<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>FAQ/RegressionPart</title><revhistory><revision><revnumber>11</revnumber><date>2015-08-03 14:01:05</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>10</revnumber><date>2013-03-08 10:17:18</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>9</revnumber><date>2012-01-24 12:20:07</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2006-11-08 17:36:45</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2006-11-08 17:00:02</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2006-11-08 16:46:40</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2006-11-08 16:45:41</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2006-11-08 16:44:57</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2006-11-08 16:43:33</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2006-11-08 16:40:19</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2006-11-08 16:38:05</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Explaining Part (also known as semi-partial) correlations</title><para>Try to assess the importance of phonological awareness on predicting Reading Ability which is independent of dysphraxia. You can do this using General Linear Model:univariate. Suppose putting both phonological  awareness and dysphraxia as covariates gives  </para><para>Suppose we have </para><para>Dependent Variable=Reading Ability </para><informaltable><tgroup cols="11"><colspec colname="col_0" colwidth="16*"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3"/><colspec colname="col_4"/><colspec colname="col_5"/><colspec colname="col_6"/><colspec colname="col_7"/><colspec colname="col_8"/><colspec colname="col_9"/><colspec colname="col_10"/><tbody><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para>  Source </para></entry><entry colsep="1" rowsep="1"><para> df </para></entry><entry colsep="1" rowsep="1"><para> Type III SS </para></entry><entry colsep="1" rowsep="1"><para> MS </para></entry><entry colsep="1" rowsep="1"><para> F </para></entry><entry colsep="1" rowsep="1"><para> p </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> Dysphraxia </para></entry><entry colsep="1" rowsep="1"><para> 1 </para></entry><entry colsep="1" rowsep="1"><para> 13.59 </para></entry><entry colsep="1" rowsep="1"><para> 13.59 </para></entry><entry colsep="1" rowsep="1"><para> 9.44 </para></entry><entry colsep="1" rowsep="1"><para> .013 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> Phonological Awareness </para></entry><entry colsep="1" rowsep="1"><para> 1 </para></entry><entry colsep="1" rowsep="1"><para> 8.45 </para></entry><entry colsep="1" rowsep="1"><para> 8.45 </para></entry><entry colsep="1" rowsep="1"><para>5.87 </para></entry><entry colsep="1" rowsep="1"><para> .038 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> Error </para></entry><entry colsep="1" rowsep="1"><para> 9 </para></entry><entry colsep="1" rowsep="1"><para> 12.96 </para></entry><entry colsep="1" rowsep="1"><para> 1.44 </para></entry><entry colsep="1" rowsep="1"/><entry colsep="1" rowsep="1"/></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> Corrected Total </para></entry><entry colsep="1" rowsep="1"><para> 11 </para></entry><entry colsep="1" rowsep="1"><para> 35.00 </para></entry><entry colsep="1" rowsep="1"/><entry colsep="1" rowsep="1"/><entry colsep="1" rowsep="1"/></row></tbody></tgroup></informaltable><para>R-squared=0.630 </para><para>This tells us that phonological Awareness has a statistically significant influence on reading ability after taking dysphraxia into account  (F(1,9)=8.45, p&lt;0.05). </para><para>Fitting just dysphraxia gives </para><para>Dependent Variable=Reading Ability </para><informaltable><tgroup cols="11"><colspec colname="col_0" colwidth="16*"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3"/><colspec colname="col_4"/><colspec colname="col_5"/><colspec colname="col_6"/><colspec colname="col_7"/><colspec colname="col_8"/><colspec colname="col_9"/><colspec colname="col_10"/><tbody><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para>  Source </para></entry><entry colsep="1" rowsep="1"><para> df </para></entry><entry colsep="1" rowsep="1"><para> Type III SS </para></entry><entry colsep="1" rowsep="1"><para> MS </para></entry><entry colsep="1" rowsep="1"><para> F </para></entry><entry colsep="1" rowsep="1"><para> p </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> Dysphraxia </para></entry><entry colsep="1" rowsep="1"><para> 1 </para></entry><entry colsep="1" rowsep="1"><para> 15.50 </para></entry><entry colsep="1" rowsep="1"><para> 15.50 </para></entry><entry colsep="1" rowsep="1"><para> 7.95 </para></entry><entry colsep="1" rowsep="1"><para> .018 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> Error </para></entry><entry colsep="1" rowsep="1"><para> 10 </para></entry><entry colsep="1" rowsep="1"><para> 19.50 </para></entry><entry colsep="1" rowsep="1"><para> 1.95 </para></entry><entry colsep="1" rowsep="1"/><entry colsep="1" rowsep="1"/></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> Corrected Total </para></entry><entry colsep="1" rowsep="1"><para> 11 </para></entry><entry colsep="1" rowsep="1"><para> 35.00 </para></entry><entry colsep="1" rowsep="1"/><entry colsep="1" rowsep="1"/><entry colsep="1" rowsep="1"/></row></tbody></tgroup></informaltable><para>R-squared=0.443  </para><para>Comparing the two R-squareds tells us that phonological awareness accounts for 0.630-0.443 = 0.187 or 18.7% of total variance in reading ability over and  above that predicted by dysphraxia. The signed square root of this Sqrt(0.187)=sgn(0.432) is the <emphasis role="strong">Part correlation</emphasis>, also called the <emphasis role="strong">semi-partial correlation</emphasis> of phonological awareness adjusted for dysphraxia with reading ability. </para><para>In other words: The square of the (Part) correlation which relates aspects of phonological  awareness, unrelated to dysphraxia, to reading ability is the difference in </para><itemizedlist><listitem override="none"><para>R-squareds of a model with dysphraxia and phonological awareness and </para></listitem></itemizedlist><para>the R-squared of a model with dysphraxia only with reading ability as dependent (outcome) variable. </para><para>R-squared (or equivalently its signed square root, the part correlation) is  often given as a measure of the strength of an association between one or  more predictor variables of interest, adjusted for other confounding predictors, with an outcome. Since this is a regression term R-squared can also be used to describe analysis of (co)variance. </para></section></article>