# Fisher's criterion distribution

My task is to show that Fisher's criterion distribution when the null hypothesis is true follows $F(k-m,N-k)$ when df increases. Here $k-m$ is number of restriction.

So I can write a null hypothesis H0: $b_1=b_2=\ldots b_k=0$.
And I think that I can show that F-statistic follows $F(k-m,N-k)$ using restricted and unrestricted models. where $F=R^2u-R^2r/(1-R^2u) (k-m/N-k)$ or I can find this value from the table of Wald test.

When I compare it critical value =@qfdist(.95,eq.@ncoef-eq2.@ncoef,eq.@regobs-eq.@ncoef).

Is my thinking right? How use should use the condition of task that degrees of freedom increases?