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| <div class="title">Pearson's Correlation<div class="ingroups"><a class="el" href="group__grp__desc__stats.html">Descriptive Statistics</a></div></div> </div> |
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| <div class="contents"> |
| <div class="toc"><b>Contents</b> </p> |
| <ul> |
| <li> |
| <a href="#usage">Correlation Function</a> </li> |
| <li> |
| <a href="#examples">Examples</a> </li> |
| <li> |
| <a href="#seealso">See Also</a> </li> |
| </ul> |
| </div><p>A correlation function is the degree and direction of association of two variables—how well one random variable can be predicted from the other. The coefficient of correlation varies from -1 to 1. A coefficient of 1 implies perfect correlation, 0 means no correlation, and -1 means perfect anti-correlation.</p> |
| <p>This function provides a cross-correlation matrix for all pairs of numeric columns in a <em>source_table</em>. A correlation matrix describes correlation among \( M \) variables. It is a square symmetrical \( M \)x \(M \) matrix with the \( (ij) \)th element equal to the correlation coefficient between the \(i\)th and the \(j\)th variable. The diagonal elements (correlations of variables with themselves) are always equal to 1.0.</p> |
| <p><a class="anchor" id="usage"></a></p> |
| <dl class="section user"><dt>Correlation Function</dt><dd></dd></dl> |
| <p>The correlation function has the following syntax: </p> |
| <pre class="syntax"> |
| correlation( source_table, |
| output_table, |
| target_cols |
| ) |
| </pre> <dl class="arglist"> |
| <dt>source_table </dt> |
| <dd>TEXT. The name of the data containing the input data. </dd> |
| <dt>output_table </dt> |
| <dd>TEXT. The name of the table where the cross-correlation matrix will be saved. The output is a table with N+2 columns and N rows, where N is the number of target columns. It contains the following columns. <table class="output"> |
| <tr> |
| <th>column_position </th><td>The first column contains the position of the variable in the '<em>source_table</em>'. </td></tr> |
| <tr> |
| <th>variable </th><td>The second column contains the row-header for the variables. </td></tr> |
| <tr> |
| <th>remaining columns </th><td>The remainder of the table is the NxN correlation matrix for the pairs of numeric '<em>source_table</em>' columns. </td></tr> |
| </table> |
| The output table is arranged as a lower-triangular matrix with the upper triangle set to NULL and the diagonal elements set to 1.0. To obtain the result from the '<em>output_table</em>' in this matrix format ensure to order the elements using the '<em>column_position</em>', as shown in the example below. <pre class="example"> |
| SELECT * FROM output_table ORDER BY column_position; |
| </pre> </dd> |
| <dt>target_cols (optional) </dt> |
| <dd>TEXT, default: '*'. A comma-separated list of the columns to correlate. If NULL or <code>'*'</code>, results are produced for all numeric columns. </dd> |
| </dl> |
| <p><a class="anchor" id="examples"></a></p> |
| <dl class="section user"><dt>Examples</dt><dd><ol type="1"> |
| <li>View online help for the correlation function. <pre class="example"> |
| SELECT madlib.correlation(); |
| </pre></li> |
| <li>Create an input data set. <pre class="example"> |
| DROP TABLE IF EXISTS example_data; |
| CREATE TABLE example_data( |
| id SERIAL, outlook TEXT, |
| temperature FLOAT8, humidity FLOAT8, |
| windy TEXT, class TEXT); |
| COPY example_data FROM STDIN WITH DELIMITER '|'; |
| 1 | sunny | 85 | 85 | false | Don't Play |
| 2 | sunny | 80 | 90 | true | Don't Play |
| 3 | overcast | 83 | 78 | false | Play |
| 4 | rain | 70 | 96 | false | Play |
| 5 | rain | 68 | 80 | false | Play |
| 6 | rain | 65 | 70 | true | Don't Play |
| 7 | overcast | 64 | 65 | true | Play |
| 8 | sunny | 72 | 95 | false | Don't Play |
| 9 | sunny | 69 | 70 | false | Play |
| 10 | rain | 75 | 80 | false | Play |
| 11 | sunny | 75 | 70 | true | Play |
| 12 | overcast | 72 | 90 | true | Play |
| 13 | overcast | 81 | 75 | false | Play |
| 14 | rain | 71 | 80 | true | Don't Play |
| 15 | | 100 | 100 | true | |
| 16 | | 110 | 100 | true | |
| \. |
| </pre></li> |
| <li>Run the <a class="el" href="correlation_8sql__in.html#a1d17ea5ec13e198d6d310b6aa79173de">correlation()</a> function on the data set. <pre class="example"> |
| -- Correlate all numeric columns |
| SELECT madlib.correlation( 'example_data', |
| 'example_data_output' |
| ); |
| -- Setting target_cols to NULL or '*' also correlates all numeric columns |
| SELECT madlib.correlation( 'example_data', |
| 'example_data_output', |
| '*' |
| ); |
| -- Correlate only the temperature and humidity columns |
| SELECT madlib.correlation( 'example_data', |
| 'example_data_output', |
| 'temperature, humidity' |
| ); |
| </pre></li> |
| <li>View the correlation matrix. <pre class="example"> |
| SELECT * FROM example_data_output ORDER BY column_position; |
| </pre> Result: <pre class="result"> |
| column_position | variable | temperature | humidity |
| -----------------+-------------+-------------------+---------- |
| 1 | temperature | 1 | |
| 2 | humidity | 0.616876934548786 | 1.0 |
| (2 rows) |
| </pre></li> |
| </ol> |
| </dd></dl> |
| <p><a class="anchor" id="related"></a></p> |
| <dl class="section user"><dt>Related Topics</dt><dd></dd></dl> |
| <p>File <a class="el" href="correlation_8sql__in.html" title="SQL functions for correlation computation. ">correlation.sql_in</a> documenting the SQL functions</p> |
| <p><a class="el" href="group__grp__summary.html">Summary</a> for general descriptive statistics for a table </p> |
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