Which statement best describes Adjusted R-squared according to the material?

Which statement best describes Adjusted R-squared according to the material?

• A. A measure of the loss of predictive power or shrinkage in regression.
• B. A small value represents a better fit to the data.
• C. It indicates the total variance explained by the model.
• D. It cannot be compared across models.

Answer: (B)

Adjusted R-squared reflects how well the model explains the variability in the outcome after accounting for the number of predictors. It starts from the regular R-squared (which tends to rise when you add more variables) but subtracts a penalty for each extra predictor. This means a new variable only improves the adjusted value if it provides enough additional explanatory power beyond what’s already in the model. Because of this penalty, the statistic is used to compare models with different numbers of predictors: you generally prefer the model with the higher adjusted R-squared, up to a maximum of 1. It can even be negative if the model explains less variation than the mean would. It is not a measure of the total variance explained (that’s R-squared), and it isn't a measure of predictive power loss or shrinkage in the sense implied by that phrasing. So the idea that a smaller value indicates a better fit is not correct; larger adjusted R-squared values indicate a better-fitting model after adjusting for complexity.

Adjusted R-squared reflects how well the model explains the variability in the outcome after accounting for the number of predictors. It starts from the regular R-squared (which tends to rise when you add more variables) but subtracts a penalty for each extra predictor. This means a new variable only improves the adjusted value if it provides enough additional explanatory power beyond what’s already in the model.

Because of this penalty, the statistic is used to compare models with different numbers of predictors: you generally prefer the model with the higher adjusted R-squared, up to a maximum of 1. It can even be negative if the model explains less variation than the mean would.

It is not a measure of the total variance explained (that’s R-squared), and it isn't a measure of predictive power loss or shrinkage in the sense implied by that phrasing. So the idea that a smaller value indicates a better fit is not correct; larger adjusted R-squared values indicate a better-fitting model after adjusting for complexity.