e mean-squared residual on the training data, and <span class="arithmatex">\(\hat\beta\)</span> the estimated coefficient. Denote by <span class="arithmatex">\(RSS_j^\ast\)</span> the mean-squared residual on the training data using the same <span class="arithmatex">\(\hat\beta\)</span>, but with the <span class="arithmatex">\(N\)</span> values for the <span class="arithmatex">\(j\)</span>th variable randomly permuted before the predictions are calculated. Show that</p>
<div class="arithmatex">\[\begin{equa