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<p class="MsoNormal">Hi Heinz,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">For the regression errors, I am not an expert but from wikipedia or from reference below, I would risk the following code (at your peril):<o:p></o:p></p>
<p class="MsoNormal"><i><span style="font-family:"Monospaced",serif;color:#64AE64"><a href="https://pages.mtu.edu/~fmorriso/cm3215/UncertaintySlopeInterceptOfLeastSquaresFit.pdf">https://pages.mtu.edu/~fmorriso/cm3215/UncertaintySlopeInterceptOfLeastSquaresFit.pdf</a><o:p></o:p></span></i></p>
<p class="MsoNormal"><span style="font-family:"Monospaced",serif"><o:p> </o:p></span></p>
<pre><i><span style="font-family:"Monospaced",serif;color:#64AE64">// Note: for degrees of freedom>=6, t-distribution ~2</span></i><span style="font-family:"Monospaced",serif"><o:p></o:p></span></pre>
<pre><span style="font-family:"Monospaced",serif;color:black">N</span><span style="font-family:"Monospaced",serif"> <span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">length</span><span style="color:#4A55DB">(</span><span style="color:black">MW</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-family:"Monospaced",serif;color:black">mx</span><span style="font-family:"Monospaced",serif"> <span style="color:#5C5C5C">=</span> <u><span style="color:#AE5CB0">mean</span></u><span style="color:#4A55DB">(</span><span style="color:black">MW</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-family:"Monospaced",serif;color:black">SSxx</span><span style="font-family:"Monospaced",serif"> <span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">sum</span><span style="color:#4A55DB">((</span><span style="color:black">MW</span> <span style="color:#5C5C5C">-</span><span style="color:black">mx</span><span style="color:#4A55DB">)</span><span style="color:#5C5C5C">.^</span><span style="color:rosybrown">2</span><span style="color:#4A55DB">)</span><span style="color:black">;</span><o:p></o:p></span></pre>
<pre><span style="font-family:"Monospaced",serif;color:black">Ea</span><span style="font-family:"Monospaced",serif"> <span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">diag</span><span style="color:#4A55DB">(</span><span style="color:rosybrown">2</span><span style="color:#5C5C5C">*</span><span style="color:black">sig</span><span style="color:#5C5C5C">/</span><span style="color:#32B9B9">sqrt</span><span style="color:#4A55DB">(</span><span style="color:black">SSxx</span><span style="color:#4A55DB">))</span> <i><span style="color:#64AE64">// take Ea diagonals; slope 95% confidence </span></i><o:p></o:p></span></pre>
<pre><span style="font-family:"Monospaced",serif;color:black">Eb</span><span style="font-family:"Monospaced",serif"> <span style="color:#5C5C5C">=</span> <span style="color:#32B9B9">diag</span><span style="color:#4A55DB">(</span><span style="color:rosybrown">2</span><span style="color:#5C5C5C">*</span><span style="color:black">sig</span><span style="color:#5C5C5C">*</span><span style="color:#32B9B9">sqrt</span><span style="color:#4A55DB">(</span><span style="color:rosybrown">1</span><span style="color:#5C5C5C">/</span><span style="color:black">N</span><span style="color:#5C5C5C">+</span><span style="color:black">mx</span><span style="color:#5C5C5C">^</span><span style="color:rosybrown">2</span><span style="color:#5C5C5C">/</span><span style="color:black">SSxx</span><span style="color:#4A55DB">))</span> <i><span style="color:#64AE64">// take Eb diagonals; intercept 95% confidence</span></i><o:p></o:p></span></pre>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Concerning the least squares regression part, it seems the code may be written more compactly using reglin:<o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:8.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB">[</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:black">a,b,sig</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB">]</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#5C5C5C">=</span><u><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#AE5CB0">reglin</span></u><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB">(</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:black">MW</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#5C5C5C">'</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:black">,Y</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#5C5C5C">'</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB">)</span><span style="font-size:10.0pt;font-family:"Monospaced",serif">
<i><span style="color:#64AE64">// simple least squares linear regression</span></i><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:black">GG</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#5C5C5C">=</span><span style="font-size:10.0pt;font-family:"Monospaced",serif">
<span style="color:black">a</span><span style="color:#5C5C5C">.*.</span><span style="color:black">xx</span><span style="color:#5C5C5C">'</span>
<span style="color:#5C5C5C">+</span> <u><span style="color:#AE5CB0">repmat</span></u><span style="color:#4A55DB">(</span><span style="color:black">b,</span><span style="color:#32B9B9">size</span><span style="color:#4A55DB">(</span><span style="color:black">xx</span><span style="color:#5C5C5C">'</span><span style="color:#4A55DB">))</span><o:p></o:p></span></p>
<p class="MsoNormal"><u><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#AE5CB0">plot</span></u><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB">(</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:black">xx,GG</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#5C5C5C">'</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:black">,</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:rosybrown">'LineWidth'</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:black">,</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:rosybrown">1</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:#4A55DB">)</span><span style="font-size:10.0pt;font-family:"Monospaced",serif;color:black">;</span><span style="font-size:10.0pt;font-family:"Monospaced",serif"><o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Regards,<o:p></o:p></p>
<p class="MsoNormal">Rafael<o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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