Consider a general linear model with n p design matrix Z,
Chapter 11, Problem 18(choose chapter or problem)
Consider a general linear model with n p design matrix Z, and let W = Y Z denote the vector of residuals. (In other words, the ith coordinate of W is Yi Y i, where Y i = zi0 0 + ... + zip1 p1. a. Show that W = DY, where D = I Z(Z Z) 1 Z . b. Show that the matrix D is idempotent; that is, DD = D. c. Show that Cov(W ) = 2D.
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