Evaluating regression models

Metrics for regression evaluation are typically based on the distance between the actual values for the target variable and a model’s predicted values. The most common measures – mean squared error, root mean squared error, mean absolute error, and R-squared – all track how successfully our predictions capture variation in a target.

The distance between the actual value and our prediction is known as the residual, or error. The mean squared error (MSE) is the mean of the square of the residuals:

Here, is the actual target variable value at the ith observation and is our prediction for the target. The residuals are squared to handle negative values, where the predicted value is higher than the actual value. To return our measurement to a more meaningful scale, we often use the square root of MSE. That is known as root mean squared error (RMSE).

Due to the squaring, MSE will penalize larger residuals...