The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to

Question

The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (xi) and newspaper advertising (x2). The estimated regression equation was Weekly Gross Televison Newspaper Revenue Advertising Advertising (s1000s) (s1000s) ($1000s) 96 91 96 92 95 95 94 95 2.5 1.5 2.5 4.3 3.3 2.5 3.5 2.5 2.5 = 85.6 + 1.7x1 + 0.97x2 The computer solution provided SST-23.5 and SSR-22.846. a. Compute R2 and R2a (to 3 decimals). b, when television advertising was the only independent variable, R2-.653 and R2a = .595. Are the multiple regression analysis results preferable? Select Yes, because greater variability is explained when both independent variables are used No, because less variability is explained when both independent variables are used

Explanation / Answer

here R2 =SSR/SST=22.846/23.5 =0.972

SSE =SST-SSR =0.654

n=8 and number of paramters p=3

and R2a =1-(SSE/(n-p))/(SST/(n-1))=1- (0.654/(8-3))/(23.5/(8-1))=0.961

b)Yes becasue greater vairability is explained when both independent variables are used.

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