# Is there an analog for the coefficient of determination with absolute error?

Typically to measure the predictive power of a model, R^2 is more useful than RMSE because a RMSE score isn't very meaningful without a basis of comparison. If you are using mean absolute error (MAE) instead of RMSE however there doesn't seem to be any R^2 analog I can find in the literature. It's easy enough to define one, but I haven't been able to find a name for such a measure

The closest I could find was mean absolute percentage error (MAPE), but that seems to mostly be used in forecasting, and the mean isn't subtracted in the denominator as it is in RMSE.

Is there a name for the measure I have described, or is there a good reason not to use it?

• $R^2$ is not meaningful as a measure of forecast accuracy unless the forecasts are unbiased. Otherwise an arbitrarily high $R^2$ is compatible with arbitrarily poor forecasts. – Richard Hardy Aug 21 '17 at 18:48
• If I am getting my terminology correctly, forecasting refers to predicting $y_{t+1}$ using the preceding $y_k$, and wouldn't be used to describe predicting a dependent variable $y$ with an independent variable $X$, correct? I am asking about the type of predictions done in latter case. – Fletcher Stump Smith Aug 21 '17 at 23:37
• My comment holds in both cases. – Richard Hardy Aug 22 '17 at 5:31