The larger the value of the coefficient of multiple determination the larger the value of the F-test statistic that is used for testing the usefulness of the multiple regression model.

Question

The larger the value of the coefficient of multiple determination  the larger the value of the F-test statistic that is used for testing the usefulness of the multiple regression model.

Quizplus · Accepted Answer

The coefficient of multiple determination (R-squared) measures the proportion of the total variation in the dependent variable that is explained by the independent variables in the regression model. A larger R-squared value indicates a better fit of the model to the data. The F-test statistic, on the other hand, tests the null hypothesis that all of the regression coefficients (except for the intercept) are equal to zero, indicating that the model is not useful in explaining the variation in the dependent variable. A larger F-test statistic indicates stronger evidence against the null hypothesis and in favor of the alternative hypothesis that at least one variable in the model is useful in explaining the dependent variable. Therefore, a larger R-squared value is associated with a larger F-test statistic for testing the usefulness of the regression model.

The Larger the Value of the Coefficient of Multiple Determination