44. Coupon Redemption. Refer to the Simmons Stores example introduced in this section. The dependent variable is coded as y = 1 if the customer used the coupon and 0 if not. Suppose that the only information available to help predict whether the customer will use the coupon is the customer’s credit card status, coded as x = 1 if the customer has a Simmons credit card and x = 0 if not.

a. Write the logistic regression equation relating x to y.

b. What is the interpretation of E( y) when x = 0?

c. For the Simmons data in Table 15.11, use statistical software to compute the estimated logit.

d. Use the estimated logit computed in part

(c) to estimate the probability of using the coupon for customers who do not have a Simmons credit card and to estimate the probability of using the coupon for customers who have a Simmons credit card.

e. What is the estimated odds ratio? What is its interpretation?