Which of the following is most appropriate for adjusted R²?

A. It is always positive.
B. It may or may not increase when one adds an independent variable.
C. It is non-decreasing in the number of independent variables.

Correct Answer: B

The value of the adjusted R² increases only when the added independent variables improve the fit of the regression model. Moreover, it decreases when the added variables do not improve the model fit sufficiently.

A is incorrect: The adjusted R² can be negative if R² is low enough. However, multiple R² is always positive.

C is incorrect: The adjusted R² can decrease when the added variables do not improve the model fit by a good enough amount. However, multiple R² is non-decreasing in the number of independent variables. For this reason, it is less reliable as a measure of goodness of fit in regression with more than one independent variable than in a one-independent variable regression.