What are the various measures of error (MSE, RMSE, MAE)?

After confirming that the fitted model meets the assumptions necessary for linear regression, the next step of a regression analysis is usually to evaluate how well the model is performing in terms of fit and accuracy. Different measures of error such as MSE, RMSE and MAE can be used for that purpose.

MSE stands for Mean Squared Error and it is calculated using the following formula:

RMSE stands for Root Mean Squared Error and it is calculated using the following formula:

MAE stands for Mean Absolute Error and it is calculated using the following formula:

Measures of error (MSE, MAE, RMSE), or a measure of the overall variability in the model, can also be used as a goodness of fit criteria, in which lower values indicate less noise and thus are preferred. Squared loss (MSE) is generally preferred over absolute loss (MAE) because it gives a higher penalty to cases that the model performs poorly on. As it is difficult to interpret in terms of squared units, the square root of MSE (RMSE) is usually preferred in order to report the error on the same scale as the target variable is measured.