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 <div class="title">linear.sql_in File Reference</div>  </div>
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 <div class="contents">

 <p>SQL functions for linear regression.
 <a href="#details">More...</a></p>

 <p><a href="linear_8sql__in_source.html">Go to the source code of this file.</a></p>
 <table class="memberdecls">
 <tr><td colspan="2"><h2><a name="func-members"></a>
 Functions</h2></td></tr>
 <tr><td class="memItemLeft" align="right" valign="top">aggregate <br class="typebreak"/>
 heteroskedasticity_test_result&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="linear_8sql__in.html#a85d6d11ff2c93855061515d92d4785c2">heteroskedasticity_test_linregr</a> (float8 dependentVariable, float8[] independentVariables, float8[] olsCoefficients)</td></tr>
 <tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute studentized Breuch-Pagan heteroskedasticity test for linear regression.  <a href="#a85d6d11ff2c93855061515d92d4785c2"></a><br/></td></tr>
 <tr><td class="memItemLeft" align="right" valign="top">aggregate linregr_result&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="linear_8sql__in.html#a71d8295a18e93619b3331cefabe6e79b">linregr</a> (float8 dependentVariable, float8[] independentVariables)</td></tr>
 <tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute linear regression coefficients and diagnostic statistics.  <a href="#a71d8295a18e93619b3331cefabe6e79b"></a><br/></td></tr>
 </table>
 <hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
 <div class="textblock"><dl class="date"><dt><b>Date:</b></dt><dd>January 2011</dd></dl>
 <dl class="see"><dt><b>See also:</b></dt><dd>For a brief introduction to linear regression, see the module description <a class="el" href="group__grp__linreg.html">Linear Regression</a>. </dd></dl>

 <p>Definition in file <a class="el" href="linear_8sql__in_source.html">linear.sql_in</a>.</p>
 </div><hr/><h2>Function Documentation</h2>
 <a class="anchor" id="a85d6d11ff2c93855061515d92d4785c2"></a><!-- doxytag: member="linear.sql_in::heteroskedasticity_test_linregr" ref="a85d6d11ff2c93855061515d92d4785c2" args="(float8 dependentVariable, float8[] independentVariables, float8[] olsCoefficients)" -->
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
           <td class="memname">aggregate heteroskedasticity_test_result heteroskedasticity_test_linregr </td>
           <td>(</td>
           <td class="paramtype">float8&#160;</td>
           <td class="paramname"><em>dependentVariable</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">float8[]&#160;</td>
           <td class="paramname"><em>independentVariables</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">float8[]&#160;</td>
           <td class="paramname"><em>olsCoefficients</em>&#160;</td>
         </tr>
         <tr>
           <td></td>
           <td>)</td>
           <td></td><td></td>
         </tr>
       </table>
 </div>
 <div class="memdoc">
 <dl><dt><b>Parameters:</b></dt><dd>
   <table class="params">
     <tr><td class="paramname">dependentVariable</td><td>Column containing the dependent variable </td></tr>
     <tr><td class="paramname">independentVariables</td><td>Column containing the array of independent variables </td></tr>
     <tr><td class="paramname">olsCoefficients</td><td>Column containing the array of the OLS coefficients (as obtained by linregr)</td></tr>
   </table>
   </dd>
 </dl>
 <dl class="user"><dt><b></b></dt><dd>To include an intercept in the model, set one coordinate in the <code>independentVariables</code> array to 1.</dd></dl>
 <dl class="return"><dt><b>Returns:</b></dt><dd>A composite value:<ul>
 <li><code>test_statistic FLOAT8[]</code> - Prob &gt; test_statistc</li>
 <li><code>p_value FLOAT8[]</code> - Prob &gt; test_statistc</li>
 </ul>
 </dd></dl>
 <dl class="user"><dt><b>Usage:</b></dt><dd><pre> SELECT (heteoskedasticity_test_linregr(<em>dependentVariable</em>,
   <em>independentVariables</em>, coef)).*
   FROM (
     SELECT linregr(<em>dependentVariable</em>, <em>independentVariables</em>).coef
   ) AS ols_coef, <em>sourceName</em> as src;
  </pre> </dd></dl>

