# chex56.s                         J F Monahan, June 2001
 # QR factorization of simple design matrix
 X <- matrix(c(rep(1,4),1:4),4,2)
 "design matrix"
 X
 I <- diag(1,4)
 Q <- qr.qy(qr(X),I)
 "orthogonal matrix"
 Q
 "R matrix -- upper triangular"
 t(Q) %*% X
 "QQ' -- is it identity?"
 Q %*% t(Q)
 "Q'Q -- is it identity?"
 t(Q) %*% Q
 rm(list=ls())