Show that for the linear regression model Y = XTB + , the leave-one-out cross validation...

 

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Show that for the linear regression model Y = XTB + , the leave-one-out cross validation identity: where H = n (Yi - (-i)) n Yi - i=1 i 2 Hii 2 " X(XX)-XT is the hat matrix and H; is the ith diagonal entry, is the ith prediction value for the training point x; and (-i) is the leave-one-out prediction at x. Show that for the linear regression model Y = XTB + , the leave-one-out cross validation identity: where H = n (Yi - (-i)) n Yi - i=1 i 2 Hii 2 " X(XX)-XT is the hat matrix and H; is the ith diagonal entry, is the ith prediction value for the training point x; and (-i) is the leave-one-out prediction at x.