R squared

R², or the coefficient of determination, measures the proportion of variance in the dependent variable that is explained by the independent variables in a regression model.

Interpretation:

• R² values range from 0 to 1.
• A value of 1 indicates perfect predictions, meaning the model explains all the variability of the response data around its mean.
• Higher R² values signify a better fit of the model to the data. However, it can be misleading when adding more predictors, as R² will never decrease when more variables are added to a model. See Adjusted R squared.

Formula:
$R^2=1-\frac{{\sum }_{i=1}^n(y_i-{\hat{y}}_i{)}^2}{{\sum }_{i=1}^n(y_i-\bar{y}{)}^2}$

Where:

• $y_i$ = actual values
• ${\hat{y}}_i$ = predicted values
• $\bar{y}$ = mean of the actual values

Example:
An R² of 0.60 indicates that 60% of the variability observed in the target variable is explained by the regression model.