Consider a general linear model with n p design matrix Z, and let denote the vector

Question:

Consider a general linear model with n × p design matrix Z, and let denote the vector of residuals. (In other words, the ith coordinate of where
a. Show that W = DY, where
D = I − Z(Z'Z)−1Z'.
b. Show that the matrix D is idempotent; that is, DD = D.
c. Show that Cov(W ) = σ2D.