Question

What is the relationship between R-squared and the adjusted R-squared?

a.the adjusted R-squared is larger than regular R-squared

b. for a simple linear regression the adjusted R-squared is equal to regular R-squared

c. the adjusted R-squared adjusts explanatory power by the degrees of freedom

d. the adjusted R-squared adjusts explanatory power by division by the standard error of each coefficient

e. the adjusted R-squared always increases as more independent variables are added to the model

Answer 1

Answer :

c) adjusted R-squared adjusts explanatory power by the degrees of freedom.

Note that,

The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. The adjusted R-squared increases only if the new term improves the model more than would be expected by chance. It decreases when a predictor improves the model by less than expected by chance. The adjusted R-squared can be negative, but it’s usually not. It is always lower than the R-squared.