Which statement best describes adjusted R-squared in regression analysis?

Which statement best describes adjusted R-squared in regression analysis?

• A. It is the square root of R-squared
• B. It measures multicollinearity
• C. It accounts for the number of predictors in the model
• D. It always equals R-squared

Answer: (C)

Adjusted R-squared shows how much of the outcome’s variation your predictors explain, but with a penalty for adding more predictors. This means it guards against overfitting: while R-squared can only go up or stay the same when you add variables, adjusted R-squared may go down if the new predictors don’t genuinely improve the model fit relative to the amount of data. The penalty depends on the number of predictors and the sample size, so in smaller samples or when adding many variables, the adjustment can have a noticeable effect. It’s not about multicollinearity, isn’t simply the square root of R-squared, and won’t always equal R-squared; the adjustment is specifically about balancing explanatory power with model complexity.

Adjusted R-squared shows how much of the outcome’s variation your predictors explain, but with a penalty for adding more predictors. This means it guards against overfitting: while R-squared can only go up or stay the same when you add variables, adjusted R-squared may go down if the new predictors don’t genuinely improve the model fit relative to the amount of data. The penalty depends on the number of predictors and the sample size, so in smaller samples or when adding many variables, the adjustment can have a noticeable effect. It’s not about multicollinearity, isn’t simply the square root of R-squared, and won’t always equal R-squared; the adjustment is specifically about balancing explanatory power with model complexity.