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| <a href="linear_8sql__in.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* ----------------------------------------------------------------------- */</span><span class="comment">/**</span></div> |
| <div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * @file linear.sql_in</span></div> |
| <div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * @brief SQL functions for linear regression</span></div> |
| <div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * @date January 2011</span></div> |
| <div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * @sa For a brief introduction to linear regression, see the module</span></div> |
| <div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * description \ref grp_linreg.</span></div> |
| <div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> */</span><span class="comment">/* ----------------------------------------------------------------------- */</span></div> |
| <div class="line"><a name="l00012"></a><span class="lineno"> 12</span> </div> |
| <div class="line"><a name="l00013"></a><span class="lineno"> 13</span> m4_include(`SQLCommon.m4<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">@addtogroup grp_linreg</span></div> |
| <div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"><div class="toc"><b>Contents</b><ul></span></div> |
| <div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"><li class="level1"><a href="#about">About</a></li></span></div> |
| <div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"><li class="level1"><a href="#train">Usage</a></li></span></div> |
| <div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"><li class="level2"><a href="#train">Training Function</a></li></span></div> |
| <div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"><li class="level2"><a href="#output">Output Table</a></li></span></div> |
| <div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"><li class="level2"><a href="#predict">Prediction Function</a></li></span></div> |
| <div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"><li class="level1"><a href="#examples">Examples</a></li></span></div> |
| <div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"><li class="level1"><a href="#seealso">See Also</a></li></span></div> |
| <div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"><li class="level1"><a href="#background">Technical Background</a></li></span></div> |
| <div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"><li class="level1"><a href="#literature">Literature</a></li></span></div> |
| <div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"></ul></div></span></div> |
| <div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">@anchor about</span></div> |
| <div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">@about</span></div> |
| <div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">Ordinary Least Squares Regression, also called Linear Regression, is a</span></div> |
| <div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">statistical model used to fit linear models.</span></div> |
| <div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">It models a linear relationship of a scalar dependent variable \f$ y \f$ to one</span></div> |
| <div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">or more explanatory independent variables \f$ x \f$ to build a</span></div> |
| <div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">model of coefficients.</span></div> |
| <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">@anchor train</span></div> |
| <div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">@par Training Function</span></div> |
| <div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">@verbatim</span></div> |
| <div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">linregr_train(source_table, out_table,</span></div> |
| <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment"> dependent_varname,</span></div> |
| <div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment"> independent_varname,</span></div> |
| <div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment"> input_group_cols := NULL,</span></div> |
| <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment"> heteroskedasticity_option := NULL)</span></div> |
| <div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">@endverbatim</span></div> |
| <div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment"><DL class="arglist"></span></div> |
| <div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment"><DT>source_table</DT></span></div> |
| <div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment"><DD>Text value. The name of the table containing the training data.</DD></span></div> |
| <div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment"><DT>out_table</DT></span></div> |
| <div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment"><DD>Text value. Name of the generated table containing the output model.</DD></span></div> |
| <div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment"><DT>dependent_varname</DT></span></div> |
| <div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment"><DD>Text value. Expression to evaluate for the dependent variable.</DD></span></div> |
| <div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment"><DT>independent_varname</DT></span></div> |
| <div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"><DD>Text value. Expression list to evaluate for the independent variables. An intercept variable is not assumed. It is common to provide an explicit intercept term by including a single constant <tt>1</tt> term in the independent variable list.</DD></span></div> |
| <div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment"><DT>input_group_cols</DT></span></div> |
| <div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment"><DD>Text value. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL <tt>GROUP BY</tt> clause. When this value is null, no grouping is used and a single result model is generated. Default value: NULL.</DD></span></div> |
| <div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment"><DT>heteroskedasticity_option</DT></span></div> |
| <div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment"><DD>Boolean value. When True, the heteroskedacity of the model is also calculated and returned with the results. Default value: False.</DD></span></div> |
| <div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment"></DL></span></div> |
| <div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">@anchor output</span></div> |
| <div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment">@par Output Table</span></div> |
| <div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">The output table produced by the linear regression training function contains the following columns.</span></div> |
| <div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"><DL class="arglist"></span></div> |
| <div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"><DT><...></DT></span></div> |
| <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment"><DD>Any grouping columns provided during training.</span></div> |
| <div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment">Present only if the grouping option is used.</DD></span></div> |
| <div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"><DT>coef</DT></span></div> |
| <div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"><DD>Float array. Vector of the coefficients of the regression.</DD></span></div> |
| <div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"><DT>r2</DT></span></div> |
| <div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"><DD>Float. R-squared coefficient of determination of the model.</DD></span></div> |
| <div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment"><DT>std_err</DT></span></div> |
| <div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment"><DD>Float array. Vector of the standard error of the coefficients.</DD></span></div> |
| <div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"><DT>t_stats</DT></span></div> |
| <div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"><DD>Float array. Vector of the t-statistics of the coefficients.</DD></span></div> |
| <div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment"><DT>p_values</DT></span></div> |
| <div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment"><DD>Float array. Vector of the p-values of the coefficients.</DD></span></div> |
| <div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"><DT>condition_no</DT></span></div> |
| <div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment"><DD>Float array. The condition number of the \f$X^{*}X\f$</span></div> |
| <div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment">matrix. A high condition number is usually an indication that there may be</span></div> |
| <div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment">some numeric instability in the result yielding a less reliable model. A high</span></div> |
| <div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment">condition number often results when there is a significant amount of</span></div> |
| <div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment">colinearity in the underlying design matrix, in which case other regression</span></div> |
| <div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment">techniques, such as elastic net regression, may be more appropriate.</DD></span></div> |
| <div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"><DT>bp_stats</DT></span></div> |
| <div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment"><DD>Float. The Breush-Pagan statistic of heteroskedacity. Present</span></div> |
| <div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment">only if the heteroskedacity argument was set to True when the model was</span></div> |
| <div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment">trained.</DD></span></div> |
| <div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment"><DT>bp_p_value</DT></span></div> |
| <div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"><DD>Float. The Breush-Pagan calculated p-value. Present only if</span></div> |
| <div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment">the heteroskedacity parameter was set to True when the model was</span></div> |
| <div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment">trained.</DD></span></div> |
| <div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"></DL></span></div> |
| <div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment">@anchor predict</span></div> |
| <div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment">@par Prediction Function</span></div> |
| <div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment">@verbatim</span></div> |
| <div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment">linregr_predict(</span></div> |
| <div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"> coef,</span></div> |
| <div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"> col_ind</span></div> |
| <div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment">)</span></div> |
| <div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment">@endverbatim</span></div> |
| <div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment"><dl class="arglist"></span></div> |
| <div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment"><dt>coef</dt></span></div> |
| <div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment"><dd>Float array. Vector of the coefficients of regression.</dd></span></div> |
| <div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment"><dt>col_ind</dt></span></div> |
| <div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment"><dd>Float array. An array containing the independent variable column names. </dd></span></div> |
| <div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment">@anchor examples</span></div> |
| <div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment">@par Examples</span></div> |
| <div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment">-# Create an input data set.</span></div> |
| <div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment">@verbatim</span></div> |
| <div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment">CREATE TABLE houses (id INT, tax INT, bedroom INT, bath FLOAT, price INT,</span></div> |
