I have a question please about the mean squre error resulting from the analysis of standardized data. How should I unscale it and use the real units of the variable.
I have standardized the data (Z) by removing the mean (average) and scaling to unit variance which make it unitless. Now, I want to return the resulting errors MSE and MAE to the actual unit. Regarding the MAE, should I multiply it the SD and add the data average of the output variable ?? and what about the MSE which should have a squared unit ? Should I multiply the standardized value to the squared SD and add the squared average (mean) ?
Since Z=(X−average)/SD , So can it be returned as .. X=Z∗SD+average .. or this will be wrong ?