Regression of matrix

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9.6 Let U be an n x 1 vector with 1 as its ?rst element and 0s elsewhere.Consider computing the regression of U on an n x p’ full rank matrix X.As usual, let H = X(X’X)‘1X’ be the hat matrix with elements 11,].9.6.1 Show that the elements of the vector of ?tted values from theregression of U on X are the h”, j = l, 2, . . ., 11.9.6.2 Show that the ?rst element of the vector of residuals is l — h“, andthe other elements are 411,-, j > 1.

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