| <div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"> size INT, lot INT);</span></div> |
| <div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment">COPY houses FROM STDIN WITH DELIMITER '|';</span></div> |
| <div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"> 1 | 590 | 2 | 1 | 50000 | 770 | 22100</span></div> |
| <div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment"> 2 | 1050 | 3 | 2 | 85000 | 1410 | 12000</span></div> |
| <div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"> 3 | 20 | 3 | 1 | 22500 | 1060 | 3500</span></div> |
| <div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"> 4 | 870 | 2 | 2 | 90000 | 1300 | 17500</span></div> |
| <div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment"> 5 | 1320 | 3 | 2 | 133000 | 1500 | 30000</span></div> |
| <div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment"> 6 | 1350 | 2 | 1 | 90500 | 820 | 25700</span></div> |
| <div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment"> 7 | 2790 | 3 | 2.5 | 260000 | 2130 | 25000</span></div> |
| <div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment"> 8 | 680 | 2 | 1 | 142500 | 1170 | 22000</span></div> |
| <div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment"> 9 | 1840 | 3 | 2 | 160000 | 1500 | 19000</span></div> |
| <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment"> 10 | 3680 | 4 | 2 | 240000 | 2790 | 20000</span></div> |
| <div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"> 11 | 1660 | 3 | 1 | 87000 | 1030 | 17500</span></div> |
| <div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> 12 | 1620 | 3 | 2 | 118600 | 1250 | 20000</span></div> |
| <div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment"> 13 | 3100 | 3 | 2 | 140000 | 1760 | 38000</span></div> |
| <div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment"> 14 | 2070 | 2 | 3 | 148000 | 1550 | 14000</span></div> |
| <div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"> 15 | 650 | 3 | 1.5 | 65000 | 1450 | 12000</span></div> |
| <div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment">\.</span></div> |
| <div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment">@endverbatim</span></div> |
| <div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment">-# Train a regression model.</span></div> |
| <div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment">@verbatim</span></div> |
| <div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment">-- A single regression for all the data</span></div> |
| <div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment">SELECT madlib.linregr_train(</span></div> |
| <div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"> 'houses', 'houses_linregr', 'price', 'array[1, tax, bath, size]');</span></div> |
| <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment">-- 3 output models, one for each value of "bedroom"</span></div> |
| <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment">SELECT madlib.linregr_train(</span></div> |
| <div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment"> 'houses', 'houses_linregr_bedroom', 'price', 'array[1, tax, bath, size]',</span></div> |
| <div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"> 'bedroom');</span></div> |
| <div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment">@endverbatim</span></div> |
| <div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment">-# Examine the resulting models.</span></div> |
| <div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment">@verbatim</span></div> |
| <div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment">-- Set extended display on for easier reading of output</span></div> |
| <div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment">\x on</span></div> |
| <div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment">SELECT * from houses_linregr;</span></div> |
| <div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment">SELECT * FROM houses_linregr_bedroom;</span></div> |
| <div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment">-- Alternatively you can unnest the results for easier reading of output</span></div> |
| <div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">\x off</span></div> |
| <div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment">SELECT unnest(array['intercept','tax','bath','size']) as attribute,</span></div> |
| <div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment"> unnest(coef) as coefficient,</span></div> |
| <div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment"> unnest(std_err) as standard_error,</span></div> |
| <div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment"> unnest(t_stats) as t_stat,</span></div> |
| <div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment"> unnest(p_values) as pvalue</span></div> |
| <div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment">FROM houses_linregr;</span></div> |
| <div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment">@endverbatim</span></div> |
| <div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment">-# Use the prediction function to evaluate residuals.</span></div> |
| <div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment">@verbatim</span></div> |
| <div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment">SELECT houses.*,</span></div> |
| <div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment"> madlib.linregr_predict(array[1,tax,bath,size], m.coef) as predict,</span></div> |
| <div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment"> price - madlib.linregr_predict(array[1,tax,bath,size], m.coef)</span></div> |
| <div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"> as residual</span></div> |
| <div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment">FROM houses, houses_linregr m;</span></div> |
| <div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="comment">@endverbatim</span></div> |
| <div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment">@anchor seealso</span></div> |
| <div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment">@sa File linear.sql_in, documenting the SQL training functions</span></div> |
| <div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment">@sa linregr()</span></div> |
| <div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment">@sa logregr_train()</span></div> |
| <div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment">@sa elastic_net_train()</span></div> |
| <div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment">@sa grp_robust</span></div> |
| <div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment">@sa grp_clustered_errors</span></div> |
| <div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment">@sa grp_validation</span></div> |
| <div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment">@anchor background</span></div> |
| <div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment">@par Technical Background</span></div> |
| <div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment">Ordinary least-squares (OLS) linear regression refers to a stochastic model in</span></div> |
| <div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment">which the conditional mean of the dependent variable (usually denoted \f$ Y \f$)</span></div> |
| <div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment">is an affine function of the vector of independent variables (usually denoted</span></div> |
| <div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment">\f$ \boldsymbol x \f$). That is,</span></div> |
| <div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment"> E[Y \mid \boldsymbol x] = \boldsymbol c^T \boldsymbol x</span></div> |
| <div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment">for some unknown vector of coefficients \f$ \boldsymbol c \f$. The assumption is</span></div> |
| <div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment">that the residuals are i.i.d. distributed Gaussians. That is, the (conditional)</span></div> |
| <div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment">probability density of \f$ Y \f$ is given by</span></div> |
| <div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment"> f(y \mid \boldsymbol x)</span></div> |
| <div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment"> = \frac{1}{\sqrt{2 \pi \sigma^2}}</span></div> |
| <div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="comment"> \cdot \exp\left(-\frac{1}{2 \sigma^2}</span></div> |
| <div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="comment"> \cdot (y - \boldsymbol x^T \boldsymbol c)^2 \right)</span></div> |
| <div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment"> \,.</span></div> |
| <div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment">OLS linear regression finds the vector of coefficients \f$ \boldsymbol c \f$</span></div> |
| <div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment">that maximizes the likelihood of the observations.</span></div> |
| <div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="comment">Let</span></div> |
| <div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="comment">- \f$ \boldsymbol y \in \mathbf R^n \f$ denote the vector of observed dependent</span></div> |
| <div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="comment"> variables, with \f$ n \f$ rows, containing the observed values of the</span></div> |
| <div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="comment"> dependent variable,</span></div> |
| <div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="comment">- \f$ X \in \mathbf R^{n \times k} \f$ denote the design matrix with \f$ k \f$</span></div> |
| <div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="comment"> columns and \f$ n \f$ rows, containing all observed vectors of independent</span></div> |
| <div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="comment"> variables.</span></div> |
| <div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="comment"> \f$ \boldsymbol x_i \f$ as rows,</span></div> |
| <div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="comment">- \f$ X^T \f$ denote the transpose of \f$ X \f$,</span></div> |
| <div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="comment">- \f$ X^+ \f$ denote the pseudo-inverse of \f$ X \f$.</span></div> |
| <div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment">Maximizing the likelihood is equivalent to maximizing the log-likelihood</span></div> |
| <div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment">\f$ \sum_{i=1}^n \log f(y_i \mid \boldsymbol x_i) \f$, which simplifies to</span></div> |
| <div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="comment">minimizing the <b>residual sum of squares</b> \f$ RSS \f$ (also called sum of</span></div> |
| <div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="comment">squared residuals or sum of squared errors of prediction),</span></div> |
| <div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment"> RSS = \sum_{i=1}^n ( y_i - \boldsymbol c^T \boldsymbol x_i )^2</span></div> |
| <div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment"> = (\boldsymbol y - X \boldsymbol c)^T (\boldsymbol y - X \boldsymbol c)</span></div> |
| <div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="comment"> \,.</span></div> |
| <div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="comment">The first-order conditions yield that the \f$ RSS \f$ is minimized at</span></div> |
| <div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="comment"> \boldsymbol c = (X^T X)^+ X^T \boldsymbol y</span></div> |
| <div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="comment"> \,.</span></div> |
| <div class="line"><a name="l00243"></a><span class="lineno"> 243</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="comment">Computing the <b>total sum of squares</b> \f$ TSS \f$, the <b>explained</span></div> |
| <div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="comment">sum of squares</b> \f$ ESS \f$ (also called the regression sum of</span></div> |
| <div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="comment">squares), and the <b>coefficient of determination</b> \f$ R^2 \f$ is</span></div> |
| <div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="comment">done according to the following formulas:</span></div> |
| <div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="comment">\f{align*}{</span></div> |
| <div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="comment"> ESS & = \boldsymbol y^T X \boldsymbol c</span></div> |
