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Given a Full and Reduced model, the F-test to see if the reduced model is significant is given by

$$ {{SSE_R-SSE_F}\over{(n-q)-(n-p)}}/{{SSE_F}\over{n-p}} $$

I'm trying to understand how this is equal to ${MSR}\over{MSE}$. It's trivial to observe that $MSE = {{SSE_F}\over{n-p}}$, but what are the steps needed to show that $$ {{SSE_R-SSE_F}\over{(n-q)-(n-p)}} = MSR $$ i.e. is this based on an assumption, or can they be shown to be equal algebraically?

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  • $\begingroup$ Please define MSR. $\endgroup$ – Christoph Hanck May 19 '18 at 14:39
  • $\begingroup$ Are you talking about the homoskedasticity only F-statistic? Where did you find that it is equal to $MSR/MSE$, could you include some references? Usually this statistic is expressed either in terms of $SSR$ or $R^2$. $\endgroup$ – byouness May 19 '18 at 14:40

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