Adjusted R-squared
A modified version of R-squared that accounts for the number of predictors in a regression model.
What is Adjusted R-squared?
While standard R-squared measures the proportion of variance in the dependent variable explained by the model, it artificially increases every time a new predictor is added, even if that predictor is useless. Adjusted R-squared penalizes the score for adding unnecessary variables, increasing only if the new term improves the model more than would be expected by chance.
Why Adjusted R-squared Matters
It prevents researchers from being misled by overfitting, providing a more accurate and unbiased measure of a model's true explanatory power when comparing models with different numbers of predictors.
Example
A data scientist evaluating two models predicting stock prices chooses the model with the higher adjusted R-squared, knowing the standard R-squared was only higher in the alternative model because it included 50 noisy variables.
Common Mistakes
- Using adjusted R-squared to strictly determine if a model is 'good' or 'bad' without considering the research context or clinical relevance.
- Interpreting it as the absolute percentage of variance explained (it can technically be negative).