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General Linear Test
https://stats.libretexts.org/Bookshelves/Computing_and_Modeling/Supplemental_Modules_(Computing_and_Modeling)/Regression_Analysis/Simple_linear_regression/General_Linear_Test
Observe that d.f. $(SSE_{full}) = n-2$ , d.f. $(SSE_{red}) = n-1$ and $SSE_{red} - SSE_{full} = SSR$ . $$F^\ast =\dfrac{\dfrac{SSE_{red}-SSE_{full}}{d.f.(SSE_{red})-d.f.(SSE_{full})}}{\dfrac{SSE_{fu...Observe that d.f. $(SSE_{full}) = n-2$ , d.f. $(SSE_{red}) = n-1$ and $SSE_{red} - SSE_{full} = SSR$ . $F^\ast =\dfrac{\dfrac{SSE_{red}-SSE_{full}}{d.f.(SSE_{red})-d.f.(SSE_{full})}}{\dfrac{SSE_{full}}{d.f.(SSE_{full})}} = \dfrac{\dfrac{SSR}{d.f.(SSR)}}{\dfrac{SSE}{d.f.(SSE)}}=\dfrac{MSR}{MSE}$ Under normal error model, and under $H_0 : \beta_1 = 0, F^\ast$ has the $F$ distribution with (paired) degress of freedom $(d.f.(SSE_{red}) - d.f.(SSE_{full}), d.f.(SSE_{full}))$ .

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