STA302H1 Midterm: UTSG STA 302 t2solf06
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Sta 302 / 1001 f - fall 2006. 1: for the multiple linear regression model y = x + , assume x is non-random. (a) (3 marks) assume the gauss-markov assumptions hold. Show that the variance-covariance matrix of b, the least squares estimates of is 2(x x) 1. We will still assume that e( ) = 0. To obtain the gernalized least squares estimate, the quantity (y x ) 1(y x ) is minimized with respect to : (4 marks) show that the generalized least squares estimate is b = (x 1x) 1x 1y. Need to minimise q = (y x ) 1(y x ) with respect to . Q = y 1y x 1y y 1x + x 1x . = 0 gives x 1y = x 1xb so b = (cid:16)x 1x(cid:17) 1. X 1y: (2 marks) in this case h = x(x 1x) 1x 1.
