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| |
| <p>SQL functions for linear regression. |
| <a href="#details">More...</a></p> |
| <table class="memberdecls"> |
| <tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a> |
| Functions</h2></td></tr> |
| <tr class="memitem:aa2b87a3e60272176bfa2fb859f99461a"><td class="memItemLeft" align="right" valign="top">bytea8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linear_8sql__in.html#aa2b87a3e60272176bfa2fb859f99461a">linregr_transition</a> (bytea8 state, float8 y, float8[] x)</td></tr> |
| <tr class="separator:aa2b87a3e60272176bfa2fb859f99461a"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a042536820ffbad498a4e1c410f949e35"><td class="memItemLeft" align="right" valign="top">bytea8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linear_8sql__in.html#a042536820ffbad498a4e1c410f949e35">linregr_merge_states</a> (bytea8 state1, bytea8 state2)</td></tr> |
| <tr class="separator:a042536820ffbad498a4e1c410f949e35"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a28b69254ba5cd513b35ba6b17efd2c35"><td class="memItemLeft" align="right" valign="top">linregr_result </td><td class="memItemRight" valign="bottom"><a class="el" href="linear_8sql__in.html#a28b69254ba5cd513b35ba6b17efd2c35">linregr_final</a> (bytea8 state)</td></tr> |
| <tr class="separator:a28b69254ba5cd513b35ba6b17efd2c35"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a4a583204053716bbece6321f5d9332b1"><td class="memItemLeft" align="right" valign="top">bytea8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linear_8sql__in.html#a4a583204053716bbece6321f5d9332b1">hetero_linregr_transition</a> (bytea8 state, float8 y, float8[] x, float8[] coef)</td></tr> |
| <tr class="separator:a4a583204053716bbece6321f5d9332b1"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:ad10649c8460c337a285cf20f2b87d0c5"><td class="memItemLeft" align="right" valign="top">bytea8 </td><td class="memItemRight" valign="bottom"><a class="el" href="linear_8sql__in.html#ad10649c8460c337a285cf20f2b87d0c5">hetero_linregr_merge_states</a> (bytea8 state1, bytea8 state2)</td></tr> |
| <tr class="separator:ad10649c8460c337a285cf20f2b87d0c5"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a4b2e38f45a8e519af5947fcc2eb02829"><td class="memItemLeft" align="right" valign="top">heteroskedasticity_test_result </td><td class="memItemRight" valign="bottom"><a class="el" href="linear_8sql__in.html#a4b2e38f45a8e519af5947fcc2eb02829">hetero_linregr_final</a> (bytea8 state)</td></tr> |
| <tr class="separator:a4b2e38f45a8e519af5947fcc2eb02829"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a85d6d11ff2c93855061515d92d4785c2"><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 class="memdesc:a85d6d11ff2c93855061515d92d4785c2"><td class="mdescLeft"> </td><td class="mdescRight">Compute studentized Breuch-Pagan heteroskedasticity test for linear regression. <a href="#a85d6d11ff2c93855061515d92d4785c2">More...</a><br/></td></tr> |
| <tr class="separator:a85d6d11ff2c93855061515d92d4785c2"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a71d8295a18e93619b3331cefabe6e79b"><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 class="memdesc:a71d8295a18e93619b3331cefabe6e79b"><td class="mdescLeft"> </td><td class="mdescRight">Compute linear regression coefficients and diagnostic statistics. <a href="#a71d8295a18e93619b3331cefabe6e79b">More...</a><br/></td></tr> |
| <tr class="separator:a71d8295a18e93619b3331cefabe6e79b"><td class="memSeparator" colspan="2"> </td></tr> |
| </table> |
| <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2> |
| <div class="textblock"><dl class="section date"><dt>Date</dt><dd>January 2011</dd></dl> |
| <dl class="section see"><dt>See Also</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> |
| </div><h2 class="groupheader">Function Documentation</h2> |
| <a class="anchor" id="a4b2e38f45a8e519af5947fcc2eb02829"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">heteroskedasticity_test_result hetero_linregr_final </td> |
| <td>(</td> |
| <td class="paramtype">bytea8 </td> |
| <td class="paramname"><em>state</em>)</td><td></td> |
| <td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ad10649c8460c337a285cf20f2b87d0c5"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">bytea8 hetero_linregr_merge_states </td> |
| <td>(</td> |
| <td class="paramtype">bytea8 </td> |
| <td class="paramname"><em>state1</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">bytea8 </td> |
| <td class="paramname"><em>state2</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a4a583204053716bbece6321f5d9332b1"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">bytea8 hetero_linregr_transition </td> |
| <td>(</td> |
| <td class="paramtype">bytea8 </td> |
| <td class="paramname"><em>state</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>y</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>coef</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a85d6d11ff2c93855061515d92d4785c2"></a> |
| <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 class="params"><dt>Parameters</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="section user"><dt></dt><dd>To include an intercept in the model, set one coordinate in the <code>independentVariables</code> array to 1.</dd></dl> |
| <dl class="section return"><dt>Returns</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="section user"><dt>Usage</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> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a71d8295a18e93619b3331cefabe6e79b"></a> |
| <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 class="params"><dt>Parameters</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="section user"><dt></dt><dd>To include an intercept in the model, set one coordinate in the <code>independentVariables</code> array to 1.</dd></dl> |
| <dl class="section return"><dt>Returns</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="section user"><dt>Usage</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> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a28b69254ba5cd513b35ba6b17efd2c35"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">linregr_result linregr_final </td> |
| <td>(</td> |
| <td class="paramtype">bytea8 </td> |
| <td class="paramname"><em>state</em>)</td><td></td> |
| <td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a042536820ffbad498a4e1c410f949e35"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">bytea8 linregr_merge_states </td> |
| <td>(</td> |
| <td class="paramtype">bytea8 </td> |
| <td class="paramname"><em>state1</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">bytea8 </td> |
| <td class="paramname"><em>state2</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aa2b87a3e60272176bfa2fb859f99461a"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">bytea8 linregr_transition </td> |
| <td>(</td> |
| <td class="paramtype">bytea8 </td> |
| <td class="paramname"><em>state</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>y</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
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