| <div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="comment"> - \frac{ \| y \|_1^2 }{n} \\</span></div> |
| <div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment"> TSS & = \sum_{i=1}^n y_i^2</span></div> |
| <div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="comment"> - \frac{ \| y \|_1^2 }{n} \\</span></div> |
| <div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="comment"> R^2 & = \frac{ESS}{TSS}</span></div> |
| <div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="comment">\f}</span></div> |
| <div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="comment">Note: The last equality follows from the definition</span></div> |
| <div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="comment">\f$ R^2 = 1 - \frac{RSS}{TSS} \f$ and the fact that for linear regression</span></div> |
| <div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="comment">\f$ TSS = RSS + ESS \f$. A proof of the latter can be found, e.g., at:</span></div> |
| <div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="comment">http://en.wikipedia.org/wiki/Sum_of_squares</span></div> |
| <div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="comment">We estimate the variance</span></div> |
| <div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="comment">\f$ Var[Y - \boldsymbol c^T \boldsymbol x \mid \boldsymbol x] \f$ as</span></div> |
| <div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="comment"> \sigma^2 = \frac{RSS}{n - k}</span></div> |
| <div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="comment">and compute the t-statistic for coefficient \f$ i \f$ as</span></div> |
| <div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="comment"> t_i = \frac{c_i}{\sqrt{\sigma^2 \cdot \left( (X^T X)^{-1} \right)_{ii} }}</span></div> |
| <div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="comment"> \,.</span></div> |
| <div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment">The \f$ p \f$-value for coefficient \f$ i \f$ gives the probability of seeing a</span></div> |
| <div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="comment">value at least as extreme as the one observed, provided that the null hypothesis</span></div> |
| <div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="comment">(\f$ c_i = 0 \f$) is true. Letting \f$ F_\nu \f$ denote the</span></div> |
| <div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="comment">cumulative density function of student-t with \f$ \nu \f$ degrees of freedom,</span></div> |
| <div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="comment">the \f$ p \f$-value for coefficient \f$ i \f$</span></div> |
| <div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="comment">is therefore</span></div> |
| <div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="comment"> p_i = \Pr(|T| \geq |t_i|) = 2 \cdot (1 - F_{n - k}( |t_i| ))</span></div> |
| <div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="comment">where \f$ T \f$ is a student-t distributed random variable with mean 0.</span></div> |
| <div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="comment">The condition number [2] \f$ \kappa(X) = \|X\|_2\cdot\|X^{-1}\|_2\f$ is computed</span></div> |
| <div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="comment">as the product of two spectral norms [3]. The spectral norm of a matrix \f$X\f$</span></div> |
| <div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="comment">is the largest singular value of \f$X\f$ i.e. the square root of the largest</span></div> |
| <div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="comment">eigenvalue of the positive-semidefinite matrix \f$X^{*}X\f$:</span></div> |
| <div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="comment"> \|X\|_2 = \sqrt{\lambda_{\max}\left(X^{*}X\right)}\ ,</span></div> |
| <div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="comment">where \f$X^{*}\f$ is the conjugate transpose of \f$X\f$.</span></div> |
| <div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="comment">The condition number of a linear regression problem</span></div> |
| <div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="comment">is a worst-case measure of how sensitive the</span></div> |
| <div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="comment">result is to small perturbations of the input. A large condition number (say,</span></div> |
| <div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="comment">more than 1000) indicates the presence of significant multicollinearity.</span></div> |
| <div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="comment">@anchor literature</span></div> |
| <div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="comment">@literature</span></div> |
| <div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="comment">[1] Cosma Shalizi: Statistics 36-350: Data Mining, Lecture Notes, 21 October</span></div> |
| <div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="comment"> 2009, http://www.stat.cmu.edu/~cshalizi/350/lectures/17/lecture-17.pdf</span></div> |
| <div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00303"></a><span class="lineno"> 303</span> <span class="comment">[2] Wikipedia: Condition Number, http://en.wikipedia.org/wiki/Condition_number.</span></div> |
| <div class="line"><a name="l00304"></a><span class="lineno"> 304</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="comment">[3] Wikipedia: Spectral Norm,</span></div> |
| <div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="comment"> http://en.wikipedia.org/wiki/Spectral_norm#Spectral_norm</span></div> |
| <div class="line"><a name="l00307"></a><span class="lineno"> 307</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="comment">[4] Wikipedia: Breusch–Pagan test,</span></div> |
| <div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="comment"> http://en.wikipedia.org/wiki/Breusch%E2%80%93Pagan_test</span></div> |
| <div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="comment">[5] Wikipedia: Heteroscedasticity-consistent standard errors,</span></div> |
| <div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="comment">http://en.wikipedia.org/wiki/Heteroscedasticity-consistent_standard_errors</span></div> |
| <div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="comment">@internal</span></div> |
| <div class="line"><a name="l00316"></a><span class="lineno"> 316</span> <span class="comment">@sa Namespace \ref madlib::modules::regress</span></div> |
| <div class="line"><a name="l00317"></a><span class="lineno"> 317</span> <span class="comment"> documenting the implementation in C++</span></div> |
| <div class="line"><a name="l00318"></a><span class="lineno"> 318</span> <span class="comment">@endinternal</span></div> |
| <div class="line"><a name="l00319"></a><span class="lineno"> 319</span> <span class="comment">*/</span></div> |
| <div class="line"><a name="l00320"></a><span class="lineno"> 320</span> ---------------------------------------------------------------------------</div> |
| <div class="line"><a name="l00321"></a><span class="lineno"> 321</span> CREATE TYPE MADLIB_SCHEMA.linregr_result AS (</div> |
| <div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  coef DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  r2 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  std_err DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  t_stats DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  p_values DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  condition_no DOUBLE PRECISION</div> |
| <div class="line"><a name="l00328"></a><span class="lineno"> 328</span> );</div> |
| <div class="line"><a name="l00329"></a><span class="lineno"> 329</span> </div> |
| <div class="line"><a name="l00330"></a><span class="lineno"> 330</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.linregr_transition(</div> |
| <div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  state MADLIB_SCHEMA.bytea8,</div> |
| <div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  y DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  x DOUBLE PRECISION[])</div> |
| <div class="line"><a name="l00334"></a><span class="lineno"> 334</span> RETURNS MADLIB_SCHEMA.bytea8</div> |
| <div class="line"><a name="l00335"></a><span class="lineno"> 335</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00336"></a><span class="lineno"> 336</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00339"></a><span class="lineno"> 339</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.linregr_merge_states(</span></div> |
| <div class="line"><a name="l00340"></a><span class="lineno"> 340</span> <span class="stringliteral"> state1 MADLIB_SCHEMA.bytea8,</span></div> |
| <div class="line"><a name="l00341"></a><span class="lineno"> 341</span> <span class="stringliteral"> state2 MADLIB_SCHEMA.bytea8)</span></div> |
| <div class="line"><a name="l00342"></a><span class="lineno"> 342</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.bytea8</span></div> |
| <div class="line"><a name="l00343"></a><span class="lineno"> 343</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00344"></a><span class="lineno"> 344</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="stringliteral">-- Final functions</span></div> |
| <div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.linregr_final(</span></div> |
| <div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="stringliteral"> state MADLIB_SCHEMA.bytea8)</span></div> |
| <div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.linregr_result</span></div> |
| <div class="line"><a name="l00351"></a><span class="lineno"> 351</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="stringliteral">LANGUAGE C IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00354"></a><span class="lineno"> 354</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00355"></a><span class="lineno"> 355</span> <span class="stringliteral">CREATE TYPE MADLIB_SCHEMA.heteroskedasticity_test_result AS (</span></div> |
| <div class="line"><a name="l00356"></a><span class="lineno"> 356</span> <span class="stringliteral"> bp_stats DOUBLE PRECISION,</span></div> |
| <div class="line"><a name="l00357"></a><span class="lineno"> 357</span> <span class="stringliteral"> bp_p_value DOUBLE PRECISION</span></div> |
| <div class="line"><a name="l00358"></a><span class="lineno"> 358</span> <span class="stringliteral">);</span></div> |
| <div class="line"><a name="l00359"></a><span class="lineno"> 359</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00360"></a><span class="lineno"> 360</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.hetero_linregr_transition(</span></div> |
| <div class="line"><a name="l00361"></a><span class="lineno"> 361</span> <span class="stringliteral"> state MADLIB_SCHEMA.bytea8,</span></div> |
| <div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="stringliteral"> y DOUBLE PRECISION,</span></div> |
| <div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="stringliteral"> x DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="stringliteral"> coef DOUBLE PRECISION[])</span></div> |
| <div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.bytea8</span></div> |
| <div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00369"></a><span class="lineno"> 369</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00370"></a><span class="lineno"> 370</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.hetero_linregr_merge_states(</span></div> |
| <div class="line"><a name="l00371"></a><span class="lineno"> 371</span> <span class="stringliteral"> state1 MADLIB_SCHEMA.bytea8,</span></div> |
| <div class="line"><a name="l00372"></a><span class="lineno"> 372</span> <span class="stringliteral"> state2 MADLIB_SCHEMA.bytea8)</span></div> |
| <div class="line"><a name="l00373"></a><span class="lineno"> 373</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.bytea8</span></div> |
| <div class="line"><a name="l00374"></a><span class="lineno"> 374</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00375"></a><span class="lineno"> 375</span> <span class="stringliteral">LANGUAGE C</span></div> |
| <div class="line"><a name="l00376"></a><span class="lineno"> 376</span> <span class="stringliteral">IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00377"></a><span class="lineno"> 377</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00378"></a><span class="lineno"> 378</span> <span class="stringliteral">-- Final functions</span></div> |
