which dependent variable to choose for benchmarking purpose? I am trying to develop a benchmark method for energy efficiency analysis.
The idea is to predict energy consumption and use the difference between predicted and real energy consumption as a measures of inefficiency.
I developed two model that predict energy consumption using the same explanatory variables and I have to choose the best.
The only difference in the two model is the dependent variable. In one case Y (say Y1) is total energy consumption and in the other one Y (say Y2) is energy intensity (kWh/m2).
As I said the two model are identical, but model 1 has a much higher adj. R2 (0.95), while the second has adj. R2 = 0.7.
What I can say is that SIZE is one of the explanatory variable and has a huge impact on the first model explaining the majority of the variability on energy consumption. In the other case (model 2), SIZE has a much smaller impact comparable with the other explanatory variables.
My question is which one should I choose? The first one? The higher R2 is useful for my objective?
thanks, Stefano
 A: So as I think about your problem, I see two issues.  The second issue is which model is better given the same independent variables.  The first issue is the theoretical soundness of doing that.
Measurements like $R^2$ are irrelevant for this type of question.  You need to ignore it.  Let us work on the first issue, which is soundness.  Y1 is consumption.  Y2 is intensity.  Consumption over time is fundamentally an integral.  It is a series of additions.  Intensity is fundamentally a derivative and is basically a set of ratios.  If these are your left-hand side of the equations, how is it even remotely possible they are the same on the right-hand side?  If they are of the same form, then one of them is theoretically unsound.  They are not even in the same units.
When one does a regression model, one  hopes to find the model that matches nature.  
For the second question, you can calculate the BIC for each.  Before you do that, I would graphically map out all my univariate densities and bivariate relationships to see if there are any joint relationships that could make everything else problematic.
I become deeply worried when I see a model with a very high $R^2$ unless I can explain it away because of very obvious mathematical relationships.  There is a real danger of over-fitting.
