If adding a predictor to a regression model increases R-squared but leaves adjusted R-squared nearly unchanged, what is the likely interpretation?

If adding a predictor to a regression model increases R-squared but leaves adjusted R-squared nearly unchanged, what is the likely interpretation?

• A. The model fit improved dramatically.
• B. The new predictor does not add meaningful explanatory power.
• C. The data are overfitting.
• D. The predictor is highly collinear with existing predictors.

Answer: (B)

When you add a predictor, R-squared can rise because the model can fit the training data better, but adjusted R-squared accounts for the number of predictors and penalizes extra complexity. If R-squared increases while adjusted R-squared stays about the same, the extra predictor isn’t providing substantial new information beyond what the existing variables already explain. It’s likely capturing noise or information that’s largely redundant with what’s already in the model. In short, the new predictor does not have meaningful explanatory power.

When you add a predictor, R-squared can rise because the model can fit the training data better, but adjusted R-squared accounts for the number of predictors and penalizes extra complexity. If R-squared increases while adjusted R-squared stays about the same, the extra predictor isn’t providing substantial new information beyond what the existing variables already explain. It’s likely capturing noise or information that’s largely redundant with what’s already in the model. In short, the new predictor does not have meaningful explanatory power.