| <div class="line"><a name="l00379"></a><span class="lineno"> 379</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.hetero_linregr_final(</span></div> |
| <div class="line"><a name="l00380"></a><span class="lineno"> 380</span> <span class="stringliteral"> state MADLIB_SCHEMA.bytea8)</span></div> |
| <div class="line"><a name="l00381"></a><span class="lineno"> 381</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.heteroskedasticity_test_result</span></div> |
| <div class="line"><a name="l00382"></a><span class="lineno"> 382</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00383"></a><span class="lineno"> 383</span> <span class="stringliteral">LANGUAGE C IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00384"></a><span class="lineno"> 384</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00385"></a><span class="lineno"> 385</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="comment"> * @brief Compute studentized Breuch-Pagan heteroskedasticity test for</span></div> |
| <div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="comment"> * linear regression.</span></div> |
| <div class="line"><a name="l00388"></a><span class="lineno"> 388</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00389"></a><span class="lineno"> 389</span> <span class="comment"> * @param dependentVariable Column containing the dependent variable</span></div> |
| <div class="line"><a name="l00390"></a><span class="lineno"> 390</span> <span class="comment"> * @param independentVariables Column containing the array of independent variables</span></div> |
| <div class="line"><a name="l00391"></a><span class="lineno"> 391</span> <span class="comment"> * @param olsCoefficients Column containing the array of the OLS coefficients (as obtained by linregr)</span></div> |
| <div class="line"><a name="l00392"></a><span class="lineno"> 392</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00393"></a><span class="lineno"> 393</span> <span class="comment"> * @par</span></div> |
| <div class="line"><a name="l00394"></a><span class="lineno"> 394</span> <span class="comment"> * To include an intercept in the model, set one coordinate in the</span></div> |
| <div class="line"><a name="l00395"></a><span class="lineno"> 395</span> <span class="comment"> * <tt>independentVariables</tt> array to 1.</span></div> |
| <div class="line"><a name="l00396"></a><span class="lineno"> 396</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00397"></a><span class="lineno"> 397</span> <span class="comment"> * @return A composite value:</span></div> |
| <div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="comment"> * - <tt>test_statistic FLOAT8[]</tt> - Prob > test_statistc</span></div> |
| <div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="comment"> * - <tt>p_value FLOAT8[]</tt> - Prob > test_statistc</span></div> |
| <div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="comment"> * @usage</span></div> |
| <div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="comment"> * <pre> SELECT (heteoskedasticity_test_linregr(<em>dependentVariable</em>,</span></div> |
| <div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="comment"> * <em>independentVariables</em>, coef)).*</span></div> |
| <div class="line"><a name="l00404"></a><span class="lineno"> 404</span> <span class="comment"> * FROM (</span></div> |
| <div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="comment"> * SELECT linregr(<em>dependentVariable</em>, <em>independentVariables</em>).coef</span></div> |
| <div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="comment"> * ) AS ols_coef, <em>sourceName</em> as src;</span></div> |
| <div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment"> * </pre></span></div> |
| <div class="line"><a name="l00408"></a><span class="lineno"> 408</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00409"></a><span class="lineno"> 409</span> CREATE AGGREGATE MADLIB_SCHEMA.heteroskedasticity_test_linregr(</div> |
| <div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  /*+ "dependentVariable" */ DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  /*+ "independentVariables" */ DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  /*+ "olsCoefficients" */ DOUBLE PRECISION[]) (</div> |
| <div class="line"><a name="l00413"></a><span class="lineno"> 413</span> </div> |
| <div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  SFUNC=MADLIB_SCHEMA.hetero_linregr_transition,</div> |
| <div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  STYPE=MADLIB_SCHEMA.bytea8,</div> |
| <div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  FINALFUNC=MADLIB_SCHEMA.hetero_linregr_final,</div> |
| <div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  m4_ifdef(`GREENPLUM',`prefunc=MADLIB_SCHEMA.hetero_linregr_merge_states,<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00418"></a><span class="lineno"> 418</span> <span class="stringliteral"> INITCOND='</span><span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="stringliteral">);</span></div> |
| <div class="line"><a name="l00420"></a><span class="lineno"> 420</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="comment"> * @brief Compute linear regression coefficients and diagnostic statistics.</span></div> |
| <div class="line"><a name="l00423"></a><span class="lineno"> 423</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="comment"> * @param dependentVariable Column containing the dependent variable</span></div> |
| <div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="comment"> * @param independentVariables Column containing the array of independent variables</span></div> |
| <div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00427"></a><span class="lineno"> 427</span> <span class="comment"> * @par</span></div> |
| <div class="line"><a name="l00428"></a><span class="lineno"> 428</span> <span class="comment"> * To include an intercept in the model, set one coordinate in the</span></div> |
| <div class="line"><a name="l00429"></a><span class="lineno"> 429</span> <span class="comment"> * <tt>independentVariables</tt> array to 1.</span></div> |
| <div class="line"><a name="l00430"></a><span class="lineno"> 430</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00431"></a><span class="lineno"><a class="code" href="linear_8sql__in.html#a85d6d11ff2c93855061515d92d4785c2"> 431</a></span> <span class="comment"> * @return A composite value:</span></div> |
| <div class="line"><a name="l00432"></a><span class="lineno"> 432</span> <span class="comment"> * - <tt>coef FLOAT8[]</tt> - Array of coefficients, \f$ \boldsymbol c \f$</span></div> |
| <div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="comment"> * - <tt>r2 FLOAT8</tt> - Coefficient of determination, \f$ R^2 \f$</span></div> |
| <div class="line"><a name="l00434"></a><span class="lineno"> 434</span> <span class="comment"> * - <tt>std_err FLOAT8[]</tt> - Array of standard errors,</span></div> |
| <div class="line"><a name="l00435"></a><span class="lineno"> 435</span> <span class="comment"> * \f$ \mathit{se}(c_1), \dots, \mathit{se}(c_k) \f$</span></div> |
| <div class="line"><a name="l00436"></a><span class="lineno"> 436</span> <span class="comment"> * - <tt>t_stats FLOAT8[]</tt> - Array of t-statistics, \f$ \boldsymbol t \f$</span></div> |
| <div class="line"><a name="l00437"></a><span class="lineno"> 437</span> <span class="comment"> * - <tt>p_values FLOAT8[]</tt> - Array of p-values, \f$ \boldsymbol p \f$</span></div> |
| <div class="line"><a name="l00438"></a><span class="lineno"> 438</span> <span class="comment"> * - <tt>condition_no FLOAT8</tt> - The condition number of matrix</span></div> |
| <div class="line"><a name="l00439"></a><span class="lineno"> 439</span> <span class="comment"> * \f$ X^T X \f$.</span></div> |
| <div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00441"></a><span class="lineno"> 441</span> <span class="comment"> * @usage</span></div> |
| <div class="line"><a name="l00442"></a><span class="lineno"> 442</span> <span class="comment"> * - Get vector of coefficients \f$ \boldsymbol c \f$ and all diagnostic</span></div> |
| <div class="line"><a name="l00443"></a><span class="lineno"> 443</span> <span class="comment"> * statistics:\n</span></div> |
| <div class="line"><a name="l00444"></a><span class="lineno"> 444</span> <span class="comment"> * <pre>SELECT (linregr(<em>dependentVariable</em>,</span></div> |
| <div class="line"><a name="l00445"></a><span class="lineno"> 445</span> <span class="comment"> * <em>independentVariables</em>)).*</span></div> |
| <div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="comment"> *FROM <em>sourceName</em>;</pre></span></div> |
| <div class="line"><a name="l00447"></a><span class="lineno"> 447</span> <span class="comment"> * - Get vector of coefficients \f$ \boldsymbol c \f$:\n</span></div> |
| <div class="line"><a name="l00448"></a><span class="lineno"> 448</span> <span class="comment"> * <pre>SELECT (linregr(<em>dependentVariable</em>,</span></div> |
| <div class="line"><a name="l00449"></a><span class="lineno"> 449</span> <span class="comment"> * <em>independentVariables</em>)).coef</span></div> |
| <div class="line"><a name="l00450"></a><span class="lineno"> 450</span> <span class="comment"> *FROM <em>sourceName</em>;</pre></span></div> |
| <div class="line"><a name="l00451"></a><span class="lineno"> 451</span> <span class="comment"> * - Get a subset of the output columns, e.g., only the array of coefficients</span></div> |
| <div class="line"><a name="l00452"></a><span class="lineno"> 452</span> <span class="comment"> * \f$ \boldsymbol c \f$, the coefficient of determination \f$ R^2 \f$, and</span></div> |
| <div class="line"><a name="l00453"></a><span class="lineno"> 453</span> <span class="comment"> * the array of p-values \f$ \boldsymbol p \f$:</span></div> |
| <div class="line"><a name="l00454"></a><span class="lineno"> 454</span> <span class="comment"> * <pre>SELECT (lr).coef, (lr).r2, (lr).p_values</span></div> |
| <div class="line"><a name="l00455"></a><span class="lineno"> 455</span> <span class="comment"> *FROM (</span></div> |
| <div class="line"><a name="l00456"></a><span class="lineno"> 456</span> <span class="comment"> * SELECT linregr( <em>dependentVariable</em>,</span></div> |
| <div class="line"><a name="l00457"></a><span class="lineno"> 457</span> <span class="comment"> * <em>independentVariables</em>) AS lr</span></div> |
| <div class="line"><a name="l00458"></a><span class="lineno"> 458</span> <span class="comment"> * FROM <em>sourceName</em></span></div> |
| <div class="line"><a name="l00459"></a><span class="lineno"> 459</span> <span class="comment"> *) AS subq;</pre></span></div> |
| <div class="line"><a name="l00460"></a><span class="lineno"> 460</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00461"></a><span class="lineno"> 461</span> </div> |
| <div class="line"><a name="l00462"></a><span class="lineno"> 462</span> CREATE AGGREGATE MADLIB_SCHEMA.linregr(</div> |
| <div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  /*+ "dependentVariable" */ DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  /*+ "independentVariables" */ DOUBLE PRECISION[]) (</div> |
| <div class="line"><a name="l00465"></a><span class="lineno"> 465</span> </div> |
| <div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  SFUNC=MADLIB_SCHEMA.linregr_transition,</div> |
| <div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  STYPE=MADLIB_SCHEMA.bytea8,</div> |
| <div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  FINALFUNC=MADLIB_SCHEMA.linregr_final,</div> |
| <div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  m4_ifdef(`__GREENPLUM__',`prefunc=MADLIB_SCHEMA.linregr_merge_states,<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00470"></a><span class="lineno"> 470</span> <span class="stringliteral"> INITCOND='</span><span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00471"></a><span class="lineno"> 471</span> <span class="stringliteral">);</span></div> |
| <div class="line"><a name="l00472"></a><span class="lineno"> 472</span> <span class="stringliteral">--------------------------- INTERNAL ---------------------------------------</span></div> |
