# Sums of square and general linear test

1. Feb 23, 2008

### dori

1. The problem statement, all variables and given/known data
Not sure this is the right forum to ask a question regarding F-statistics, but please help if you are familiar with this stuff.

The first part of homework was to prove mathematically that if a model has k variables, then F-statistic for testing model significance is:
F=[R^2/k]/[(1-R^2)/(n-k-1)]

I solved this problem by using sums of squares.
F= SSR(n-k-1)/k(SSE/SST) = SSR(n-k-1)/SSE(k) then plugged in appropriate numbers from ANOVA table.

The second part is what I'm having trouble with. In fact, I'm not sure where and how to start. It asks to prove mathematically following formula for the general linear test. In the formula, k is the number of variables in the full model and p is the number of variables in the reduce model, the equation is as follows.

2. Relevant equations
F= [(R^2(full) - R^2(reduced)/(k-p)]/ [(1-R^2(full))/(n-k-1)]

3. The attempt at a solution
I've tried to set up hypothesis to solve this problem, but did not get too far.
Could anybody help me with this problem? Thanks!