In the multiple regression model, the adjusted $R ^ { 2 } , \bar { R } ^ { 2 }$
A) cannot be negative.
B) will never be greater than the regression $R ^ { 2 }$
C) equals the square of the correlation coefficient r .
D) cannot decrease when an additional explanatory variable is added.

Question

In the multiple regression model, the adjusted $R ^ { 2 } , \bar { R } ^ { 2 }$
A) cannot be negative.
B) will never be greater than the regression $R ^ { 2 }$
C) equals the square of the correlation coefficient  r .
D) cannot decrease when an additional explanatory variable is added.

Quizplus · Accepted Answer

The adjusted $R^2$ accounts for the number of predictors in the model and can be less than the regular $R^2$ if the added variables do not improve the model significantly.

In the Multiple Regression Model, the Adjusted R2,Rˉ2R ^ { 2 } , \bar { R } ^ { 2 }R2,Rˉ2

In the Multiple Regression Model, the Adjusted $R ^ { 2 } , \bar { R } ^ { 2 }$