 <p>Definition at line <a class="el" href="linear_8sql__in_source.html#l00456">456</a> of file <a class="el" href="linear_8sql__in_source.html">linear.sql_in</a>.</p>

 </div>
 </div>
 <a class="anchor" id="a71d8295a18e93619b3331cefabe6e79b"></a><!-- doxytag: member="linear.sql_in::linregr" ref="a71d8295a18e93619b3331cefabe6e79b" args="(float8 dependentVariable, float8[] independentVariables)" -->
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
           <td class="memname">aggregate linregr_result linregr </td>
           <td>(</td>
           <td class="paramtype">float8&#160;</td>
           <td class="paramname"><em>dependentVariable</em>, </td>
         </tr>
         <tr>
           <td class="paramkey"></td>
           <td></td>
           <td class="paramtype">float8[]&#160;</td>
           <td class="paramname"><em>independentVariables</em>&#160;</td>
         </tr>
         <tr>
           <td></td>
           <td>)</td>
           <td></td><td></td>
         </tr>
       </table>
 </div>
 <div class="memdoc">
 <dl><dt><b>Parameters:</b></dt><dd>
   <table class="params">
     <tr><td class="paramname">dependentVariable</td><td>Column containing the dependent variable </td></tr>
     <tr><td class="paramname">independentVariables</td><td>Column containing the array of independent variables</td></tr>
   </table>
   </dd>
 </dl>
 <dl class="user"><dt><b></b></dt><dd>To include an intercept in the model, set one coordinate in the <code>independentVariables</code> array to 1.</dd></dl>
 <dl class="return"><dt><b>Returns:</b></dt><dd>A composite value:<ul>
 <li><code>coef FLOAT8[]</code> - Array of coefficients, \( \boldsymbol c \)</li>
 <li><code>r2 FLOAT8</code> - Coefficient of determination, \( R^2 \)</li>
 <li><code>std_err FLOAT8[]</code> - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)</li>
 <li><code>t_stats FLOAT8[]</code> - Array of t-statistics, \( \boldsymbol t \)</li>
 <li><code>p_values FLOAT8[]</code> - Array of p-values, \( \boldsymbol p \)</li>
 <li><code>condition_no FLOAT8</code> - The condition number of matrix \( X^T X \).</li>
 </ul>
 </dd></dl>
 <dl class="user"><dt><b>Usage:</b></dt><dd><ul>
 <li>Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:<br/>
  <pre>SELECT (linregr(<em>dependentVariable</em>,
         <em>independentVariables</em>)).*
 FROM <em>sourceName</em>;</pre></li>
 <li>Get vector of coefficients \( \boldsymbol c \):<br/>
  <pre>SELECT (linregr(<em>dependentVariable</em>,
         <em>independentVariables</em>)).coef
 FROM <em>sourceName</em>;</pre></li>
 <li>Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the coefficient of determination \( R^2 \), and the array of p-values \( \boldsymbol p \): <pre>SELECT (lr).coef, (lr).r2, (lr).p_values
 FROM (
     SELECT linregr( <em>dependentVariable</em>,
                     <em>independentVariables</em>) AS lr
     FROM <em>sourceName</em>
 ) AS subq;</pre> </li>
 </ul>
 </dd></dl>

 <p>Definition at line <a class="el" href="linear_8sql__in_source.html#l00510">510</a> of file <a class="el" href="linear_8sql__in_source.html">linear.sql_in</a>.</p>

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	<div class="title">linear.sql_in File Reference</div> </div>
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	<div class="contents">

