Adjusted R2

The adjusted $R^2$ (adjusted coefficient of determination) measures how well a regression model explains the variation in the dependent variable ($Y$), while adjusting for the number of predictors.

Unlike regular $R^2$, it penalizes the addition of unnecessary independent variables that don’t improve model fit.

Formula

Adjusted $R^2$ is calculated as:

$$R_{\text{adj}}^2=1-\left(1-R^2\right)\frac{n-1}{n-k-1}$$

where:

• $R^2$ = coefficient of determination
• $n$ = number of observations
• $k$ = number of independent variables (predictors)