Adjusted R-squared evaluates regression fit while penalizing unnecessary predictors. Unlike R-squared, which typically increases when variables are added, it balances explanatory power against model complexity. section 4.2.3
Use adjusted R-squared to interpret competing regression models:
- Prioritize adjusted R-squared when it diverges substantially from R-squared, because the divergence indicates that added predictors may contribute little explanatory value. section 4.2.3
- Reduce the model systematically by removing statistically insignificant predictors, improving interpretability and potentially accuracy. section 4.2.3
- Interpret both measures in the context of explained variance: R-squared ranges from 0 to 1 and represents variance explained by the predictors. section 4.2.3
Comparing regression fit
A simple regression of marathon Stage 2 time on Stage 1 time produces R-squared of approximately 0.575. With additional predictors, compare adjusted R-squared rather than assuming the larger R-squared represents a better model. section 4.2.3