	<p>SQL functions for linear regression.
	<a href="#details">More...</a></p>

	<p><a href="linear_8sql__in_source.html">Go to the source code of this file.</a></p>
	<table class="memberdecls">
	<tr><td colspan="2"><h2><a name="func-members"></a>
	Functions</h2></td></tr>
	<tr><td class="memItemLeft" align="right" valign="top">aggregate <br class="typebreak"/>
	heteroskedasticity_test_result </td><td class="memItemRight" valign="bottom"><a class="el" href="linear_8sql__in.html#a85d6d11ff2c93855061515d92d4785c2">heteroskedasticity_test_linregr</a> (float8 dependentVariable, float8[] independentVariables, float8[] olsCoefficients)</td></tr>
	<tr><td class="mdescLeft"> </td><td class="mdescRight">Compute studentized Breuch-Pagan heteroskedasticity test for linear regression. <a href="#a85d6d11ff2c93855061515d92d4785c2"></a><br/></td></tr>
	<tr><td class="memItemLeft" align="right" valign="top">aggregate linregr_result </td><td class="memItemRight" valign="bottom"><a class="el" href="linear_8sql__in.html#a71d8295a18e93619b3331cefabe6e79b">linregr</a> (float8 dependentVariable, float8[] independentVariables)</td></tr>
	<tr><td class="mdescLeft"> </td><td class="mdescRight">Compute linear regression coefficients and diagnostic statistics. <a href="#a71d8295a18e93619b3331cefabe6e79b"></a><br/></td></tr>
	</table>
	<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
	<div class="textblock"><dl class="date"><dt><b>Date:</b></dt><dd>January 2011</dd></dl>
	<dl class="see"><dt><b>See also:</b></dt><dd>For a brief introduction to linear regression, see the module description <a class="el" href="group__grp__linreg.html">Linear Regression</a>. </dd></dl>

	<p>Definition in file <a class="el" href="linear_8sql__in_source.html">linear.sql_in</a>.</p>
	</div><hr/><h2>Function Documentation</h2>
	<a class="anchor" id="a85d6d11ff2c93855061515d92d4785c2"></a><!-- doxytag: member="linear.sql_in::heteroskedasticity_test_linregr" ref="a85d6d11ff2c93855061515d92d4785c2" args="(float8 dependentVariable, float8[] independentVariables, float8[] olsCoefficients)" -->
	<div class="memitem">
	<div class="memproto">
	<table class="memname">
	<tr>
	<td class="memname">aggregate heteroskedasticity_test_result heteroskedasticity_test_linregr </td>
	<td>(</td>
	<td class="paramtype">float8 </td>
	<td class="paramname"><em>dependentVariable</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">float8[] </td>
	<td class="paramname"><em>independentVariables</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">float8[] </td>
	<td class="paramname"><em>olsCoefficients</em> </td>
	</tr>
	<tr>
	<td></td>
	<td>)</td>
	<td></td><td></td>
	</tr>
	</table>
	</div>
	<div class="memdoc">
	<dl><dt><b>Parameters:</b></dt><dd>
	<table class="params">
	<tr><td class="paramname">dependentVariable</td><td>Column containing the dependent variable </td></tr>
	<tr><td class="paramname">independentVariables</td><td>Column containing the array of independent variables </td></tr>
	<tr><td class="paramname">olsCoefficients</td><td>Column containing the array of the OLS coefficients (as obtained by linregr)</td></tr>
	</table>
	</dd>
	</dl>
	<dl class="user"><dt><b></b></dt><dd>To include an intercept in the model, set one coordinate in the <code>independentVariables</code> array to 1.</dd></dl>
	<dl class="return"><dt><b>Returns:</b></dt><dd>A composite value:<ul>
	<li><code>test_statistic FLOAT8[]</code> - Prob > test_statistc</li>
	<li><code>p_value FLOAT8[]</code> - Prob > test_statistc</li>
	</ul>
	</dd></dl>
	<dl class="user"><dt><b>Usage:</b></dt><dd><pre> SELECT (heteoskedasticity_test_linregr(<em>dependentVariable</em>,
	<em>independentVariables</em>, coef)).*
	FROM (
	SELECT linregr(<em>dependentVariable</em>, <em>independentVariables</em>).coef
	) AS ols_coef, <em>sourceName</em> as src;
	</pre> </dd></dl>

