When an additional explanatory variable is introduced into a multiple regression model, coefficient of multiple determination adjusted for degrees of freedom can never decrease.

Question

Quizplus · Accepted Answer

The coefficient of multiple determination adjusted for degrees of freedom can decrease when an additional explanatory variable is introduced into a multiple regression model. This happens when the new variable does not significantly contribute to explaining the variability in the dependent variable or when it is correlated with one or more of the existing explanatory variables, leading to issues of multicollinearity.

When an Additional Explanatory Variable Is Introduced into a Multiple