Table of Contents
What Is the Coefficient of Determination?
R-squared (R²) measures the proportion of variance in the dependent variable that is explained by the independent variable(s) in a regression model. It ranges from 0 to 1, where 0 means the model explains none of the variance and 1 means it explains all of it.
R² is the square of the Pearson correlation coefficient for simple linear regression. It is the most commonly reported measure of model fit.
Formula
Interpretation Guide
| R² | Interpretation |
|---|---|
| 0.90-1.00 | Excellent fit |
| 0.70-0.90 | Good fit |
| 0.50-0.70 | Moderate fit |
| 0.30-0.50 | Weak fit |
| 0.00-0.30 | Poor fit |
FAQ
Can R² be negative?
In simple linear regression, no. But with models fit without an intercept, or with out-of-sample predictions, effective R² can be negative, meaning the model performs worse than a horizontal line at the mean.
Is high R² always good?
Not necessarily. Overfitting (too many predictors) inflates R². Always check adjusted R², residual plots, and use cross-validation for reliable model assessment.