The marketing manager for a chain of hardware stores needed more information about the effectiveness of the three types of advertising that the chain used. These are localized direct mailing (in which flyers describing sales and featured products are distributed to homes in the area surrounding a store), newspaper advertising, and local television advertisements. To determine which type is most effective, the manager collected 1 week’s data from 100 randomly selected stores. For each store, the following variables were recorded:

Weekly gross sales

Weekly expenditures on direct mailing

Weekly expenditures on newspaper advertising

Weekly expenditures on television commercials

All variables were recorded in thousands of dollars.

a. Find the regression equation.

b. What are the coefficient of determination and the coefficient of determination adjusted for degrees of freedom? What do these statistics tell you about the regression equation?

c. What does the standard error of estimate tell you about the regression model?

d. Test the validity of the model.

e. Which independent variables are linearly related to weekly gross sales in this model? Explain.

f. Compute the 95% interval of the week’s gross sales if a local store spent $800 on direct mailing, $1,200 on newspaper advertisements, and $2,000 on television commercials.

g. Calculate the 95% interval of the mean weekly gross sales for all stores that spend $800 on direct mailing, $1,200 on newspaper advertising, and $2,000 on television commercials.

h. Discuss the difference between the two intervals found in parts (f) and (g).