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<title>PSPP: REGRESSION</title>

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<a name="REGRESSION"></a>
<div class="header">
<p>
Next: <a href="RELIABILITY.html#RELIABILITY" accesskey="n" rel="next">RELIABILITY</a>, Previous: <a href="RANK.html#RANK" accesskey="p" rel="prev">RANK</a>, Up: <a href="Statistics.html#Statistics" accesskey="u" rel="up">Statistics</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="REGRESSION-1"></a>
<h3 class="section">15.15 REGRESSION</h3>

<a name="index-regression"></a>
<a name="index-linear-regression-1"></a>
<p>The <code>REGRESSION</code> procedure fits linear models to data via least-squares
estimation. The procedure is appropriate for data which satisfy those
assumptions typical in linear regression:
</p>
<ul>
<li> The data set contains <em>n</em> observations of a dependent variable, say
<em>Y_1,&hellip;,Y_n</em>, and <em>n</em> observations of one or more explanatory
variables.
Let <em>X_{11}, X_{12}</em>, &hellip;, <em>X_{1n}</em> denote the <em>n</em> observations
of the first explanatory variable;
<em>X_{21}</em>,&hellip;,<em>X_{2n}</em> denote the <em>n</em> observations of the second
explanatory variable;
<em>X_{k1}</em>,&hellip;,<em>X_{kn}</em> denote the <em>n</em> observations of 
the <em>k</em>th explanatory variable.

</li><li> The dependent variable <em>Y</em> has the following relationship to the 
explanatory variables:
<em>Y_i = b_0 + b_1 X_{1i} + ... + b_k X_{ki} + Z_i</em> 
where <em>b_0, b_1, &hellip;, b_k</em> are unknown
coefficients, and <em>Z_1,&hellip;,Z_n</em> are independent, normally
distributed <em>noise</em> terms with mean zero and common variance.
The noise, or <em>error</em> terms are unobserved.
This relationship is called the <em>linear model</em>.
</li></ul>

<p>The <code>REGRESSION</code> procedure estimates the coefficients
<em>b_0,&hellip;,b_k</em> and produces output relevant to inferences for the
linear model. 
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="Syntax.html#Syntax" accesskey="1">Syntax</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Syntax definition.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Examples.html#Examples" accesskey="2">Examples</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Using the REGRESSION procedure.
</td></tr>
</table>




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