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tabs="inherit"><f family="Arial" charset="0"><u><inlineAttr line-through="false"><c val="#808000"><link href="./regression.xmcd" title="Links to Section Contents" popup="false"><sp count="6" />REGRESSION</link></c></inlineAttr></u></f></p></text></region><region region-id="1321" left="36" top="90.75" width="144.75" height="13.5" align-x="36" align-y="102" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Sous-titre" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Median-Median Regression</p></text><indexes><phrase>median-median regression </phrase><phrase> regression, median-median </phrase><phrase> functions, median-median regression </phrase><phrase> medfit function </phrase><phrase> functions, medfit </phrase><phrase> median-median fit line </phrase><phrase> line, median-median fit </phrase><phrase> line of least absolute deviation </phrase><phrase> least absolute deviation, line of </phrase></indexes></region><region region-id="1320" left="66" top="115.5" width="51" height="12.75" align-x="66" align-y="126" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="functions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">medfit(x,y)</p></text></region><region region-id="1326" left="36" top="146.25" width="303" height="120" align-x="36" align-y="156" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The <f 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As shown in the previous section, the goal of the <b><u><link href="./linreg.xmcd" title="Links to section" popup="false">least-squares linear fit</link></u></b> is to minimize the sum of the squared distances from data points to the desired line. If the data contains <b><u><link href="./outlier.xmcd" title="Links to section" popup="false">outliers</link></u></b>, however, the least-squares fit may be thrown off while trying to minimize the distance to the outlier. 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You'll find that the median-median line moves hardly at all, while the least-squares line will track the outlier until it is no longer an outlier.</p></text></region><region region-id="1330" left="0" top="600" width="6000" height="6" align-x="0" align-y="600" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><pageBreak /></region><region region-id="1331" left="36" top="613.5" width="139.5" height="12.75" align-x="36" align-y="624" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The median-median algorithm</p></text></region><region region-id="1332" left="36" top="638.25" width="322.5" height="48" align-x="36" align-y="648" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Data is divided into 3 smaller sets of approximately the same size. Each set is then represented by a single point determined by the medians of the x and y data in the set. A line is then fit to these 3 points.</p></text></region><region region-id="1338" left="36" top="702" width="9" height="9" align-x="36" align-y="702" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><png item-idref="13" /><rendering item-idref="14" /></region><region region-id="1342" left="66" top="698.25" width="268.5" height="12" align-x="66" align-y="708" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">The subsets must consist of consecutive data points.</p></text></region><region region-id="1340" left="36" top="720" width="9" height="9" align-x="36" align-y="720" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><png item-idref="15" /><rendering item-idref="16" /></region><region region-id="1343" left="66" top="716.25" width="297.75" height="24" align-x="66" align-y="726" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">No two subsets can have a common x value, repeated values are put in the same set.</p></text></region><region region-id="1337" left="36" top="758.25" width="300.75" height="60" align-x="36" align-y="768" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The slope of the line is determined by the difference in medians of the x and y data between the first and the third groups. 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