R-squared
A goodness-of-fit measure for regression models indicating the percentage of variance in the dependent variable explained by the independent variables.
What is R-squared?
R-squared (the coefficient of determination) is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. It ranges from 0 to 1.
Why R-squared Matters
It provides a simple, intuitive metric for how well the regression model fits the observed data.
How to Interpret
A higher R-squared generally indicates a better fit. However, what constitutes a 'good' R-squared depends heavily on the field (e.g., 0.30 might be excellent in psychology, but 0.90 is expected in physics).
Example
If a regression model predicting salary based on years of education and years of experience has an R-squared of 0.65, it means 65% of the variation in salaries is explained by education and experience.
Common Mistakes
- Believing a high R-squared means the model is practically useful or causally valid (a model predicting today's temperature from yesterday's has a high R-squared but reveals no underlying mechanism).
- Using R-squared to compare models with different numbers of predictors (Adjusted R-squared must be used instead to penalize for added complexity).