The market research department of a soft drink manufacturer is investigat- ing 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 are shown below. Discount, x Sample Size, n Number Redeemed, r 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 a. Fit a logistic regression model to the data. Use a simple linear regression model as the structure for the linear predictor. b. Does the model deviance indicate that the logistic regression model from part a is adequate? c. Draw a graph of the data and the tted logistic regression model. (1. 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 t to the data than the original model from part a? f. For the quadratic model in part d, nd Wald statistics for each individual model parameter. g. Find approximate 95% condence intervals on the model parameters for the quadratic logistic regression model from part d