer who does not currently use payroll direct deposit. As an incentive to sign up for payroll direct deposit, each customer contacted will be offered free checking for two years. Because of the time and cost associated with the new campaign, management would like to focus their efforts on customers who have the highest probability of signing up for payroll direct deposit. Management believes that the average monthly balance in a customer’s checking account may be a useful predictor of whether the customer will sign up for direct payroll deposit. To investigate the relationship between these two variables, Community Bank tried the new campaign using a sample of 50 checking account customers who do not currently use payroll direct deposit. The sample data show the average monthly checking account balance (in hundreds of dollars) and whether the customer contacted signed up for payroll direct deposit (coded 1 if the customer signed up for payroll direct deposit and 0 if not). The data are contained in the data set named Bank; a portion of the data follows.

Customer	x = Monthly Balance	y = Direct Deposit
1	1.22	0
2	1.56	0
3	2.10	0
4	2.25	0
5	2.89	0
6	3.55	0
7	3.56	0
8	3.65	1.
.	.	.
.	.	.
.	.	.
48	1 8.45	1
49	24.98	0
50	26.05	1

1. a. Write the logistic regression equation relating x to y.
2. b. For the Community Bank data, use Minitab to compute the estimated logistic regression equation.
3. c. Conduct a test of significance using the χ² test statistic. Use α = .05.
4. d. Estimate the probability that customers with an average monthly balance of $1000 will sign up for direct payroll deposit.
5. e. Suppose Community Bank only wants to contact customers who have a .50 or higher probability of signing up for direct payroll deposit. What is the average monthly balance required to achieve this level of probability?
6. f. What is the estimated odds ratio? What is its interpretation?