Regression Metrics

Quick Summary

SSE: Sensitive to large errors, not same unit (squared unit).
MSE: Sensitive to large errors, not same unit (squared unit).
MAE: Same unit as target, treats all errors equally.
RMSE: Same unit as target, sensitive to large errors.

Key Points

SSE (Sum of Squared Errors)

$$\text{SSE} = \sum_{i=1}^n ( y_{\text{true},i} - y_{\text{predicted},i} )^2$$

• Measures total squared error.
• Sensitive to large errors.
• Units are squared (e.g., $², m²).

MSE (Mean Squared Error)

$$\text{MSE} = \frac{1}{n} \sum_{i=1}^n ( y_{\text{true},i} - y_{\text{predicted},i} )^2$$

• Average of squared errors.
• Sensitive to large errors.
• Still squared units.

MAE (Mean Absolute Error)

$$\text{MAE} = \frac{1}{n} \sum_{i=1}^n | y_{\text{true},i} - y_{\text{predicted},i} |$$

• Measures average absolute error.
• Same unit as target variable.
• Treats all errors equally, no exaggeration of big errors.

RMSE (Root Mean Squared Error)

$$\text{RMSE} = \sqrt{ \frac{1}{n} \sum_{i=1}^n ( y_{\text{true},i} - y_{\text{predicted},i} )^2 }$$

• Square root of MSE.
• Same unit as target variable.
• Sensitive to large errors because it squares first before root.

Final Takeaway

• SSE and MSE punish large errors heavily but have squared units.
• MAE is easy to interpret because it keeps the same unit and treats all errors equally.
• RMSE is both interpretable (same unit) and sensitive to large errors (because it squares before taking square root).