Question

When we add another independent variable, Adjusted R2 increases only if the new variable explains _____.

A) More variance
B) Less variance
C) No variance
D) Only the mean

Answer 1

Adjusted R-squared increases only if a new independent variable added to a regression model explains more variance, which means it contributes to the model's explanatory power.

Step-by-step explanation:

When we add another independent variable to a regression model, the Adjusted R-squared increases only if the new variable explains More variance. Adjusted R-squared is a modification of R-squared that adjusts for the number of predictors in the model. Unlike R-squared, which always goes up as more variables are added, Adjusted R-squared increases only if the new variable improves the model more than would be expected by chance. It takes into account the number of independent variables used relative to the number of data points and penalizes for adding variables that do not contribute to the explanatory power of the model. If the new variable does not explain more variance, it means it isn't significantly contributing to the model, and therefore, Adjusted R-squared may decrease or stay the same.