Mean Squared Error (MSE)
Description
MSE is a regression metric that measures the average of the squared differences between the predicted values and the actual values. It gives a sense of how far off predictions are from the true values, with a heavier penalty for larger errors.
- Penalizes large errors more heavily than MAE, due to the squaring of differences
- Sensitive to outliers, as large errors are disproportionately penalized
- Less interpretable than MAE due to squaring of errors
- Lower values indicate better model performance, but values are in squared units of the target variable.
Formula
\[ \text{MSE} = \dfrac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 \]
- \(y_i\) = actual value
- \(\hat{y}_i\) = predicted value
- \(n\) = number of samples
Example
| Actual | Predicted | Squared Error |
|---|---|---|
| 5 | 3 | 4 |
| 7 | 9 | 4 |
| 10 | 8 | 4 |
Average of squared errors (MSE): \((4 + 4 + 4) / 3 = 4.0\)