2. Advertising and Sales A department store investigated the effects of advertising expenditures on the weekly sales for its men’s wear, children’s wear, and women’s wear departments. Five weeks were randomly selected for each department, and an advertising budget 1 x (in thousands of dollars)

was assigned to each. The weekly sales (in thousands of dollars) are shown in the accompanying table for each of the 15 one-week sales periods. If we expect weekly sales E(y) to be linearly related to advertising expenditure 1 x , 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 1 x 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 0 2 3 x 5x 5 .]

b. Find the equation of the line relating E(y) to 1 x for the children’s wear department B.

c. Find the equation of the line relating E(y) to 1 x 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.

Transcribed Image Text:

E(y) = B + Bx + B+B+ B x x z + B xxx 3 Quantitative Dummy variables Interaction terms that variable "advertising expenditure" used to introduce the qualitative variable department" into the model introduce differences in slopes where x = Advertising expenditure 1 if children's wear department B if not X2 0 1 x3 0 if not if women's wear department C