As the value of the multiple coefficient of determination increases, A) the value of the adjusted multiple coefficient of determination decreases. B) the value of the regression equation's constant b₀ decreases. C) the goodness of fit for the estimated multiple regression equation increases. D) the value of the correlation coefficient decreases.

Question

Quizplus · Accepted Answer

The multiple coefficient of determination, also known as R-squared, measures the proportion of variance in the dependent variable that is explained by the independent variables in the multiple regression equation. As the value of R-squared increases, it indicates a better fit of the estimated multiple regression equation to the data, implying that the goodness of fit increases. The adjusted multiple coefficient of determination, on the other hand, takes into account the number of independent variables and adjusts for sample size, and may decrease as more variables are added to the regression equation. The value of the regression equation's constant (intercept) and the correlation coefficient are not directly affected by the value of R-squared.

As the Value of the Multiple Coefficient of Determination Increases