In studying the model for the one-way layout in Section 2.3.2, we found the projection matrices and

Question:

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 (XTX)

− stated there is in fact a generalized inverse.

b. Verify the corresponding projection matrix PX specified there.

c. Verify that yT(I − PX)y is the within-groups sum of squares stated there.

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