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 = 83.1 + 2.23x₁ + 1.30x₂.

The computer solution, based on a sample of eight weeks, provided SST = 25.4 and SSR = 23.395.

(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. Do you prefer the multiple regression results?

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

Answer 1

a)

R2=SSR/SST =

0.921

R2adj=1-(1-R2)*(n-1)/(n-k-1)=

0.889

The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is 0.921 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 0.889

b)

Multiple regression analysis is preferred since both R² and R_a² show an increased percentage of the variability of y explained when both independent variables are used.