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
Determine which of the following conclusions is valid regarding the coefficient of determination:
A) More analysis is needed. The coefficient of determination leaves much unexplained.
B) The regression line fits the data used in the sample very well. There is a strong indication of the relationship of the two variables with sales.
C) The coefficient of determination is positive because the constant term is positive.
D) The coefficient of determination should always be greater than one.

Question

Quizplus · Accepted Answer

A coefficient of determination of 0.96 indicates that the regression line explains 96% of the variability in sales that is attributable to advertising expenditures and per capita income. This is a high value and suggests a strong relationship between the variables and sales. Therefore, the regression line fits the data used in the sample very well. Choice A is incorrect as the coefficient of determination already explains a high percentage of the variability in sales. Choice C is incorrect as the positivity of the constant term does not affect the coefficient of determination. Choice D is incorrect as the coefficient of determination can only range from 0 to 1.

A Manager Uses Regression to Express Sales as a Function