| <div class="line"><a name="l00473"></a><span class="lineno"> 473</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00474"></a><span class="lineno"> 474</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00475"></a><span class="lineno"> 475</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00476"></a><span class="lineno"> 476</span> <span class="comment"> * @brief Return heteroskedasticity values for specific linear regression</span></div> |
| <div class="line"><a name="l00477"></a><span class="lineno"> 477</span> <span class="comment"> * coefficients</span></div> |
| <div class="line"><a name="l00478"></a><span class="lineno"> 478</span> <span class="comment">**/</span></div> |
| <div class="line"><a name="l00479"></a><span class="lineno"> 479</span> CREATE FUNCTION MADLIB_SCHEMA.__internal_get_hsk_result(</div> |
| <div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  source_table VARCHAR -- name of input table</div> |
| <div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  , dependent_varname VARCHAR -- name of dependent variable</div> |
| <div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  , independent_varname VARCHAR -- name of independent variable</div> |
| <div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  , linregr_coeffs DOUBLE PRECISION[] -- coeffs from linear regression</div> |
| <div class="line"><a name="l00484"></a><span class="lineno"><a class="code" href="linear_8sql__in.html#a71d8295a18e93619b3331cefabe6e79b"> 484</a></span> )</div> |
| <div class="line"><a name="l00485"></a><span class="lineno"> 485</span> RETURNS MADLIB_SCHEMA.heteroskedasticity_test_result AS $$</div> |
| <div class="line"><a name="l00486"></a><span class="lineno"> 486</span> DECLARE</div> |
| <div class="line"><a name="l00487"></a><span class="lineno"> 487</span> hsk_value MADLIB_SCHEMA.heteroskedasticity_test_result;</div> |
| <div class="line"><a name="l00488"></a><span class="lineno"> 488</span> BEGIN</div> |
| <div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  EXECUTE '</div> |
| <div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  SELECT (MADLIB_SCHEMA.heteroskedasticity_test_linregr(<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00491"></a><span class="lineno"> 491</span> <span class="stringliteral"> || dependent_varname || '</span> , <span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00492"></a><span class="lineno"> 492</span> <span class="stringliteral"> || independent_varname || '</span> , <span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00493"></a><span class="lineno"> 493</span> <span class="stringliteral"> || '</span>ARRAY[<span class="stringliteral">' || array_to_string(linregr_coeffs, '</span>,<span class="stringliteral">') || '</span>])).*</div> |
| <div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  FROM <span class="stringliteral">' || source_table</span></div> |
| <div class="line"><a name="l00495"></a><span class="lineno"> 495</span> <span class="stringliteral"> INTO hsk_value;</span></div> |
| <div class="line"><a name="l00496"></a><span class="lineno"> 496</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00497"></a><span class="lineno"> 497</span> <span class="stringliteral"> RETURN hsk_value;</span></div> |
| <div class="line"><a name="l00498"></a><span class="lineno"> 498</span> <span class="stringliteral">END</span></div> |
| <div class="line"><a name="l00499"></a><span class="lineno"> 499</span> <span class="stringliteral">$$ LANGUAGE plpgsql VOLATILE;</span><span class="comment"></span></div> |
| <div class="line"><a name="l00500"></a><span class="lineno"> 500</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00501"></a><span class="lineno"> 501</span> <span class="comment"> * @brief Return linear regression output for source data</span></div> |
| <div class="line"><a name="l00502"></a><span class="lineno"> 502</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00503"></a><span class="lineno"> 503</span> <span class="comment">**/</span></div> |
| <div class="line"><a name="l00504"></a><span class="lineno"> 504</span> CREATE FUNCTION MADLIB_SCHEMA.__internal_get_linreg_result(</div> |
| <div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  source_table VARCHAR -- name of input table</div> |
| <div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  , dependent_varname VARCHAR -- name of dependent variable</div> |
| <div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  , independent_varname VARCHAR -- name of independent variable</div> |
| <div class="line"><a name="l00508"></a><span class="lineno"> 508</span> )</div> |
| <div class="line"><a name="l00509"></a><span class="lineno"> 509</span> RETURNS MADLIB_SCHEMA.linregr_result AS $$</div> |
| <div class="line"><a name="l00510"></a><span class="lineno"> 510</span> DECLARE</div> |
| <div class="line"><a name="l00511"></a><span class="lineno"> 511</span> lin_rst MADLIB_SCHEMA.linregr_result;</div> |
| <div class="line"><a name="l00512"></a><span class="lineno"> 512</span> BEGIN</div> |
| <div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  EXECUTE '</div> |
| <div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  SELECT (MADLIB_SCHEMA.linregr( <span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00515"></a><span class="lineno"> 515</span> <span class="stringliteral"> || dependent_varname || '</span> , <span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00516"></a><span class="lineno"> 516</span> <span class="stringliteral"> || independent_varname || '</span>)</div> |
| <div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  ).*</div> |
| <div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  FROM <span class="stringliteral">' || source_table</span></div> |
| <div class="line"><a name="l00519"></a><span class="lineno"> 519</span> <span class="stringliteral"> INTO lin_rst;</span></div> |
| <div class="line"><a name="l00520"></a><span class="lineno"> 520</span> <span class="stringliteral"> RETURN lin_rst;</span></div> |
| <div class="line"><a name="l00521"></a><span class="lineno"> 521</span> <span class="stringliteral">END</span></div> |
| <div class="line"><a name="l00522"></a><span class="lineno"> 522</span> <span class="stringliteral">$$ LANGUAGE plpgsql VOLATILE;</span></div> |
| <div class="line"><a name="l00523"></a><span class="lineno"> 523</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00524"></a><span class="lineno"> 524</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00525"></a><span class="lineno"> 525</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.__internal_get_linregr_insert_string(</span></div> |
| <div class="line"><a name="l00526"></a><span class="lineno"> 526</span> <span class="stringliteral"> lin_rst MADLIB_SCHEMA.linregr_result,</span></div> |
| <div class="line"><a name="l00527"></a><span class="lineno"> 527</span> <span class="stringliteral"> out_table TEXT</span></div> |
| <div class="line"><a name="l00528"></a><span class="lineno"> 528</span> <span class="stringliteral">)</span></div> |
| <div class="line"><a name="l00529"></a><span class="lineno"> 529</span> <span class="stringliteral">RETURNS VARCHAR AS $$</span></div> |
| <div class="line"><a name="l00530"></a><span class="lineno"> 530</span> <span class="stringliteral">DECLARE</span></div> |
| <div class="line"><a name="l00531"></a><span class="lineno"> 531</span> <span class="stringliteral"> insert_string VARCHAR;</span></div> |
| <div class="line"><a name="l00532"></a><span class="lineno"> 532</span> <span class="stringliteral">BEGIN</span></div> |
| <div class="line"><a name="l00533"></a><span class="lineno"> 533</span> <span class="stringliteral"> insert_string := '</span>INSERT INTO <span class="stringliteral">' || out_table || '</span> VALUES (<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00534"></a><span class="lineno"> 534</span> <span class="stringliteral"> insert_string := insert_string ||</span></div> |
| <div class="line"><a name="l00535"></a><span class="lineno"> 535</span> <span class="stringliteral"> CASE</span></div> |
| <div class="line"><a name="l00536"></a><span class="lineno"> 536</span> <span class="stringliteral"> WHEN (lin_rst).coef is NULL</span></div> |
| <div class="line"><a name="l00537"></a><span class="lineno"> 537</span> <span class="stringliteral"> THEN '</span><span class="stringliteral">''</span>{}<span class="stringliteral">''</span>,<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00538"></a><span class="lineno"> 538</span> <span class="stringliteral"> ELSE '</span>ARRAY[<span class="stringliteral">' || array_to_string((lin_rst).coef, '</span>,<span class="stringliteral">') || '</span>], <span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00539"></a><span class="lineno"> 539</span> <span class="stringliteral"> END ||</span></div> |
| <div class="line"><a name="l00540"></a><span class="lineno"> 540</span> <span class="stringliteral"> CASE</span></div> |
| <div class="line"><a name="l00541"></a><span class="lineno"> 541</span> <span class="stringliteral"> WHEN (lin_rst).r2 is NULL</span></div> |
| <div class="line"><a name="l00542"></a><span class="lineno"> 542</span> <span class="stringliteral"> THEN '</span>0.0,<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00543"></a><span class="lineno"> 543</span> <span class="stringliteral"> ELSE (lin_rst).r2 || '</span>,<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00544"></a><span class="lineno"> 544</span> <span class="stringliteral"> END ||</span></div> |
| <div class="line"><a name="l00545"></a><span class="lineno"> 545</span> <span class="stringliteral"> CASE</span></div> |
| <div class="line"><a name="l00546"></a><span class="lineno"> 546</span> <span class="stringliteral"> WHEN (lin_rst).std_err is NULL</span></div> |
| <div class="line"><a name="l00547"></a><span class="lineno"> 547</span> <span class="stringliteral"> THEN '</span><span class="stringliteral">''</span>{}<span class="stringliteral">''</span>,<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00548"></a><span class="lineno"> 548</span> <span class="stringliteral"> ELSE '</span>ARRAY[<span class="stringliteral">' || array_to_string((lin_rst).std_err, '</span>,<span class="stringliteral">') || '</span>], <span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00549"></a><span class="lineno"> 549</span> <span class="stringliteral"> END ||</span></div> |
| <div class="line"><a name="l00550"></a><span class="lineno"> 550</span> <span class="stringliteral"> CASE</span></div> |
| <div class="line"><a name="l00551"></a><span class="lineno"> 551</span> <span class="stringliteral"> WHEN (lin_rst).t_stats is NULL</span></div> |
| <div class="line"><a name="l00552"></a><span class="lineno"> 552</span> <span class="stringliteral"> THEN '</span><span class="stringliteral">''</span>{}<span class="stringliteral">''</span>,<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00553"></a><span class="lineno"> 553</span> <span class="stringliteral"> ELSE '</span>ARRAY[<span class="stringliteral">' || array_to_string((lin_rst).t_stats, '</span>,<span class="stringliteral">') || '</span>], <span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00554"></a><span class="lineno"> 554</span> <span class="stringliteral"> END ||</span></div> |
| <div class="line"><a name="l00555"></a><span class="lineno"> 555</span> <span class="stringliteral"> CASE</span></div> |
| <div class="line"><a name="l00556"></a><span class="lineno"> 556</span> <span class="stringliteral"> WHEN (lin_rst).p_values is NULL</span></div> |
| <div class="line"><a name="l00557"></a><span class="lineno"> 557</span> <span class="stringliteral"> THEN '</span><span class="stringliteral">''</span>{}<span class="stringliteral">''</span>,<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00558"></a><span class="lineno"> 558</span> <span class="stringliteral"> ELSE '</span>ARRAY[<span class="stringliteral">' || array_to_string((lin_rst).p_values, '</span>,<span class="stringliteral">') || '</span>], <span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00559"></a><span class="lineno"> 559</span> <span class="stringliteral"> END ||</span></div> |
| <div class="line"><a name="l00560"></a><span class="lineno"> 560</span> <span class="stringliteral"> CASE</span></div> |
| <div class="line"><a name="l00561"></a><span class="lineno"> 561</span> <span class="stringliteral"> WHEN (lin_rst).condition_no is NULL</span></div> |
| <div class="line"><a name="l00562"></a><span class="lineno"> 562</span> <span class="stringliteral"> THEN '</span>0.0<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00563"></a><span class="lineno"> 563</span> <span class="stringliteral"> ELSE (lin_rst).condition_no</span></div> |
