Mean Squared Error - Yousef's Notes
Mean Squared Error

Mean Squared Error

A measure of the average squared difference between actual and predicted values in regression analysis. $$ MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 $$
  • $y_i$: observed value
  • $\hat{y}_i$: predicted value
  • $n$: number of observations

Baseline: the mean model predicts the average of the training data labels and is the best model when no information about the target variable can be learned from the features.

#Purpose

Quantifies prediction accuracy; lower values indicate better performance.

#Properties

  • Non-negative: MSE is always zero or positive.
  • Penalizes large errors more due to squaring differences.

#Limitations

  • Sensitive to outliers, as larger errors have a greater impact on the MSE.
  • Units are squared units of the target variable, which may not be interpretable.

#Use Cases

Evaluating model fit and comparing different models; often used alongside other metrics like RMSE (Root Mean Squared Error) for interpretability.

#Related to