{error} = \text{target} – \text{model-based guess} ]
This prediction error serves as a crucial metric for evaluating model performance. By calculating the total error or average error across all observations and predictions, we can compare different models and parameter sets. The model with less total or average error is generally considered better. However, achieving the least possible error is not always feasible due to the inherent limitations in estimating true error.
Mean Squared Error (MSE) as a Metric
For many common models, simply taking the average of errors results in a value close to zero, which does not provide meaningful insight into model performance. To address this, using the squared error value or absolute value becomes necessary. Both of these methods ensure that errors of similar magnitude above and below the observed value are equally costly. The Mean Squared Error (MSE), calculated as the mean of the squared errors for all predictions, emerges as a preferred metric:
[ \text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (y_i – \hat{y}_i)^2 ]
where (y_i) is the actual target value, (\hat{y}
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