| <div class="line"><a name="l00564"></a><span class="lineno"> 564</span> <span class="stringliteral"> END;</span></div> |
| <div class="line"><a name="l00565"></a><span class="lineno"> 565</span> <span class="stringliteral"> RETURN insert_string;</span></div> |
| <div class="line"><a name="l00566"></a><span class="lineno"> 566</span> <span class="stringliteral">END;</span></div> |
| <div class="line"><a name="l00567"></a><span class="lineno"> 567</span> <span class="stringliteral">$$ LANGUAGE plpgsql VOLATILE;</span></div> |
| <div class="line"><a name="l00568"></a><span class="lineno"> 568</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00569"></a><span class="lineno"> 569</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00570"></a><span class="lineno"> 570</span> <span class="comment"> * @brief Compute linear regression coefficients and heterskedasticity values</span></div> |
| <div class="line"><a name="l00571"></a><span class="lineno"> 571</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00572"></a><span class="lineno"> 572</span> <span class="comment"> **/</span></div> |
| <div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  CREATE FUNCTION MADLIB_SCHEMA.__internal_linregr_train_hetero(</div> |
| <div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  source_table VARCHAR -- name of input table</div> |
| <div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  , out_table VARCHAR -- name of output table</div> |
| <div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  , dependent_varname VARCHAR -- name of dependent variable</div> |
| <div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  , independent_varname VARCHAR -- name of independent variable</div> |
| <div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  , heteroskedasticity_option BOOLEAN -- do you want heteroskedasticity output</div> |
| <div class="line"><a name="l00579"></a><span class="lineno"> 579</span> )</div> |
| <div class="line"><a name="l00580"></a><span class="lineno"> 580</span> RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00581"></a><span class="lineno"> 581</span> DECLARE</div> |
| <div class="line"><a name="l00582"></a><span class="lineno"> 582</span> insert_string VARCHAR;</div> |
| <div class="line"><a name="l00583"></a><span class="lineno"> 583</span> lin_rst MADLIB_SCHEMA.linregr_result;</div> |
| <div class="line"><a name="l00584"></a><span class="lineno"> 584</span> hsk_value MADLIB_SCHEMA.heteroskedasticity_test_result;</div> |
| <div class="line"><a name="l00585"></a><span class="lineno"> 585</span> BEGIN</div> |
| <div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  IF (source_table IS NULL OR source_table = '<span class="stringliteral">') THEN</span></div> |
| <div class="line"><a name="l00587"></a><span class="lineno"> 587</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Invalid input table name given.<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00588"></a><span class="lineno"> 588</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00589"></a><span class="lineno"> 589</span> <span class="stringliteral"> IF (out_table IS NULL OR out_table = '</span><span class="stringliteral">') THEN</span></div> |
| <div class="line"><a name="l00590"></a><span class="lineno"> 590</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Invalid output table name given.<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00591"></a><span class="lineno"> 591</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00592"></a><span class="lineno"> 592</span> <span class="stringliteral"> IF (dependent_varname IS NULL OR dependent_varname = '</span><span class="stringliteral">') THEN</span></div> |
| <div class="line"><a name="l00593"></a><span class="lineno"> 593</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Invalid dependent variable name given.<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00594"></a><span class="lineno"> 594</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00595"></a><span class="lineno"> 595</span> <span class="stringliteral"> IF (independent_varname IS NULL OR independent_varname = '</span><span class="stringliteral">') THEN</span></div> |
| <div class="line"><a name="l00596"></a><span class="lineno"> 596</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Invalid independent variable name given.<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00597"></a><span class="lineno"> 597</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00598"></a><span class="lineno"> 598</span> <span class="stringliteral"> IF (MADLIB_SCHEMA.__table_exists(out_table)) THEN</span></div> |
| <div class="line"><a name="l00599"></a><span class="lineno"> 599</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Output table name already exists. Drop the table before calling the <span class="keyword">function</span>.<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00600"></a><span class="lineno"> 600</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00601"></a><span class="lineno"> 601</span> <span class="stringliteral"> -- create output table with appropriate column names</span></div> |
| <div class="line"><a name="l00602"></a><span class="lineno"> 602</span> <span class="stringliteral"> EXECUTE '</span>DROP TABLE IF EXISTS <span class="stringliteral">' || out_table;</span></div> |
| <div class="line"><a name="l00603"></a><span class="lineno"> 603</span> <span class="stringliteral"> EXECUTE '</span></div> |
| <div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  CREATE TABLE <span class="stringliteral">' || out_table || '</span> (</div> |
| <div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  coef DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  r2 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  std_err DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  t_stats DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  p_values DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  condition_no DOUBLE PRECISION)<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00611"></a><span class="lineno"> 611</span> <span class="stringliteral"> IF heteroskedasticity_option THEN</span></div> |
| <div class="line"><a name="l00612"></a><span class="lineno"> 612</span> <span class="stringliteral"> -- Alter output table to add heteroskedasticity values</span></div> |
| <div class="line"><a name="l00613"></a><span class="lineno"> 613</span> <span class="stringliteral"> EXECUTE '</span></div> |
| <div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  ALTER TABLE <span class="stringliteral">' || out_table || '</span></div> |
| <div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  ADD COLUMN bp_stats DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  ADD COLUMN bp_p_value DOUBLE PRECISION<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00617"></a><span class="lineno"> 617</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00618"></a><span class="lineno"> 618</span> <span class="stringliteral"> -- compute linear regression and heteroskedasticity values (if required)</span></div> |
| <div class="line"><a name="l00619"></a><span class="lineno"> 619</span> <span class="stringliteral"> lin_rst := MADLIB_SCHEMA.__internal_get_linreg_result(</span></div> |
| <div class="line"><a name="l00620"></a><span class="lineno"> 620</span> <span class="stringliteral"> source_table, dependent_varname, independent_varname);</span></div> |
| <div class="line"><a name="l00621"></a><span class="lineno"> 621</span> <span class="stringliteral"> insert_string := MADLIB_SCHEMA.__internal_get_linregr_insert_string(</span></div> |
| <div class="line"><a name="l00622"></a><span class="lineno"> 622</span> <span class="stringliteral"> lin_rst, out_table);</span></div> |
| <div class="line"><a name="l00623"></a><span class="lineno"> 623</span> <span class="stringliteral"> -- Ensure Infinity and NaN are cast properly</span></div> |
| <div class="line"><a name="l00624"></a><span class="lineno"> 624</span> <span class="stringliteral"> insert_string := REGEXP_REPLACE(insert_string, '</span>Infinity<span class="stringliteral">',</span></div> |
| <div class="line"><a name="l00625"></a><span class="lineno"> 625</span> <span class="stringliteral"> '</span><span class="stringliteral">''</span>Infinity<span class="stringliteral">''</span>::<span class="keywordtype">double</span> precision<span class="stringliteral">', '</span>gi<span class="stringliteral">');</span></div> |
| <div class="line"><a name="l00626"></a><span class="lineno"> 626</span> <span class="stringliteral"> insert_string := REGEXP_REPLACE(insert_string, '</span>NaN<span class="stringliteral">',</span></div> |
| <div class="line"><a name="l00627"></a><span class="lineno"> 627</span> <span class="stringliteral"> '</span><span class="stringliteral">''</span>NaN<span class="stringliteral">''</span>::<span class="keywordtype">double</span> precision<span class="stringliteral">', '</span>gi<span class="stringliteral">');</span></div> |
| <div class="line"><a name="l00628"></a><span class="lineno"> 628</span> <span class="stringliteral"> IF heteroskedasticity_option THEN</span></div> |
| <div class="line"><a name="l00629"></a><span class="lineno"> 629</span> <span class="stringliteral"> -- add hsk values in the sql string and execute</span></div> |
| <div class="line"><a name="l00630"></a><span class="lineno"> 630</span> <span class="stringliteral"> hsk_value := MADLIB_SCHEMA.__internal_get_hsk_result(</span></div> |
| <div class="line"><a name="l00631"></a><span class="lineno"> 631</span> <span class="stringliteral"> source_table, dependent_varname,</span></div> |
| <div class="line"><a name="l00632"></a><span class="lineno"> 632</span> <span class="stringliteral"> independent_varname, (lin_rst).coef);</span></div> |
| <div class="line"><a name="l00633"></a><span class="lineno"> 633</span> <span class="stringliteral"> EXECUTE</span></div> |
| <div class="line"><a name="l00634"></a><span class="lineno"> 634</span> <span class="stringliteral"> insert_string || '</span>,<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00635"></a><span class="lineno"> 635</span> <span class="stringliteral"> || (hsk_value).bp_stats || '</span>,<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00636"></a><span class="lineno"> 636</span> <span class="stringliteral"> || (hsk_value).bp_p_value || '</span>)<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00637"></a><span class="lineno"> 637</span> <span class="stringliteral"> ELSE</span></div> |
| <div class="line"><a name="l00638"></a><span class="lineno"> 638</span> <span class="stringliteral"> -- complete the sql string and execute</span></div> |
| <div class="line"><a name="l00639"></a><span class="lineno"> 639</span> <span class="stringliteral"> EXECUTE insert_string || '</span>)<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00640"></a><span class="lineno"> 640</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00641"></a><span class="lineno"> 641</span> <span class="stringliteral">END</span></div> |
| <div class="line"><a name="l00642"></a><span class="lineno"> 642</span> <span class="stringliteral">$$ LANGUAGE plpgsql VOLATILE;</span></div> |
| <div class="line"><a name="l00643"></a><span class="lineno"> 643</span> <span class="stringliteral">---------------------------------------------------------------------------</span><span class="comment"></span></div> |
| <div class="line"><a name="l00644"></a><span class="lineno"> 644</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00645"></a><span class="lineno"> 645</span> <span class="comment"> * @brief Compute linear regression coefficients and insert into an output</span></div> |
| <div class="line"><a name="l00646"></a><span class="lineno"> 646</span> <span class="comment"> * table. The function drops the table if it already exists before creating</span></div> |
| <div class="line"><a name="l00647"></a><span class="lineno"> 647</span> <span class="comment"> * the table.</span></div> |
| <div class="line"><a name="l00648"></a><span class="lineno"> 648</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00649"></a><span class="lineno"> 649</span> <span class="comment">**/</span></div> |
| <div class="line"><a name="l00650"></a><span class="lineno"> 650</span> CREATE FUNCTION MADLIB_SCHEMA.linregr_train(</div> |
