Advertising and Sales A departmentstore conducted an experiment to investigate

Chapter 13, Problem 26

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Advertising and Sales A departmentstore conducted an experiment to investigate theeffects of advertising expenditures on the weekly salesfor its mens wear, childrens wear, and womens wear departments. Five weeks for observation were randomlyselected from each department, and an advertisingbudget x1 (in hundreds of dollars) was assigned foreach. The weekly sales (in thousands of dollars) areshown in the accompanying table for each of the 15one-week sales periods. If we expect weekly salesE(y) to be linearly related to advertising expenditurex1, and if we expect the slopes of the lines correspondingto the three departments to differ, then an appropriatemodel for E(y) isE(y) b0b1x1 b2x2 b3x3 b4x1x2 b5x1x3 quantitative dummy variables interaction terms thatvariable used to introduce introduce differencesadvertising the qualitative in slopesexpenditure variable departmentinto the modelwherex1 Advertising expenditure1 if childrens wear department B x2 0 if not1 if womens wear department C x3 0 if notAdvertising Expenditure(hundreds of dollars)Department 1 2 3 4 5Mens wear A 5.2 5.9 7.7 7.9 9.4Childrens wear B 8.2 9.0 9.1 10.5 10.5Womens wear C 10.0 10.3 12.1 12.7 13.6a. Find the equation of the line relating E(y) toadvertising expenditure x1 for the mens weardepartment A. [HINT: According to the codingused for the dummy variables, the model representsmean sales E(y) for the mens wear departmentA when x2 x3 0. Substitute x2 x3 0into the equation for E(y) to find the equation ofthis line.]b. Find the equation of the line relating E(y) to x1 forthe childrens wear department B. [HINT: Accordingto the coding, the model represents E(y) for thechildrens wear department when x2 1 andx3 0.]c. Find the equation of the line relating E(y) to x1 forthe womens wear department C. d. Find the difference between the intercepts of theE(y) lines corresponding to the childrens wear Band mens wear A departments.e. Find the difference in slopes between E(y) linescorresponding to the womens wear C and menswear A departments.f. Refer to part e. Suppose you want to test the nullhypothesis that the slopes of the lines correspondingto the three departments are equal. Express thisas a test of hypothesis about one or more of themodel parameters.