This is probably the most common metric used to assess the quality of a regression task. The RMSE is calculated as
is the number of samples in the set,
the actual value and
the predicted score (the difference between predicted and actual value being called the residual). This metric represents the square root of the average of the squared differences between the actual and the predicted values.
The RSS is calculated as
The RSS expresses the unexplained variance, the variance not captured by the model.
The coefficient of determination, usually indicated as
, expresses the proportion of the variance in the dependent variable that is predictable from the independent variable. It is a number smaller or equal than 1, 1 being the best situation.
the predicted values and
the actual values, we calculate the average of the actual values
the total sum of squares
and the explained sum of squares
With the definition of the RSS from above, we have
The second bit expresses the fraction of unexplained variance to the total variance in the data, so the
is the fraction of variance explained to the total variance.
The MAE is calculated as
that is, as the average of the differences of the actual to the predicted values