| <div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  source_table VARCHAR -- name of input table</div> |
| <div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  , out_table VARCHAR -- name of output table</div> |
| <div class="line"><a name="l00653"></a><span class="lineno"> 653</span>  , dependent_varname VARCHAR -- name of dependent variable</div> |
| <div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  , independent_varname VARCHAR -- name of independent variable</div> |
| <div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  )</div> |
| <div class="line"><a name="l00656"></a><span class="lineno"> 656</span> RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00657"></a><span class="lineno"> 657</span> BEGIN</div> |
| <div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  PERFORM MADLIB_SCHEMA.__internal_linregr_train_hetero(</div> |
| <div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  source_table, out_table, dependent_varname, independent_varname, False);</div> |
| <div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  -- RAISE NOTICE '</div> |
| <div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  -- Finished linear regression</div> |
| <div class="line"><a name="l00662"></a><span class="lineno"> 662</span>  -- * table : % (%, %)</div> |
| <div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  -- Output:</div> |
| <div class="line"><a name="l00664"></a><span class="lineno"> 664</span>  -- * view : SELECT * FROM % ;<span class="stringliteral">', source_table, dependent_varname,</span></div> |
| <div class="line"><a name="l00665"></a><span class="lineno"> 665</span> <span class="stringliteral"> -- independent_varname, out_table;</span></div> |
| <div class="line"><a name="l00666"></a><span class="lineno"> 666</span> <span class="stringliteral">END;</span></div> |
| <div class="line"><a name="l00667"></a><span class="lineno"> 667</span> <span class="stringliteral">$$ LANGUAGE plpgsql VOLATILE;</span></div> |
| <div class="line"><a name="l00668"></a><span class="lineno"> 668</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00669"></a><span class="lineno"> 669</span> <span class="stringliteral">--------------------- GROUPING ---------------------------------------------</span><span class="comment"></span></div> |
| <div class="line"><a name="l00670"></a><span class="lineno"> 670</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00671"></a><span class="lineno"> 671</span> <span class="comment"> * @brief Linear regression training function with grouping support and</span></div> |
| <div class="line"><a name="l00672"></a><span class="lineno"> 672</span> <span class="comment"> * option for heteroskedasticity values.</span></div> |
| <div class="line"><a name="l00673"></a><span class="lineno"> 673</span> <span class="comment"> **/</span></div> |
| <div class="line"><a name="l00674"></a><span class="lineno"> 674</span> CREATE FUNCTION MADLIB_SCHEMA.linregr_train(</div> |
| <div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  source_table VARCHAR -- name of input table</div> |
| <div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  , out_table VARCHAR -- name of output table</div> |
| <div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  , dependent_varname VARCHAR -- name of dependent variable</div> |
| <div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  , independent_varname VARCHAR -- name of independent variable</div> |
| <div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  , input_group_cols VARCHAR -- names of columns to group-by</div> |
| <div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  , heteroskedasticity_option BOOLEAN -- heteroskedasticity</div> |
| <div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  )</div> |
| <div class="line"><a name="l00682"></a><span class="lineno"> 682</span> RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00683"></a><span class="lineno"> 683</span> DECLARE</div> |
| <div class="line"><a name="l00684"></a><span class="lineno"> 684</span>  input_table_name VARCHAR[];</div> |
| <div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  group_cols VARCHAR[];</div> |
| <div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  actual_table_name VARCHAR;</div> |
| <div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  schema_name VARCHAR;</div> |
| <div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  table_creation_string VARCHAR;</div> |
| <div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  group_string VARCHAR;</div> |
| <div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  group_array_length INTEGER;</div> |
| <div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  col_data_type VARCHAR;</div> |
| <div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  each_group INTEGER;</div> |
| <div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  linregr_fitting_rst VARCHAR;</div> |
| <div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  old_msg_level TEXT;</div> |
| <div class="line"><a name="l00695"></a><span class="lineno"> 695</span> BEGIN</div> |
| <div class="line"><a name="l00696"></a><span class="lineno"> 696</span> </div> |
| <div class="line"><a name="l00697"></a><span class="lineno"> 697</span>  EXECUTE 'SELECT setting FROM pg_settings WHERE name=<span class="stringliteral">''</span>client_min_messages<span class="charliteral">'''</span> INTO old_msg_level;</div> |
| <div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  EXECUTE <span class="stringliteral">'SET client_min_messages TO warning'</span>;</div> |
| <div class="line"><a name="l00699"></a><span class="lineno"> 699</span> </div> |
| <div class="line"><a name="l00700"></a><span class="lineno"> 700</span>  IF (source_table IS NULL OR source_table = <span class="stringliteral">''</span>) THEN</div> |
| <div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  RAISE EXCEPTION 'Invalid input table name given.';</div> |
| <div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  END IF;</div> |
| <div class="line"><a name="l00703"></a><span class="lineno"> 703</span>  IF (out_table IS NULL OR out_table = '') THEN</div> |
| <div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  RAISE EXCEPTION 'Invalid output table name given.';</div> |
| <div class="line"><a name="l00705"></a><span class="lineno"> 705</span>  END IF;</div> |
| <div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  IF (dependent_varname IS NULL OR dependent_varname = '') THEN</div> |
| <div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  RAISE EXCEPTION 'Invalid dependent variable name given.';</div> |
| <div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  END IF;</div> |
| <div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  IF (independent_varname IS NULL OR independent_varname = '') THEN</div> |
| <div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  RAISE EXCEPTION 'Invalid independent variable name given.';</div> |
| <div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  END IF;</div> |
| <div class="line"><a name="l00712"></a><span class="lineno"> 712</span> </div> |
| <div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  IF (NOT MADLIB_SCHEMA.__table_exists(source_table)) THEN</div> |
| <div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  RAISE EXCEPTION 'Source table name does not exist.';</div> |
| <div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  END IF;</div> |
| <div class="line"><a name="l00716"></a><span class="lineno"> 716</span> </div> |
| <div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  IF (MADLIB_SCHEMA.__table_exists(out_table)) THEN</div> |
| <div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  RAISE EXCEPTION 'Output table name already exists. Drop the table before calling the function.';</div> |
| <div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  END IF;</div> |
| <div class="line"><a name="l00720"></a><span class="lineno"> 720</span> </div> |
| <div class="line"><a name="l00721"></a><span class="lineno"> 721</span> </div> |
| <div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  -- initial validation</div> |
| <div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  IF (input_group_cols IS NULL)</div> |
| <div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  --OR array_upper(input_group_cols, 1) IS NULL</div> |
| <div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  --OR array_upper(input_group_cols, 1) = 0)</div> |
| <div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  THEN</div> |
| <div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  PERFORM MADLIB_SCHEMA.__internal_linregr_train_hetero(</div> |
| <div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  source_table, out_table,</div> |
| <div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  dependent_varname, independent_varname,</div> |
| <div class="line"><a name="l00730"></a><span class="lineno"> 730</span>  heteroskedasticity_option);</div> |
| <div class="line"><a name="l00731"></a><span class="lineno"> 731</span>  ELSE</div> |
| <div class="line"><a name="l00732"></a><span class="lineno"> 732</span>  group_cols = MADLIB_SCHEMA._string_to_array(input_group_cols);</div> |
| <div class="line"><a name="l00733"></a><span class="lineno"> 733</span>  -- create output table</div> |
| <div class="line"><a name="l00734"></a><span class="lineno"> 734</span>  EXECUTE 'DROP TABLE IF EXISTS ' || out_table;</div> |
| <div class="line"><a name="l00735"></a><span class="lineno"> 735</span>  table_creation_string := 'CREATE TABLE ' || out_table || '(';</div> |
| <div class="line"><a name="l00736"></a><span class="lineno"> 736</span>  group_array_length = array_upper(group_cols, 1);</div> |
| <div class="line"><a name="l00737"></a><span class="lineno"> 737</span> </div> |
| <div class="line"><a name="l00738"></a><span class="lineno"> 738</span>  input_table_name = regexp_split_to_array(source_table, E'\\.');</div> |
| <div class="line"><a name="l00739"></a><span class="lineno"> 739</span>  IF array_upper(input_table_name, 1) = 1 THEN</div> |
| <div class="line"><a name="l00740"></a><span class="lineno"> 740</span>  actual_table_name = input_table_name[1];</div> |
| <div class="line"><a name="l00741"></a><span class="lineno"> 741</span>  schema_name := current_schema();</div> |
| <div class="line"><a name="l00742"></a><span class="lineno"> 742</span>  ELSIF array_upper(input_table_name, 1) = 2 THEN</div> |
| <div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  actual_table_name = input_table_name[2];</div> |
| <div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  schema_name = input_table_name[1];</div> |
| <div class="line"><a name="l00745"></a><span class="lineno"> 745</span>  ELSE</div> |
| <div class="line"><a name="l00746"></a><span class="lineno"> 746</span>  RAISE EXCEPTION 'Incorrect input source table name provided';</div> |
| <div class="line"><a name="l00747"></a><span class="lineno"> 747</span>  END IF;</div> |
| <div class="line"><a name="l00748"></a><span class="lineno"> 748</span> </div> |
| <div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  -- Check that each grouping column exists</div> |
| <div class="line"><a name="l00750"></a><span class="lineno"> 750</span>  FOR each_group in 1 .. group_array_length</div> |
| <div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  LOOP</div> |
| <div class="line"><a name="l00752"></a><span class="lineno"> 752</span>  if NOT MADLIB_SCHEMA.<a class="code" href="utilities_8sql__in.html#ac1f509bd94c6309b59eb4d479fb2a470" title="Check if a column exists in a table. ">check_if_col_exists</a>(source_table,</div> |
| <div class="line"><a name="l00753"></a><span class="lineno"> 753</span>  group_cols[each_group]) THEN</div> |
| <div class="line"><a name="l00754"></a><span class="lineno"> 754</span>  RAISE EXCEPTION 'Grouping column % does not exist',</div> |
| <div class="line"><a name="l00755"></a><span class="lineno"> 755</span>  group_cols[each_group];</div> |
| <div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  END IF;</div> |
| <div class="line"><a name="l00757"></a><span class="lineno"> 757</span> </div> |
| <div class="line"><a name="l00758"></a><span class="lineno"> 758</span> </div> |
| <div class="line"><a name="l00759"></a><span class="lineno"> 759</span>  END LOOP;</div> |
| <div class="line"><a name="l00760"></a><span class="lineno"> 760</span> </div> |
| <div class="line"><a name="l00761"></a><span class="lineno"> 761</span>  FOR each_group in 1 .. group_array_length</div> |
