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 R² change? A) R² will increase. B) R² will decrease. C) R² will not change. D) uncertain.

Question

Quizplus · Accepted Answer

The change in $R^2$ upon removing a variable 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 Y, $R^2$ might decrease. If the variable does not contribute or contributes negatively, $R^2$ might increase or not change significantly. Therefore, without specific information about the variable's contribution, the effect on $R^2$ is uncertain.

In a Multiple Regression Model, Y Is Predicted from X1

In a Multiple Regression Model, Y Is Predicted from X₁