Metrics for regression (standard and ordinal)

When working with regression problems, that is, problems that involve estimating a continuous value (that could range from minus infinity to infinity), the most commonly used error measures are RMSE (root mean squared error) and MAE (mean absolute error), but you can also find slightly different error measures useful, such as RMSLE or MCRMSLE.

Mean squared error (MSE) and R squared

The root mean squared error is the root of the mean squared error (MSE), which is nothing else but the mean of the good old sum of squared errors (SSE) that you learned about when you studied how a regression works.

Here is the formula for the MSE:

Let’s start by explaining how the formula works. First of all, n indicates the number of cases, is the ground truth, and the prediction. You first get the difference between your predictions and your real values. You square the differences (so they become positive or simply zero), then...