How would you evaluate the performance of a regression model?

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Evaluating the performance of a regression model involves analyzing how well the model's predictions match the actual continuous target values. Key metrics include:

1. Mean Absolute Error (MAE): Measures the average magnitude of errors without considering their direction. It’s simple and interpretable—lower MAE indicates better performance.

2. Mean Squared Error (MSE): Squares the errors before averaging, penalizing larger errors more than MAE. Useful when large errors are especially undesirable.

3. Root Mean Squared Error (RMSE): The square root of MSE, bringing the error back to the original unit of the target variable. It balances interpretability with sensitivity to outliers.

4. R-squared (R²): Represents the proportion of variance in the dependent variable that is predictable from the independent variables. Ranges from 0 to 1 (or negative for poorly performing models). A higher R² indicates better model fit.

5. Adjusted R-squared: Adjusts R² for the number of predictors in the model, helping to avoid overfitting in models with many variables.

In practice, visual tools such as residual plots help diagnose patterns in prediction errors, and learning curves can detect overfitting or underfitting. It's also good practice to evaluate models on validation or test sets to assess generalization. Cross-validation can provide more robust performance estimates by reducing the variance associated with a single train-test split.

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