A multiple regression equation includes five independent variables, and the coefficient of determination is 0.81. What is the percentage of the variation in y that is explained by the regression equation?
A) 90%
B) 86%
C) 81%
D) about 16%

Question

Quizplus · Accepted Answer

The coefficient of determination (R-squared) represents the proportion of variation in the dependent variable that is explained by the independent variables in the regression equation. The value of R-squared ranges between 0 and 1, where 0 indicates no linear relationship between the dependent and independent variables, and 1 indicates a perfect linear relationship.

In this case, the R-squared is 0.81, which means that the independent variables in the regression equation explain 81% of the variation in the dependent variable. Therefore, the correct answer is C, which represents 81%.

A Multiple Regression Equation Includes Five Independent Variables, and the Coefficient