Key Metrics in Regression Analysis: MSE, RMSE, and R²
MSE, RMSE, and R² are key metrics used to evaluate the performance of regression models.
What is MSE?
MSE stands for Mean Squared Error. It is basically the mean of the squares of the errors. The term errors here refers to the difference between the predicted values (predicted by the regression model) and the actual values. (In regression analysis, such errors are preferably referred to as residuals.) MSE provides a sense of how close the model’s predictions are to the actual values.
Interpretation
Lower MSE: Indicates that the model’s predictions are closer to the actual values, implying better accuracy.
Higher MSE: Suggests that the model’s predictions deviate more from the actual values, indicating poorer performance.
What is RMSE?
RMSE stands for Root Mean Squared Error. Basically, it is the square root of the MSE. RMSE is widely used because it balances the need to penalize larger errors while keeping the metric in the same units as the original data, making it easier to interpret than MSE.
Interpretation
Lower RMSE: Signifies that the model’s predictions are close to the actual values on average.
Higher RMSE: Indicates that the model’s predictions are further from the actual values on average.
What is R²?
R², also known as the coefficient of determination, is used to assess how well a regression model explains the variability of the response variable. In other words, it indicates the proportion of the variance in the dependent variable that is predictable from the independent variable(s).
Interpretation
R² = 1: The model perfectly explains the variance in the dependent variable.
R² = 0: The model does not explain any of the variance in the dependent variable.
0 < R² < 1: The model explains some, but not all, of the variance in the dependent variable.
