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 (x₂). The estimated regression equation was

Weekly Gross Revenue ($1000s)	Televison Advertising ($1000s)	Newspaper Advertising ($1000s)
96	5	2.5
90	3	3
96	5	1.5
92	3.5	2.5
96	4	4.3
94	4.5	2.3
95	3.5	5.2
95	4	3.5

ŷ = 76.3 + 3.41 x ₁ + 1.33 x ₂

The computer solution provided SST = 33.5 and SSR = 31.358.

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 = 0.563 and R _a² = 0.490. 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 usedItem 3

Answer 1

Solution:

Given: 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 (x₂)

The computer solution provided SST = 33.5 and SSR = 31.358.

Part a) Compute R ² and R _a² :

and

Part b) When television advertising was the only independent variable, R ² = 0.563 and R _a² = 0.490.

Are the multiple regression analysis results preferable?

When we use both independent variability , we have , which means 93.6% of the variability is explained.

When we use one independent variable , R ² = 0.563 = 56.3% , which explains less variability.

Thus correct option is:

Yes, because greater variability is explained when both independent variables are used