pan></p>
<p>In the linear regression case, two stages of simplification can be carried out, the first of which helpfully reduces the variance of the estimator. First, rather than averaging samples <span class="math inline">\(\tilde{y}_n^{(m)}\)</span>, the same result is obtained by averaging linear predictions, <span class="math display">\[\begin{eqnarray*}
\hat{\tilde{y}}_n
&amp; = &amp; \mathbb{E}\left[
          \alpha + \beta \cdot \tilde{x}_n
          \mid \tilde{x}_n, x, y
       \right]
\\[4pt]
&am