What Really is R2-Score in Linear Regression?

One of the most important metrics for evaluating a continuous target regression model

Figure shows how R2 Score determines goodness of fit. Image by author.

There are so many different metrics that can be used for evaluating regression models. In this article, we discuss several metrics that can be used for continuous target variable regression models. Among the many, R2 Score remains the most popular metric.

Metrics for Continuous Target Regression

If you are performing regression for a continuous outcome (i.e.linear regression, K-neighbors regression or support vector regression), then you may use metrics such as MSE, MAE, ME or R2 Score to evaluate the performance of your model.

Different metrics for evaluating a linear regression model. Image by author.

In the examples below, y represents the exact value, while y_hat represents the predicted value. We will assume our dataset has N observations.

• MSE (Mean Square Error): Uses Euclidean distance to calculate the error. MSE gives the magnitude of the error only.
• MAE (Mean Absolute Error): Uses Manhattan distance to calculate the error. MAE (like MSE) gives the magnitude of the error only.
• ME (Mean Error): keeps track of the sign of error, is model over-predicting or under-predicting?
• R2 Score

where R2 Score is between 0 and 1, the closer to 1, the better the regression fit.

Comments and Remarks

R2 Score is a very popular metric used for evaluating the performance of linear regression models. Use MSE or MAE when comparing two or more models, the lower the value of MSE or MAE, the better. Use ME when you are interested in understanding if on average, your model is over-predicting (ME > 0) or under-predicting (ME < 0). One could also use the R2 Score to compare different models. R2 score remains the most popular metric for evaluating linear regression models.

As a case study, please see the following article: Machine Learning Process Tutorial.

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