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margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">General Linear Regression </p></text><indexes><phrase>general linear regression</phrase><phrase>regression, linear</phrase><phrase>linear regression, general</phrase><phrase>linfit</phrase><phrase>functions, linfit</phrase><phrase>lnfit</phrase><phrase>functions, lnfit</phrase></indexes></region><region region-id="1320" left="66" top="115.5" width="63" height="12.75" align-x="66" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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">linfit(vx,vy,F)</p></text></region><region region-id="2079" left="162" top="115.5" width="51" height="12.75" align-x="162" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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">lnfit(vx,vy)</p></text></region><region region-id="2002" left="36" top="152.25" width="316.5" height="72" align-x="36" align-y="162" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="inherit" text-align="left" list-style-type="inherit" tabs="inherit">While data doesn't always follow a straight line, it can often be fit by a function which is a simple linear sum of terms. 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Consider the following data:</p></text></region><region region-id="2008" left="66" top="237" width="168.75" height="52.5" align-x="90" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><component hide-arguments="false" clsid-buddy="a6cfc4d6-3a88-437d-94de-30d1a591cf29" item-idref="4" disable-calc="false"><inputs /><outputs><ml:id xml:space="preserve">data</ml:id></outputs></component><rendering item-idref="5" /></region><region region-id="2009" left="66" top="303.75" width="49.5" height="18" align-x="79.5" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:id xml:space="preserve">X</ml:id><ml:apply><ml:matcol /><ml:id xml:space="preserve">data</ml:id><ml:real>0</ml:real></ml:apply></ml:define></math><rendering item-idref="6" /></region><region region-id="2010" left="144" top="303.75" width="48" height="18" align-x="156" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:id xml:space="preserve">Y</ml:id><ml:apply><ml:matcol /><ml:id xml:space="preserve">data</ml:id><ml:real>1</ml:real></ml:apply></ml:define></math><rendering item-idref="7" /></region><region region-id="2011" left="36" top="342.75" width="183" height="14.25" align-x="36" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="inherit" text-align="left" list-style-type="inherit" tabs="inherit"><f family="Verdana" charset="0" size="10"><inlineAttr line-through="false"><c val="#000">Enter the vector of functions to fit.</c></inlineAttr></f><f family="Times New Roman" charset="0" size="12"><c val="#000"><sp /></c></f></p></text></region><region region-id="2012" left="66" top="369.75" width="67.5" height="47.25" align-x="93" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:function><ml:id xml:space="preserve">F1</ml:id><ml:boundVars><ml:id xml:space="preserve">x</ml:id></ml:boundVars></ml:function><ml:matrix rows="3" cols="1"><ml:apply><ml:id xml:space="preserve">ln</ml:id><ml:id xml:space="preserve">x</ml:id></ml:apply><ml:apply><ml:sqrt /><ml:id xml:space="preserve">x</ml:id></ml:apply><ml:real>1</ml:real></ml:matrix></ml:define></math><rendering item-idref="8" /></region><region region-id="2013" left="36" top="428.25" width="313.5" height="24" align-x="36" align-y="438" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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">Call the<f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000"> linfit </c></inlineAttr></b></f>function using the data and the vector of functions, F.</p></text><indexes><phrase>linfit function</phrase></indexes></region><region region-id="2068" left="66" top="465" width="99.75" height="12.75" align-x="100.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:id xml:space="preserve">params</ml:id><ml:apply><ml:id xml:space="preserve">linfit</ml:id><ml:sequence><ml:id xml:space="preserve">X</ml:id><ml:id xml:space="preserve">Y</ml:id><ml:id xml:space="preserve">F1</ml:id></ml:sequence></ml:apply></ml:define></math><rendering item-idref="9" /></region><region region-id="2015" left="36" top="488.25" width="317.25" height="36" align-x="36" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Define a function that uses these newly found parameter values in the logarithmic model. 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style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Common linear functions</p></text></region><region region-id="2053" left="36" top="872.25" width="294" height="37.5" align-x="36" align-y="882" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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">A simpler way to perform a customized log fit is by using the<f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000"> lnfit</c></inlineAttr></b></f> function, which fits data to the model function <region region-id="842" left="36" top="897" width="427.5" height="12.75" align-x="46.5" align-y="906" show-border="false" show-highlight="false" 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margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">correlation coefficient</p></text></region><region region-id="2059" left="36" top="1226.25" width="321.75" height="60" align-x="36" align-y="1236" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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">A sum of powers of x, a polynomial regression, is another kind of linear function. 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