l="anchor" href="#regression-with-x-and-z"></a>
</h2>
<p>We carry out two regressions of <code>IQ</code> on the variables in
<code>X</code> and in <code>Z</code>. These are equivalent, in the sense
that</p>
<ul>
<li>The
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>R</mi><mn>2</mn></msup><annotation encoding="application/x-tex">R^2</annotation></semantics></math>
and MSE are the same in both models</li>
<li>Residuals are the same</li>
<li>The Type I tests given by <c