9.6 Let U be an n x 1 vector with 1 as its ﬁrst 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 ﬁtted values from the

regression of U on X are the h, j = l, 2, . . ., 11.

9.6.2 Show that the ﬁrst element of the vector of residuals is l — h, and

the other elements are 411,-, j gt; 1.

Statistics and Probability

9 6 Let U be an n × 1 vector with 1 as its