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Comparing R^2 from log and level models


Jun 26, 2012
Say we have 2 models:

[tex]ln(y) = \beta_0 + \beta_1 x_1 + \cdots + \beta_nx_n[/tex] with a known R^2


[tex]y = \beta_0 + \beta_1 x_1 + \cdots + \beta_nx_n[/tex] with a known R^2

Now I know that we can not compare the R^2's from these 2 models to determine goodness-of-fit and I am also aware of how we can manipulate the log model so that we can compare, but my question is, what is the reason for which we can't compare? Obviously the dependent variable is the natural log for the first one and the second model is level in terms of y, but is there a deeper reason? Why is it that if the dependent variable's form is different, then we cannot compare the R^2's between the models?