To study the effectiveness of a price discount coupon on a six-pack of a two-liter soft drink, Douglas Montgomery and Elizabeth Peck collected the data shown in Table 15.22. A sample of 5500 consumers was ran- domly assigned to the eleven discount categories shown in the table, 500 per category. The response variable is whether or not consumers re- deemed the coupon within one month.
a. See if the logit model ?ts the data, treating the redemption rate as the dependent variable and price discount as the explanatory variable.
b. See if the probit model does as well as the logit model.
c. What is the predicted redemption rate if the price discount was 17 cents?
d. Estimate the price discount for which 70 percent of the coupons will be redeemed.
TABLE 15.22
Price discount Sample size Number of coupons redeemed
X, ¢ Ni ni
|
5
|
500
|
100
|
|
7
|
500
|
122
|
|
9
|
500
|
147
|
|
11
|
500
|
176
|
|
13
|
500
|
211
|
|
15
|
500
|
244
|
|
17
|
500
|
277
|
|
19
|
500
|
310
|
|
21
|
500
|
343
|
|
23
|
500
|
372
|
|
25
|
500
|
391
|
Source: Douglas C. Montgomery and Elizabeth A. Peck, Introduction to Linear Regression Analysis, John Wiley & Sons, New York, 1982, p. 243 (notation changed).