In studying the model for the one-way layout in Section 2.3.2, we found the projection matrices and sums of squares and constructed the ANOVA table. a. We did the analysis for a non-full-rank model...

In studying the model for the one-way layout in Section 2.3.2, we found the projection matrices and sums of squares and constructed the ANOVA table. a. We did the analysis for a non-full-rank model matrix X. Show that the simple form for (X T X) - stated there is in fact a generalized inverse. b. Verify the corresponding projection matrix PX specified there. c. Verify that y T (I - P X )y is the within-groups sum of squares stated there.