This is the question I'm stuck on:
2. The overall regression F-statistic and adjuster R^2 are both often used to assess model fit in multiple linear regression. Show the relatonship between these two statistics algebraically, in terms of the fitted and actual y values, the number of observations, and the number of parameters estimated.
Heres my attempt at it:
the equation i use for f-stat is
(R^2/K)/(1-R^2)/(n-k-1)
= R^2/K * (n-k-1)/(1-R^2)
sub in SSE/SST for the R^2 and sub in (sigma(yHATi - yBAR)^2)/(sigma(y-yBAR)^2) for SSE/SST
so:
f-stat = (((sigma(yHATi - yBAR)^2)/(sigma(y-yBAR)^2))(n-k-1)) / (k (1-(sigma(yHATi - yBAR)^2)/(sigma(y-yBAR)^2)))
and for the adj R^2
adj R^2 = (1-(1-(sigma(yHATi - yBAR)^2)/(sigma(y-yBAR)^2))(n-1)) / (n-k-1)
How would I show the relation of these two equations algebriacally in terms of the y values, number of observations and parametes.
any help would be appreciated.thanks!