Adjusted R squared

The coefficient of determination, also known as R-squared, while widely used as a measure of how well the independent variable explains the variability of the dependent variable in a regression model, has its limitations. It never decreases when a new feature is added to the model, regardless of whether that feature is useful or not

The adjusted R-squared is an improvement over the regular R-squared because it takes into account the number of predictors in a regression model. While R-squared measures the proportion of the variance in the dependent variable that is predictable from the independent variables, the adjusted R-squared also considers the number of predictors included in the model, providing a more accurate indication of the goodness of fit. This adjustment is particularly valuable when comparing models with different numbers of predictors, as it penalizes the inclusion of unnecessary variables that do not significantly contribute to explaining the variation in the dependent variable. As a result, the adjusted R-squared is a more reliable metric for assessing the explanatory power of a regression model in practice.