# Deriving the F-test from ${{SSE_R-SSE_F}\over{(n-q)-(n-p)}}/{{SSE_F}\over{n-p}}$

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?

• Please define MSR. – Christoph Hanck May 19 '18 at 14:39
• 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 $R^2$. – byouness May 19 '18 at 14:40