How do you evaluate a regression model?

A regression model is evaluated by checking how accurately it predicts continuous values on data it did not train on.

The goal is not simply to fit the training data well, but to verify that the model generalizes to new observations.

1. Evaluate on unseen data

Use a validation or test dataset that was not used to fit the model.

If performance is strong on training data but much worse on unseen data, the model may be overfitting.

2. Measure prediction error

Common regression metrics include:

• MAE — average absolute prediction error
• MSE — average squared prediction error
• RMSE — square root of MSE, expressed in the target's units
• R² — how much of the target's variation is explained by the model relative to a simple mean baseline

No single metric is best for every problem.

For example, RMSE penalizes large errors more strongly than MAE, while MAE is often easier to interpret directly.

3. Compare against a baseline

A regression model should outperform a simple baseline.

For example, a basic baseline might predict the average target value for every observation.

If a complex model cannot beat that baseline on unseen data, the additional complexity may not be useful.

4. Analyze residuals

Metrics summarize performance, but residuals can reveal *how* the model is failing.

Look for:

• systematic curves or patterns
• changing residual spread
• unusually large errors
• time-dependent patterns

Clear structure in the residuals can indicate that the model is missing an important relationship.

5. Check performance across important groups

An acceptable overall score can hide poor performance for certain ranges or segments.

For example, a house-price model might work well for mid-priced homes but make large errors for expensive properties.

Evaluate important subgroups when the application requires it.

6. Use cross-validation when appropriate

Cross-validation evaluates the model across multiple train-validation splits instead of relying on a single split.

This gives a more stable estimate of expected performance when the dataset and problem structure allow random resampling.

Time-dependent data should instead use a splitting strategy that preserves chronological order.

7. Judge the errors in business or domain context

A metric value is useful only when interpreted in the context of the problem.

For example, an MAE of ₹5,000 may be excellent for predicting house prices but unacceptable for predicting a much smaller financial amount.

In short, evaluate a regression model on unseen data using appropriate error metrics, compare it with a simple baseline, inspect residuals, and confirm that its errors are acceptable for the real-world problem.