## Question:

Market research was conducted for a national retail company to compare the relationship between sales and advertising during the warm spring and summer seasons as compared with the cool fall and winter seasons. The data shown in the following table were collected over a period of several years.

a. Identify a single regression model that uses the data for both warm and cool seasons and that defines straight-line models relating sales revenue (Y) to advertising expenditure (X) for each season.

b. Using the computer output given next, determine and plot the fitted straight lines for each season.

c. Test whether the straight lines for cool and warm seasons coincide.

d. Test H0: "The lines are parallel" versus HA: "The lines are not parallel."

e. In light of your answers to parts (c) and (d), comment on differences and similarities in the sales-advertising expenditure relationship between cooler and warmer seasons.

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**Transcribed Image Text:**

## Season Advertising (Warm=0, Expenditure Revenue (Warm=0, Expenditure Revenue Cool 1) (Smillions) (Smillions) Cool 1) (Smillions) (Smillions) Sales Season Advertising Sales 17.0 12.5 20.5 16.0 15.0 14.5 17.5 12.5 11.5 156.1 142.6 166.8 155.4 150.5 147.5 156.9 138.8 134.3 10.0 13.8 15.0 19.5 17.0 12.5 14.5 12.5 12.0 131.0 136.8 141.5 151.8 148.3 133.3 138.0 135.9 132.0 0 Regression of Sales Revenue (X) on Adv. Expenditure CX), Season (Z), and XZ DESCRIPTIVE STATISTICS Standard Deviation Variable Sum Mean Uncorrected SS Variance Intercept 18.00000 263.80000 9.00000 126.80000 2597,50000 100000 14.65556 0.50000 7.04444 144. 30556 18.00000 4002.94000 9.00000 1851 44000 376639 8.04732 0.26471 56.36497 106.17938 2 83678 0.51450 7.50766 10.30434 xz ANALYSIS OF VARIANCE Sum of DF Squares Mean Square Source Model Error Corrected Total F Value Pr> F 1755 87993 585 29331 166.65 <0001 14 49 16951 3.51211 17 805.04944 Root MSE Dependent Mean Coeff Var 1.87406 144.30556 1.29868 R-Square 09728 Adj R-Sq 0.9669 PARAMETER ESTIMATES Parameter Standard Error | tValue | Pr채 | Type ISS 3.56516 27,16 <0001 Variablo DFI Estimate Intorcopt 96.83045 374834 3.48488 023058 1511 .0001 1461.75022 7.17269 4.88170 147 01639 260.06703 3406268 xz 11.019780327463.11 0 0.0076