Coefficient of Determination (R²)

The coefficient of determination, denoted as R², is a key output of regression analysis. It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

This formula requires two inputs: SS_res (the sum of squared residuals) and SS_tot (the total sum of squares). The sum of squared residuals is the sum of the squared differences between the observed values and the predicted values. The total sum of squares is the sum of the squared differences between the observed values and their mean.

The R² value ranges from 0 to 1, where 0 indicates that the model does not explain any of the variation in the response data around its mean, and 1 indicates that the model explains all the variation in the response data around its mean.

In practice, the Coefficient of Determination is useful for assessing the goodness of fit of a regression model. A higher R² value indicates that more variability in the response data is accounted for by the model.