span class="arithmatex">\(N\times q\)</span> orthogonal matrix and <span class="arithmatex">\(\textbf{R}_1\)</span> is a <span class="arithmatex">\(q\times a\)</span> upper triangular matrix. We know that <span class="arithmatex">\(\textbf{Q}_1\)</span> spans the column space of <span class="arithmatex">\(\textbf{X}_1\)</span>.</p>
<p>Now we consider choosing an additional predictor <span class="arithmatex">\(\textbf{x}_k\)</span>, where <span class="arithmatex">\(q &lt; k\le p\)</span>. The projection of <