Derive the appropriate F statistic under both the null and alternative hypothesis for the general linear model with hypotheses of the form H0:T*β = c and H1:T*β != c, where T is a q × p matrix of rank q.
a) Calculate the sum of squares for the full model and the reduced model under the null hypothesis to derive the F statistic.
b) Use the degrees of freedom for the full and reduced models to determine the numerator and denominator degrees of freedom for the F statistic.
c) Divide the mean sum of squares from the full model by the mean sum of squares from the reduced model to obtain the F statistic under the null hypothesis.
d) Use the F statistic under the alternative hypothesis to compare the variability of the full model to the reduced model and test for significant differences in the model fit.