Question

The owner of a move theater company used mutiple regression analysis to predict gross revenue (γ) as a function of television advertising (x₁​) and newspaper advertising (x₂​). The estimated: regression equation was

θ=832+274x₁​+196x₂​
The computer solution, based on a sample of eight weeks, provided 55 T=25.7 and 5 SR=23.365.

Compute and interpret R² and RA²​ - (Round your answer to three decimal places.)
The preportion of the varabity in the dependent variabie that can be explained by the estimated multiple regression equation is the model, the proportion of the varibety in the dependent variabie that can be explained by the estimated mutiple regression equation is _______.

Answer 1

The coefficient of determination (r²) is calculated by dividing SSR by SST to determine the proportion of variability in gross revenue that can be explained by the regression model. An example interpretation is that if r² is 0.44, then about 44% of the variation in revenue is explained by the variation in advertising.

Step-by-step explanation:

The proportion of the variability in the dependent variable (gross revenue γ) that can be explained by the estimated multiple regression equation involving television advertising (x₁) and newspaper advertising (x₂) is captured by the coefficient of determination (r²). To compute r², we divide the regression sum of squares (SSR) by the total sum of squares (SST). Here SSR is given as 23.365 and SST as 25.7. The calculation is r² = SSR/SST = 23.365 / 25.7.

r² represents the percentage of variation in γ that can be explained by variation in x₁ and x₂ using the regression line. Adjusted r² (rA²) is another measure that adjusts r² for the number of predictors in the model and the sample size, calculated using the formula: rA² = 1 - [(1 - r²)(n - 1)/(n - k - 1)], where n is the sample size and k is the number of predictors.

To interpret r² in this context, if r² is 0.44 for example, it means approximately 44 percent of the variation in revenue can be explained by the variation in television and newspaper advertising, based on the data from the eight weeks.