The market research department of a soft drink manufacturer is investigating the effectiveness of a price discount coupon on the purchase of a two-liter beverage product. A sample of 5500 customers was given coupons for varying price discounts between 5 and 25 cents. The response variable was the number of coupons in each price discount category redeemed after one month. The data follow in Table E11-15.

(a) Fit a logistic regression model to the data. Use a simple linear regression model as the structure for the linear predictor.

(b) Is the logistic regression model in part (a) adequate?

(c) Draw a graph of the data and the fitted logistic regression model.

(d) Expand the linear predictor to include a quadratic term. Is there any evidence that this quadratic term is required in the model?

(e) Draw a graph of this new model on the same plot that you prepared in part (c). Does the expanded model visually provide a better fit to the data than the original model from part (a)?

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Number Sample Size, n 500 Redeemed, r Discount, x 100 500 122 500 147 11 500 176 13 500 211 15 500 244 17 500 277 19 500 310 21 500 343 23 500 372 25 500 391