Question

The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x ₁) and newspaper advertising (x ₂). The estimated regression equation was

Weekly Gross Revenue ($1000s)	Televison Advertising ($1000s)	Newspaper Advertising ($1000s)
96	5	1.5
90	2	2
96	5	1.5
92	2.5	3.5
95	4	4.3
95	4.5	2.3
94	3.5	5.2
94	4	3.5

ŷ = 85.7 + 1.94 x ₁ + 0.3 x ₂

The computer solution provided SST = 30 and SSR = 29.424.

1. Compute R ² and R _a² (to 3 decimals).
   

   R 2
   R a2

2. When television advertising was the only independent variable, R ² = 0.946 and R _a² = 0.937. Are the multiple regression analysis results preferable?
   SelectYes, because greater variability is explained when both independent variables are usedNo, because less variability is explained when both independent variables are used

Answer 1

R2 = SSR/SST = 29.424/30 = 0.981

R a2 = 1-(1-R2)*((n-1)/(n-k-1))
= 1-(1-0.981)*((8-1)/(8-2-1))
= 0.973

Yes, because greater variability is explained when both independent variables are used
as R2 for multiple regression is higher than that with only TV advertising