ition of <span class="arithmatex">\(\hat\beta=(\bb{X}^T\bb{X})^{-1}\bb{X}^T\bb{Y}=\bb{X}^T\bb{Y}\)</span>, we have </p>
<div class="arithmatex">\[\begin{eqnarray}
    E_P[2\hat\beta_j\bb{Y}^T(x_j-x_j^\ast)] &amp;=&amp; 2\hat\beta_j \bb{Y}^Tx_j\non\\
    &amp;=&amp;2\hat\beta_j \cdot \hat\beta_j\non\\
    &amp;=&amp;2\hat\beta_j^2.\non
\end{eqnarray}\]</div>
<p>On the other hand, it is easy to verify that </p>
<div class="arithmatex">\[\begin{equation}
    E_p[\bb{X}_j^T\bb{X}_j-\bb{X}^T\bb{X}]=0\non
\end{eq