In a multiple regression model, Y is predicted from X₁, X₂, and X₃. Both R² and R_adj² are computed. If X₃ is removed from the model, how will R_adj² change? A) R_adj² will increase. B) R_adj² will decrease. C) R_adj² will not change. D) uncertain.

Question

Quizplus · Accepted Answer

The change in adjusted R-squared (R_adj²) when a variable is removed from a multiple regression model depends on the contribution of that variable to the model. If the variable significantly contributes to explaining the variance in the dependent variable, removing it could decrease the adjusted R-squared. Conversely, if the variable does not contribute significantly or adds redundancy, removing it could increase the adjusted R-squared. Therefore, without specific information about the variable's contribution, the effect on adjusted R-squared is uncertain.

In a Multiple Regression Model, Y Is Predicted from X1

In a Multiple Regression Model, Y Is Predicted from X₁