	<p>Definition at line <a class="el" href="linear_8sql__in_source.html#l00456">456</a> of file <a class="el" href="linear_8sql__in_source.html">linear.sql_in</a>.</p>

	</div>
	</div>
	<a class="anchor" id="a71d8295a18e93619b3331cefabe6e79b"></a><!-- doxytag: member="linear.sql_in::linregr" ref="a71d8295a18e93619b3331cefabe6e79b" args="(float8 dependentVariable, float8[] independentVariables)" -->
	<div class="memitem">
	<div class="memproto">
	<table class="memname">
	<tr>
	<td class="memname">aggregate linregr_result linregr </td>
	<td>(</td>
	<td class="paramtype">float8 </td>
	<td class="paramname"><em>dependentVariable</em>, </td>
	</tr>
	<tr>
	<td class="paramkey"></td>
	<td></td>
	<td class="paramtype">float8[] </td>
	<td class="paramname"><em>independentVariables</em> </td>
	</tr>
	<tr>
	<td></td>
	<td>)</td>
	<td></td><td></td>
	</tr>
	</table>
	</div>
	<div class="memdoc">
	<dl><dt><b>Parameters:</b></dt><dd>
	<table class="params">
	<tr><td class="paramname">dependentVariable</td><td>Column containing the dependent variable </td></tr>
	<tr><td class="paramname">independentVariables</td><td>Column containing the array of independent variables</td></tr>
	</table>
	</dd>
	</dl>
	<dl class="user"><dt><b></b></dt><dd>To include an intercept in the model, set one coordinate in the <code>independentVariables</code> array to 1.</dd></dl>
	<dl class="return"><dt><b>Returns:</b></dt><dd>A composite value:<ul>
	<li><code>coef FLOAT8[]</code> - Array of coefficients, \( \boldsymbol c \)</li>
	<li><code>r2 FLOAT8</code> - Coefficient of determination, \( R^2 \)</li>
	<li><code>std_err FLOAT8[]</code> - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)</li>
	<li><code>t_stats FLOAT8[]</code> - Array of t-statistics, \( \boldsymbol t \)</li>
	<li><code>p_values FLOAT8[]</code> - Array of p-values, \( \boldsymbol p \)</li>
	<li><code>condition_no FLOAT8</code> - The condition number of matrix \( X^T X \).</li>
	</ul>
	</dd></dl>
	<dl class="user"><dt><b>Usage:</b></dt><dd><ul>
	<li>Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:<br/>
	<pre>SELECT (linregr(<em>dependentVariable</em>,
	<em>independentVariables</em>)).*
	FROM <em>sourceName</em>;</pre></li>
	<li>Get vector of coefficients \( \boldsymbol c \):<br/>
	<pre>SELECT (linregr(<em>dependentVariable</em>,
	<em>independentVariables</em>)).coef
	FROM <em>sourceName</em>;</pre></li>
	<li>Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the coefficient of determination \( R^2 \), and the array of p-values \( \boldsymbol p \): <pre>SELECT (lr).coef, (lr).r2, (lr).p_values
	FROM (
	SELECT linregr( <em>dependentVariable</em>,
	<em>independentVariables</em>) AS lr
	FROM <em>sourceName</em>
	) AS subq;</pre> </li>
	</ul>
	</dd></dl>

	<p>Definition at line <a class="el" href="linear_8sql__in_source.html#l00510">510</a> of file <a class="el" href="linear_8sql__in_source.html">linear.sql_in</a>.</p>

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