\(j\)</span>’s residuals when both <span class="math inline">\(i\)</span> and <span class="math inline">\(j\)</span> are regressed on all variables
<span class="math inline">\(i&#39;\)</span> such that <span class="math inline">\(i&#39;&lt; i\)</span>. In the case of <span class="math inline">\(i=1\)</span>, there are no earlier
variables, so <span class="math inline">\(z_{1,j}\)</span> is just the Pearson correlation between <span class="math inline">\(i\)</span>
and <span class="math inline">\(j\)</span