A manager uses regression to express sales as a function of advertising expenditures (X1), and per capita income (X2) in your sales area. The following multiple linear regression equation is developed:
Y = 10 + 0.51X1 + 0.45X2
The coefficient of determination is 0.96
This coefficient of determination explains that:
A) 96% of sales variations are due to an error term.
B) The dependent variable is not related to advertising expenditures and per capita income.
C) 96% of sales variations are explained by the equation.
D) Only 4% of the sales variations are explained by advertising expenditures and per capita income.

Question

Quizplus · Accepted Answer

The coefficient of determination (R-squared) of 0.96 indicates that 96% of the variation in sales is explained by the regression equation, which includes advertising expenditures and per capita income as predictors. Therefore, option C is correct. Option A is incorrect because it suggests that 96% of the variation is due to an error term, which is not true. Option B is incorrect because the regression equation shows that the dependent variable (sales) is related to advertising expenditures and per capita income. Option D is also incorrect because it suggests that only 4% of the variation is explained by the predictors, which is also not true.

A Manager Uses Regression to Express Sales as a Function