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ANOVA Calculations in Multiple Linear Regression - Revision history
2026-05-05T14:40:48Z
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Lisa Hacker at 19:08, 15 September 2023
2023-09-15T19:08:23Z
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{Template:<del style="font-weight: bold; text-decoration: none;">DOEBOOK_SUB</del>|Appendix A|ANOVA Calculations in Multiple Linear Regression}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{Template:<ins style="font-weight: bold; text-decoration: none;">Doebook</ins>|Appendix A|ANOVA Calculations in Multiple Linear Regression}}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The sum of squares for the analysis of variance in multiple linear regression is obtained using the same relations as those in simple linear regression, except that the matrix notation is preferred in the case of multiple linear regression. In the case of both the simple and multiple linear regression models, once the observed and fitted values are available, the sum of squares are calculated in an identical manner. The difference between the two models lies in the way the fitted values are obtained. In a simple linear regression model, the fitted values are obtained from a model having only one predictor variable. In multiple linear regression analysis, the model used to obtained the fitted values contains more than one predictor variable.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The sum of squares for the analysis of variance in multiple linear regression is obtained using the same relations as those in simple linear regression, except that the matrix notation is preferred in the case of multiple linear regression. In the case of both the simple and multiple linear regression models, once the observed and fitted values are available, the sum of squares are calculated in an identical manner. The difference between the two models lies in the way the fitted values are obtained. In a simple linear regression model, the fitted values are obtained from a model having only one predictor variable. In multiple linear regression analysis, the model used to obtained the fitted values contains more than one predictor variable.</div></td></tr>
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Lisa Hacker
https://www.reliawiki.com/index.php?title=ANOVA_Calculations_in_Multiple_Linear_Regression&diff=37074&oldid=prev
Chris Kahn at 20:15, 30 January 2013
2013-01-30T20:15:01Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:15, 30 January 2013</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{Template:DOEBOOK_SUB|Appendix A|Calculations in Multiple Linear Regression}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{Template:DOEBOOK_SUB|Appendix A|<ins style="font-weight: bold; text-decoration: none;">ANOVA </ins>Calculations in Multiple Linear Regression}}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The sum of squares for the analysis of variance in multiple linear regression is obtained using the same relations as those in simple linear regression, except that the matrix notation is preferred in the case of multiple linear regression. In the case of both the simple and multiple linear regression models, once the observed and fitted values are available, the sum of squares are calculated in an identical manner. The difference between the two models lies in the way the fitted values are obtained. In a simple linear regression model, the fitted values are obtained from a model having only one predictor variable. In multiple linear regression analysis, the model used to obtained the fitted values contains more than one predictor variable.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The sum of squares for the analysis of variance in multiple linear regression is obtained using the same relations as those in simple linear regression, except that the matrix notation is preferred in the case of multiple linear regression. In the case of both the simple and multiple linear regression models, once the observed and fitted values are available, the sum of squares are calculated in an identical manner. The difference between the two models lies in the way the fitted values are obtained. In a simple linear regression model, the fitted values are obtained from a model having only one predictor variable. In multiple linear regression analysis, the model used to obtained the fitted values contains more than one predictor variable.</div></td></tr>
</table>
Chris Kahn
https://www.reliawiki.com/index.php?title=ANOVA_Calculations_in_Multiple_Linear_Regression&diff=37073&oldid=prev
Chris Kahn at 20:14, 30 January 2013
2013-01-30T20:14:46Z
