R-squared › Adjusted R-squared

When dealing with multiple regression, the standard R-squared can be misleading because it always increases (or stays the same) when adding more predictors, even if those predictors don't improve the model. Adjusted R-squared accounts for the number of predictors using the formula $R^2_{\text{adj}} = 1 - \frac{(1-R^2)(n-1)}{n-p-1}$, where $n$ is the number of observations and $p$ is the number of predictors. Unlike standard R-squared, adjusted R-squared can decrease when adding irrelevant predictors.