Let the hat matrix H x = X(XX)-'X' from a multiple linear regression model. n + n 2. For the simple linear regression mo

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Let The Hat Matrix H X X Xx X From A Multiple Linear Regression Model N N 2 For The Simple Linear Regression Mo 1 (27.67 KiB) Viewed 131 times

Let the hat matrix H x = X(XX)-'X' from a multiple linear regression model. n + n 2. For the simple linear regression model, show that the elements of the hat matrix are 1 hij 1 (Li - 7)(; – ) + and his Sex Sex where Szx = -1 (di - 7). Discuss the behavior of these quantities as moves farther from . 3. Show that trH) =p. (tr(AB) =tr(BA)) 4. (MSSC) Let ha be the i-th diagonal element of H. Show that for the multiple linear regression model . Shu s 1. 5. (MSSC) Show that the generalized least squares estimator minimizes (y - XB)'v-|(y - XB)