Let X be an m × n data matrix such that XT X is invertible, and let Add a colum...

Let X be an m × n data matrix such that X^T X is invertible, and let

Add a column x₀ to the data and form

Compute W ^T W . The (1, 1)-entry is X^T X. Show that the Schur complement (Exercise 16) of X^TX can be written in the form

It can be shown that the quantity

This entry has a useful statistical interpretation, under appropriate hypotheses.