For ordinary least-squares models with an intercept fitted to the same observations, how does adjusted R-squared differ from raw R-squared?
Correct Answer
C) It accounts for sample size and the number of fitted parameters
Adjusted R-squared adjusts the residual and total sums of squares for their degrees of freedom. In nested intercept OLS models using the same observations, adding a predictor cannot decrease raw R-squared but can reduce adjusted R-squared if fit improvement is insufficient. It is neither a mean error nor restricted to one predictor, and it need not exceed raw R-squared.
Why This Is the Correct Answer
Adjusted R-squared adjusts the residual and total sums of squares for their degrees of freedom. In nested intercept OLS models using the same observations, adding a predictor cannot decrease raw R-squared but can reduce adjusted R-squared if fit improvement is insufficient. It is neither a mean error nor restricted to one predictor, and it need not exceed raw R-squared.
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