Question: Let \({{x}_{j}}\) be the j^th row of X and \({{X}_{-J}}\) be the X matrix with the j^th row removed. Show that

\[\operatorname{var}\left( {{{\hat{\beta }}}_{J}} \right)={{\sigma }^{2}}\left[ {{x}_{j}}'{{x}_{j}}-{{x}_{j}}'{{X}_{-j}}\left( {{X}_{-J}}'{{X}_{-j}} \right){{X}_{-j}}'{{x}_{j}} \right]\]