A Comprehensive Overview of Regression Evaluation Metrics

Introduction

This article provides a comprehensive overview of various evaluation metrics used to assess the performance of regression models.

Bias

Bias is a metric that tells whether the predictions were higher or lower than the actual values. It can be positive or negative depending on the residual values of the predictions.

R²

R² is a metric that measures the proportion of variability explained by the model. It ranges from 0% to 100%, and higher values indicate better model fit. R² is calculated using the residual sum of squares (RSS) and the total sum of squares (TSS).

Mean Squared Error (MSE)

MSE is a metric that measures the average squared difference between the predicted and actual values. It is commonly used in regression analysis, but it has some limitations as it is a scale-dependent metric.

Root Mean Squared Error (RMSE)

RMSE is a metric that measures the square root of the average of squared differences between the predicted and actual values. It is also a scale-dependent metric.

Mean Absolute Error (MAE)

MAE is a metric that measures the absolute difference between the predicted and actual values. Unlike MSE and RMSE, it is not sensitive to outliers in the data.

Mean Absolute Percentage Error (MAPE)

MAPE is a metric that measures the absolute percentage difference between the predicted and actual values. It is commonly used in the business world because it is expressed as a percentage, which makes it easier to understand and interpret.

Symmetric Mean Absolute Percentage Error (sMAPE)

sMAPE is a metric that measures the percentage difference between predicted and actual values. Unlike MAPE, it takes the average of the absolute differences in both directions, making it symmetric.

Model Complexity Metrics

Model complexity metrics measure the complexity of a model and its ability to generalize to new data. Examples of such metrics include Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC).

Conclusion

The choice of evaluation metric depends on the problem and the context in which the regression model is being used. Choosing the right evaluation metric is crucial for selecting the best-performing regression model.