A multiple regression equation includes 5 independent variables,and the coefficient of determination is 0.81.The percentage of the variation in y that is explained by the regression equation is 90%.

Question

Quizplus · Accepted Answer

The coefficient of determination (R-squared) indicates the proportion of variation in the dependent variable (y) that is explained by the independent variables in the regression equation. Therefore, if R-squared is 0.81, it means that 81% of the variation in y is explained by the regression equation. To convert this to percentage of variation explained, we need to multiply it by 100. Thus, the percentage of variation in y that is explained by the regression equation is 81%. Therefore, the statement in the question that the percentage of variation explained is 90% is false.

A Multiple Regression Equation Includes 5 Independent Variables,and the Coefficient