Exercises 19 and 20 involve a design matrix X with two or more columns and a least-squares solution
(i)
(ii)
(iii)
Every statistics text that discusses regression and the linear model y = Xβ + ε introduces these numbers, though terminology and notation vary somewhat. To simplify matters, assume that the mean of the y-values is zero. In this case, SS(T) is proportional to what is called the variance of the set of y-values.
19. Justify the equation SS(T) = SS(R) + SS(E). [Hint: Use a theorem, and explain why the hypotheses of the theorem are satisfied.] This equation is extremely important in statistics, both in regression theory and in the analysis of variance.
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