| <div class="line"><a name="l00762"></a><span class="lineno"> 762</span>  LOOP</div> |
| <div class="line"><a name="l00763"></a><span class="lineno"> 763</span>  -- create a <span class="keywordtype">string</span> that makes list of</div> |
| <div class="line"><a name="l00764"></a><span class="lineno"> 764</span>  EXECUTE 'SELECT data_type FROM information_schema.columns</div> |
| <div class="line"><a name="l00765"></a><span class="lineno"> 765</span>  WHERE</div> |
| <div class="line"><a name="l00766"></a><span class="lineno"> 766</span>  table_schema = ''' || schema_name || '''</div> |
| <div class="line"><a name="l00767"></a><span class="lineno"> 767</span>  AND table_name = ''' || actual_table_name || '''</div> |
| <div class="line"><a name="l00768"></a><span class="lineno"> 768</span>  AND column_name= ''' || group_cols[each_group] || ''''</div> |
| <div class="line"><a name="l00769"></a><span class="lineno"> 769</span>  INTO col_data_type;</div> |
| <div class="line"><a name="l00770"></a><span class="lineno"> 770</span> </div> |
| <div class="line"><a name="l00771"></a><span class="lineno"> 771</span>  table_creation_string := table_creation_string</div> |
| <div class="line"><a name="l00772"></a><span class="lineno"> 772</span>  || group_cols[each_group]</div> |
| <div class="line"><a name="l00773"></a><span class="lineno"> 773</span>  || ' ' || col_data_type || ',';</div> |
| <div class="line"><a name="l00774"></a><span class="lineno"> 774</span>  END LOOP;</div> |
| <div class="line"><a name="l00775"></a><span class="lineno"> 775</span> </div> |
| <div class="line"><a name="l00776"></a><span class="lineno"> 776</span>  -- finish creating the output table</div> |
| <div class="line"><a name="l00777"></a><span class="lineno"> 777</span>  EXECUTE table_creation_string || '</div> |
| <div class="line"><a name="l00778"></a><span class="lineno"> 778</span>  coef DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00779"></a><span class="lineno"> 779</span>  r2 DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00780"></a><span class="lineno"> 780</span>  std_err DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00781"></a><span class="lineno"> 781</span>  t_stats DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00782"></a><span class="lineno"> 782</span>  p_values DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00783"></a><span class="lineno"> 783</span>  condition_no DOUBLE PRECISION)';</div> |
| <div class="line"><a name="l00784"></a><span class="lineno"> 784</span>  IF heteroskedasticity_option THEN</div> |
| <div class="line"><a name="l00785"></a><span class="lineno"> 785</span>  EXECUTE 'ALTER TABLE ' || out_table || '</div> |
| <div class="line"><a name="l00786"></a><span class="lineno"> 786</span>  ADD COLUMN bp_stats DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00787"></a><span class="lineno"> 787</span>  ADD COLUMN bp_p_value DOUBLE PRECISION';</div> |
| <div class="line"><a name="l00788"></a><span class="lineno"> 788</span>  END IF;</div> |
| <div class="line"><a name="l00789"></a><span class="lineno"> 789</span> </div> |
| <div class="line"><a name="l00790"></a><span class="lineno"> 790</span>  group_string := '';</div> |
| <div class="line"><a name="l00791"></a><span class="lineno"> 791</span>  FOR each_group in 1 .. (group_array_length-1)</div> |
| <div class="line"><a name="l00792"></a><span class="lineno"> 792</span>  LOOP</div> |
| <div class="line"><a name="l00793"></a><span class="lineno"> 793</span>  group_string := group_string || group_cols[each_group] || ',';</div> |
| <div class="line"><a name="l00794"></a><span class="lineno"> 794</span>  END LOOP;</div> |
| <div class="line"><a name="l00795"></a><span class="lineno"> 795</span>  group_string := group_string || group_cols[group_array_length];</div> |
| <div class="line"><a name="l00796"></a><span class="lineno"> 796</span> </div> |
| <div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  IF heteroskedasticity_option THEN</div> |
| <div class="line"><a name="l00798"></a><span class="lineno"> 798</span>  linregr_fitting_rst := MADLIB_SCHEMA.__unique_string();</div> |
| <div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  EXECUTE '</div> |
| <div class="line"><a name="l00800"></a><span class="lineno"> 800</span>  DROP TABLE IF EXISTS '|| linregr_fitting_rst ||';</div> |
| <div class="line"><a name="l00801"></a><span class="lineno"> 801</span>  CREATE TEMP TABLE '|| linregr_fitting_rst ||' AS</div> |
| <div class="line"><a name="l00802"></a><span class="lineno"> 802</span>  SELECT</div> |
| <div class="line"><a name="l00803"></a><span class="lineno"> 803</span>  '|| group_string ||',</div> |
| <div class="line"><a name="l00804"></a><span class="lineno"> 804</span>  (MADLIB_SCHEMA.<a class="code" href="linear_8sql__in.html#a71d8295a18e93619b3331cefabe6e79b" title="Compute linear regression coefficients and diagnostic statistics. ">linregr</a>('|| dependent_varname ||','|| independent_varname ||')).*</div> |
| <div class="line"><a name="l00805"></a><span class="lineno"> 805</span>  FROM '|| source_table ||'</div> |
| <div class="line"><a name="l00806"></a><span class="lineno"> 806</span>  GROUP BY '|| group_string;</div> |
| <div class="line"><a name="l00807"></a><span class="lineno"> 807</span> </div> |
| <div class="line"><a name="l00808"></a><span class="lineno"> 808</span>  EXECUTE '</div> |
| <div class="line"><a name="l00809"></a><span class="lineno"> 809</span>  INSERT INTO ' || out_table || '</div> |
| <div class="line"><a name="l00810"></a><span class="lineno"> 810</span>  SELECT *</div> |
| <div class="line"><a name="l00811"></a><span class="lineno"> 811</span>  FROM</div> |
| <div class="line"><a name="l00812"></a><span class="lineno"> 812</span>  '|| linregr_fitting_rst ||'</div> |
| <div class="line"><a name="l00813"></a><span class="lineno"> 813</span>  JOIN (</div> |
| <div class="line"><a name="l00814"></a><span class="lineno"> 814</span>  SELECT</div> |
| <div class="line"><a name="l00815"></a><span class="lineno"> 815</span>  '|| group_string ||',</div> |
| <div class="line"><a name="l00816"></a><span class="lineno"> 816</span>  (MADLIB_SCHEMA.<a class="code" href="linear_8sql__in.html#a85d6d11ff2c93855061515d92d4785c2" title="Compute studentized Breuch-Pagan heteroskedasticity test for linear regression. ">heteroskedasticity_test_linregr</a>('</div> |
| <div class="line"><a name="l00817"></a><span class="lineno"> 817</span>  || dependent_varname || ','</div> |
| <div class="line"><a name="l00818"></a><span class="lineno"> 818</span>  || independent_varname || ', t.coef)).*</div> |
| <div class="line"><a name="l00819"></a><span class="lineno"> 819</span>  FROM</div> |
| <div class="line"><a name="l00820"></a><span class="lineno"> 820</span>  '|| source_table ||' AS s</div> |
| <div class="line"><a name="l00821"></a><span class="lineno"> 821</span>  JOIN</div> |
| <div class="line"><a name="l00822"></a><span class="lineno"> 822</span>  '|| linregr_fitting_rst ||' AS t</div> |
| <div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  USING (' || group_string || ')</div> |
| <div class="line"><a name="l00824"></a><span class="lineno"> 824</span>  GROUP BY ' || group_string ||') z</div> |
| <div class="line"><a name="l00825"></a><span class="lineno"> 825</span>  USING ('|| group_string ||')';</div> |
| <div class="line"><a name="l00826"></a><span class="lineno"> 826</span> </div> |
| <div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  EXECUTE 'DROP TABLE IF EXISTS '|| linregr_fitting_rst;</div> |
| <div class="line"><a name="l00828"></a><span class="lineno"> 828</span>  ELSE</div> |
| <div class="line"><a name="l00829"></a><span class="lineno"> 829</span>  EXECUTE '</div> |
| <div class="line"><a name="l00830"></a><span class="lineno"> 830</span>  INSERT INTO ' || out_table || '</div> |
| <div class="line"><a name="l00831"></a><span class="lineno"> 831</span>  SELECT ' || group_string || ', (result).coef, (result).r2,</div> |
| <div class="line"><a name="l00832"></a><span class="lineno"> 832</span>  (result).std_err, (result).t_stats,</div> |
| <div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  (result).p_values, (result).condition_no</div> |
| <div class="line"><a name="l00834"></a><span class="lineno"> 834</span>  FROM (</div> |
| <div class="line"><a name="l00835"></a><span class="lineno"> 835</span>  SELECT ' || group_string ||</div> |
| <div class="line"><a name="l00836"></a><span class="lineno"> 836</span>  ', MADLIB_SCHEMA.<a class="code" href="linear_8sql__in.html#a71d8295a18e93619b3331cefabe6e79b" title="Compute linear regression coefficients and diagnostic statistics. ">linregr</a>( '</div> |
| <div class="line"><a name="l00837"></a><span class="lineno"> 837</span>  || dependent_varname || ' , '</div> |
| <div class="line"><a name="l00838"></a><span class="lineno"> 838</span>  || independent_varname || ' )</div> |
| <div class="line"><a name="l00839"></a><span class="lineno"> 839</span>  AS result</div> |
| <div class="line"><a name="l00840"></a><span class="lineno"> 840</span>  FROM ' || source_table || '</div> |
| <div class="line"><a name="l00841"></a><span class="lineno"> 841</span>  GROUP BY ' || group_string ||</div> |
| <div class="line"><a name="l00842"></a><span class="lineno"> 842</span>  ') subq';</div> |
| <div class="line"><a name="l00843"></a><span class="lineno"> 843</span>  END IF;</div> |
| <div class="line"><a name="l00844"></a><span class="lineno"> 844</span>  END IF;</div> |
| <div class="line"><a name="l00845"></a><span class="lineno"> 845</span> </div> |
| <div class="line"><a name="l00846"></a><span class="lineno"> 846</span>  EXECUTE 'SET client_min_messages TO '|| old_msg_level;</div> |
| <div class="line"><a name="l00847"></a><span class="lineno"> 847</span> END;</div> |
| <div class="line"><a name="l00848"></a><span class="lineno"> 848</span> $$ LANGUAGE plpgsql VOLATILE;</div> |
| <div class="line"><a name="l00849"></a><span class="lineno"> 849</span> ---------------------------------------------------------------------------<span class="comment"></span></div> |
| <div class="line"><a name="l00850"></a><span class="lineno"> 850</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00851"></a><span class="lineno"> 851</span> <span class="comment"> * @brief Linear regression training function with grouping support.</span></div> |
| <div class="line"><a name="l00852"></a><span class="lineno"> 852</span> <span class="comment"> **/</span></div> |
| <div class="line"><a name="l00853"></a><span class="lineno"> 853</span> CREATE FUNCTION MADLIB_SCHEMA.linregr_train(</div> |
| <div class="line"><a name="l00854"></a><span class="lineno"> 854</span>  source_table VARCHAR -- name of input table</div> |
| <div class="line"><a name="l00855"></a><span class="lineno"> 855</span>  , out_table VARCHAR -- name of output table</div> |
| <div class="line"><a name="l00856"></a><span class="lineno"> 856</span>  , dependent_varname VARCHAR -- name of dependent variable</div> |
| <div class="line"><a name="l00857"></a><span class="lineno"> 857</span>  , independent_varname VARCHAR -- name of independent variable</div> |
| <div class="line"><a name="l00858"></a><span class="lineno"> 858</span>  , group_cols VARCHAR -- names of columns to group-by</div> |
| <div class="line"><a name="l00859"></a><span class="lineno"> 859</span>  )</div> |
| <div class="line"><a name="l00860"></a><span class="lineno"> 860</span> RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00861"></a><span class="lineno"> 861</span> BEGIN</div> |
| <div class="line"><a name="l00862"></a><span class="lineno"> 862</span>  PERFORM MADLIB_SCHEMA.linregr_train( source_table, out_table,</div> |
| <div class="line"><a name="l00863"></a><span class="lineno"> 863</span>  dependent_varname,</div> |
| <div class="line"><a name="l00864"></a><span class="lineno"> 864</span>  independent_varname, group_cols, FALSE);</div> |
| <div class="line"><a name="l00865"></a><span class="lineno"> 865</span> END;</div> |
| <div class="line"><a name="l00866"></a><span class="lineno"> 866</span> $$ LANGUAGE plpgsql VOLATILE;</div> |
| <div class="line"><a name="l00867"></a><span class="lineno"> 867</span> ---------------------------------------------------------------------------</div> |
| <div class="line"><a name="l00868"></a><span class="lineno"> 868</span> </div> |
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