14.20 Advertising effect on sales Each of 100 restaurants in a fast-food chain is randomly assigned one of four media for an advertising campaign: A = radio, B = TV, C = newspaper, D = mailing. For each restaurant, the observation is the change in sales, defined as the difference between the sales for the month during which the advertising campaign took place and the sales in the same month a year ago (in thousands of dollars).

a. By creating indicator variables, write a regression equation for the analysis to compare mean change in sales for the four media.

b. Explain how you could use the regression model to test the null hypothesis of equal population mean change in sales for the four media.

c. The prediction equation is yn = 35 + 5x1 - 10x2 + 2x3 where x1, x2, and x3 are indicator variables for media A, B, and C, respectively. Estimate the difference in mean change in sales for media (i) A and D, (ii) A and B. (Hint: For part (ii), write the prediction equation for the mean for media A, then for media B, and then subtract.)