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I cannot understand what I'm doing wrong with an F-test for the regression - I get completely different answers using SSE and R2 formulas. Unrestricted model: enter image description here

Restricted model: enter image description here

1 restriction is imposed, so q=1 in both cases.

Calculation with SSE: $F=\frac{SSE_r-SSE_u}{SSE_U}*\frac{N-K}1=\frac{2.252-2.142}{2.142}*48=2.465$, same result given by Stata F-test.

Calculation with R2: $F=\frac{Ru^2-Rr^2}{1-Ru^2}*48$=1216.94
What am I doing wrong?!

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    $\begingroup$ Is your restricted model nested within your unrestricted model? $\endgroup$ – markseeto Nov 9 '12 at 9:16
  • $\begingroup$ In my model, alpha=lny-lnk and D=lnl-lnk, so these models are related. $\endgroup$ – user14386 Nov 10 '12 at 0:29
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As mark999 notes, these two models can't be compared via an F-test because they aren't nested--they are two completely different models, as is clear from the fact that the total sums of squares are wildly different in the two models.

You can only use an F-test to compare two linear models when the models are of the form $$y = \beta_0 + \beta_1 x_1 + \beta_2 x2 + \epsilon$$ and $$y = \beta_0 + \beta_1 x_1 + \epsilon,$$ i.e., where they have the same response variable and the predictors in the reduced model are a strict subset of the predictors in the full model.

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  • $\begingroup$ Hmm, but in my model, alpha=lny-lnk and D=lnl-lnk, so these models are related. $\endgroup$ – user14386 Nov 10 '12 at 0:29
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    $\begingroup$ "related" is not good enough. To use an F-test to compare them, they have to have exactly the same response and nested sets of predictors. $\endgroup$ – Jonathan Christensen Nov 10 '12 at 6:49

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