Advertising and Sales, continued Refer to Exercise 13.26. Use a computer software pa...

Advertising and Sales, continued Refer to Exercise 13.26. Use a computer software package to perform the multiple regression analysis and obtain diagnostic plots if possible.

a. Comment on the fit of the model, using the analysis of variance F-test, , and the diagnostic plots to check the regression assumptions.

b. Find the prediction equation, and graph the three department sales lines.

c. Examine the graphs in part b. Do the slopes of the lines corresponding to the children’s wear B and men’s wear A departments appear to differ? Test the null hypothesis that the slopes do not differ () versus the alternative hypothesis that the slopes are different.

d. Are the interaction terms in the model significant? Use the methods described in Section 13.5 to test . Do the results of this test suggest that the fitted model should be modified?

e. Write a short explanation of the practical implications of this regression analysis.

Reference:

Advertising and Sales A department store conducted an experiment to investigate the effects of advertising expenditures on the weekly sales for its men’s wear, children’s wear, and women’s wear departments. Five weeks for observation were randomly selected from each department, and an advertising budget , and if we expect the slopes of the lines corresponding to the three departments to differ, then an appropriate model for E(y) is

a. Find the equation of the line relating E(y) to advertising expenditure x1 for the men’s wear department A. [HINT: According to the coding used for the dummy variables, the model represents mean sales E(y) for the men’s wear department A when into the equation for E(y) to find the equation of this line.]

b. Find the equation of the line relating E(y) to .]

c. Find the equation of the line relating E(y) to for the women’s wear department C.

d. Find the difference between the intercepts of the E(y) lines corresponding to the children’s wear B and men’s wear A departments.

e. Find the difference in slopes between E(y) lines corresponding to the women’s wear C and men’s wear A departments.

f. Refer to part e. Suppose you want to test the null hypothesis that the slopes of the lines corresponding to the three departments are equal. Express this as a test of hypothesis about one or more of the model parameters.