What metrics are used for regression problems?

Regression problems involve predicting continuous numerical values, and several metrics are commonly used to evaluate model performance. The most widely used metrics include Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R-squared (R²). Each metric provides a different perspective on how well a model’s predictions align with actual values. For example, MAE measures the average absolute difference between predictions and true values, while MSE squares these differences to emphasize larger errors. RMSE, derived from MSE, scales the error back to the original data units. R² quantifies the proportion of variance in the target variable explained by the model. These metrics help developers assess accuracy, error magnitude, and model fit.

MAE and MSE/RMSE are often used together to understand error behavior. MAE is straightforward to interpret—for instance, if MAE is 5 for a house price prediction model, the average prediction is off by $5,000 (assuming prices are in thousands). However, MAE treats all errors equally, which can mask the impact of outliers. MSE, by squaring errors, penalizes larger deviations more heavily. For example, a single large error of 10 contributes 100 to MSE, whereas two errors of 5 contribute 25 each (total 50). RMSE, the square root of MSE, is useful because it shares the same unit as the target variable (e.g., dollars or meters), making it easier to communicate results. Developers often prefer RMSE when larger errors are particularly undesirable, such as in safety-critical systems.

R² and Mean Absolute Percentage Error (MAPE) provide additional context. R² measures how well the model explains variance in the data, ranging from 0 (no explanatory power) to 1 (perfect fit). For example, an R² of 0.8 means 80% of the variance in the target is captured by the model. This is useful for comparing models across different datasets or scales. MAPE calculates the average percentage error relative to actual values, which is helpful for business contexts where relative error matters more than absolute values. For instance, a MAPE of 10% in sales forecasting indicates predictions are, on average, 10% off from actual sales. Developers choose metrics based on the problem’s requirements: MAE for simplicity, RMSE for outlier sensitivity, R² for explanatory power, and MAPE for relative error analysis.