[FIXED] Is It Possible to Compare Linear Regression Model Results Between Log and Non-log Dependent Variables?

Issue

I am conducting a linear regression experiment where I have evaluated for a dependent variable, then transformed the dependent variable into a log scale and trained/executed linear regression again. Is it possible to create a ratio between the mean absolute error or root mean squared error of the model and the dependent variable statistics in order to compare the models?

I understand that linear regression should probably not be used for this evaluation; this is simply a theory experiment.

NON-LOG RESULTS
Model Mean Abs Error: 14831.26
Model Root Mean Squared Error: 21921.10
Dependent Variable count: 2925.00
Dependent Variable mean: 180815.54
Dependent Variable std dev: 79951.70
Dependent Variable min: 12789.00
Dependent Variable 25%: 129500.00
Dependent Variable 50%: 160000.00
Dependent Variable 75%: 213500.00
Dependent Variable max: 755000.00

LOG RESULTS
Model Mean Abs Error: 0.08
Model Root Mean Squared Error: 0.12
Dependent Variable count: 2925.00
Dependent Variable mean: 12.02
Dependent Variable std dev: 0.41
Dependent Variable min: 9.46
Dependent Variable 25%: 11.77
Dependent Variable 50%: 11.98
Dependent Variable 75%: 12.27
Dependent Variable max: 13.53

Solution

This is very simplistic, but I would start with comparing "R-Squared" metric of the linear regression between these two models (may be not valid comparisons for other scenarios).

But the main fundamental factor here is whether the relationship between the dependent and set of independent variables is more linear in the log or non-log case. The analysis of the distribution of the residuals (their independence (and unbiasedness) from independent variables) can potentially help with that.

Answered By - Alex