Answered: (a)Compute and interpret R2 and Ra2.…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Question

The owner of a movie theater company used multiple regression analysis to predict gross revenue

(y) as a function of television advertising (x₁) and newspaper advertising (x₂).

The estimated regression equation was

ŷ = 82.4 + 2.23x₁ + 1.40x₂.

The computer solution, based on a sample of eight weeks, provided SST = 25.5 and SSR = 23.495.
(Note: SST = SS_yy)

(a)Compute and interpret R² and R_a².

(Round your answers to three decimal places.)

The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (??) . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (??) .

(b)When television advertising was the only independent variable,

R² = 0.653 and R_a² = 0.595.

Is the multiple regression model more preferable over the simple regression model? Explain.

Multiple regression analysis (is/is not) preferred since both R² and R_a² show (an increased/ a decreased) proportion of the variability of y explained when both independent variables are used.

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