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R-squared adjusted for the number of predictors to penalize overfitting.
DESCRIPTION
Adjusted R-squared modifies the coefficient of determination to account for model complexity. It increases only if a new predictor improves the model more than expected by chance. This makes it more reliable than R-squared for comparing models with different numbers of features. It is commonly used in linear regression diagnostics and model selection. However, information criteria like AIC or BIC may provide a more principled trade-off in some contexts.
ALTERNATIVE DEFINITIONS
Investopedia
Adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model.
Emphasizes the penalty for additional predictors to deter overfitting.
Wikipedia
Adjusted R-squared, denoted RÌ„2, is a modified version of R2 that has been adjusted for the number of predictors in the model.
States notation and direct relationship to R-squared.
RELATED TERMS
Linear Model Model Overfitting Cross-Validation Model Selection F-test Mean Squared Error
COMPETING TERMS
R-squared Akaike Information Criterion Bayesian Information Criterion
RELATIONS
- Broader: R-squared
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist AI Engineer Data Analyst
EXTERNAL SOURCES
- Wikipedia - Adjusted R-squared
- Statsmodels - API docs exposing adjusted R-squared
- CRAN - R examples reporting adjusted R-squared
TOP QUESTIONS
Why use Adjusted R-squared instead of R-squared?
Adjusted R-squared penalizes adding predictors that do not meaningfully improve fit, making model comparisons fairer.
Category: Comparison
When does Adjusted R-squared increase?
It increases only when a new variable improves the model more than would be expected by chance.
Category: Interpretation
Is Adjusted R-squared always between 0 and 1?
It can be negative for poorly fitting models, though commonly positive in reasonable regressions.
Category: Theory
How do AIC and BIC compare to Adjusted R-squared?
AIC and BIC are likelihood-based criteria with explicit complexity penalties; they’re more general across model types.
Category: Alternatives
What is a common mistake with Adjusted R-squared?
Using it as the sole selection criterion; cross-validation and domain knowledge remain important.
Category: Mistakes
Does Adjusted R-squared indicate causality?
No, it measures fit, not causal relationships. Causal inference requires different assumptions and methods.
Category: Misunderstanding
Is Adjusted R-squared suitable for nonlinear models?
It’s primarily tied to linear regression; information criteria often generalize better to nonlinear models.
Category: Requirements
How should I report Adjusted R-squared?
Report alongside R-squared, model specification, and validation metrics to provide comprehensive context.
Category: Best practices
Can Adjusted R-squared decrease when adding variables?
Yes, if the added variables don’t sufficiently improve the model, Adjusted R-squared will decrease.
Category: Interpretation