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The sum of squares for the analysis of variance in multiple linear regression is obtained using the same relations as those in simple linear regression, except that the matrix notation is preferred in the case of multiple linear regression. In the case of both the simple and multiple linear regression models, once the observed and fitted values are available, the sum of squares are calculated in an identical manner. The difference between the two models lies in the way the fitted values are obtained. In a simple linear regression model, the fitted values are obtained from a model having only one predictor variable. In multiple linear regression analysis, the model used to obtained the fitted values contains more than one predictor variable.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The sum of squares for the analysis of variance in multiple linear regression is obtained using the same relations as those in simple linear regression, except that the matrix notation is preferred in the case of multiple linear regression. In the case of both the simple and multiple linear regression models, once the observed and fitted values are available, the sum of squares are calculated in an identical manner. The difference between the two models lies in the way the fitted values are obtained. In a simple linear regression model, the fitted values are obtained from a model having only one predictor variable. In multiple linear regression analysis, the model used to obtained the fitted values contains more than one predictor variable.</div></td></tr>
</table>
Chris Kahn
https://www.reliawiki.com/index.php?title=ANOVA_Calculations_in_Multiple_Linear_Regression&diff=36663&oldid=prev
Chris Kahn: /* Mean Squares */
2012-10-30T15:40:56Z
<p><span class="autocomment">Mean Squares</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:40, 30 October 2012</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>MS_E=\frac{SS_E}{n-(k+1)}\,\!</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">::</ins><math>MS_E=\frac{SS_E}{n-(k+1)}\,\!</math></div></td></tr>
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Chris Kahn
https://www.reliawiki.com/index.php?title=ANOVA_Calculations_in_Multiple_Linear_Regression&diff=36662&oldid=prev
Chris Kahn: /* Model Sum of Squares */
2012-10-30T15:39:14Z
<p><span class="autocomment">Model Sum of Squares</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:39, 30 October 2012</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align}SS_R= & \sum_{i=1}^n \hat{y}_i^2-\frac{\left(\sum_{i=1}^n y_i\right)^2}{n} \\</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align}SS_R= & \sum_{i=1}^n \hat{y}_i^2-\frac{\left(\sum_{i=1}^n y_i\right)^2}{n} \\</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>= & \hat{y}'\hat{y}-\frac{1}{n} y'Jy \\</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>= & \hat{y}'\hat{y}-<ins style="font-weight: bold; text-decoration: none;">(</ins>\frac{1}{n}<ins style="font-weight: bold; text-decoration: none;">)</ins>y'Jy \\</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>& y'[H-\frac{1}{n}J]y\end{align}\,\!</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>& y'[H-<ins style="font-weight: bold; text-decoration: none;">(</ins>\frac{1}{n}<ins style="font-weight: bold; text-decoration: none;">)</ins>J]y\end{align}\,\!</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>
Chris Kahn
https://www.reliawiki.com/index.php?title=ANOVA_Calculations_in_Multiple_Linear_Regression&diff=36661&oldid=prev
Chris Kahn: /* Mean Squares */
2012-10-30T15:16:56Z
<p><span class="autocomment">Mean Squares</span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>MS_E=\frac{SS_E}{n-(k+1)}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>MS_E=\frac{SS_E}{n-(k+1)}<ins style="font-weight: bold; text-decoration: none;">\,\!</math></ins></div></td></tr>
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</table>
Chris Kahn
https://www.reliawiki.com/index.php?title=ANOVA_Calculations_in_Multiple_Linear_Regression&diff=36660&oldid=prev
Chris Kahn at 15:16, 30 October 2012
2012-10-30T15:16:33Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:16, 30 October 2012</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The number of degrees of freedom associated with the error sum of squares is <math>n-(k+1)\,\!</math>, as there are <math>n\,\!</math> observations in all, but <math>k+1\,\!</math> degrees of freedom are lost in obtaining the estimates of <math>\beta_0\,\!</math>, <math>\beta_1\,\!</math>, <math>\beta_2\,\!</math>...<math>\beta_k\,\!</math> to calculate the predicted values, <math>\hat{y}_{i}\,\!</math>. The error mean square is:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The number of degrees of freedom associated with the error sum of squares is <math>n-(k+1)\,\!</math>, as there are <math>n\,\!</math> observations in all, but <math>k+1\,\!</math> degrees of freedom are lost in obtaining the estimates of <math>\beta_0\,\!</math>, <math>\beta_1\,\!</math>, <math>\beta_2\,\!</math>...<math>\beta_k\,\!</math> to calculate the predicted values, <math>\hat{y}_{i}\,\!</math>. The error mean square is:</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><math>MS_E=\frac{SS_E}{n-(k+1)}</ins></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>
Chris Kahn
https://www.reliawiki.com/index.php?title=ANOVA_Calculations_in_Multiple_Linear_Regression&diff=36659&oldid=prev
Chris Kahn at 23:58, 29 October 2012
2012-10-29T23:58:48Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:58, 29 October 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l40">Line 40:</td>
<td colspan="2" class="diff-lineno">Line 40:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align}SS_R= & \sum_{i=1}^n \hat{y}_i^2-\frac{\left(\sum_{i=1}^n y_i\right)^2}{n} \\</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align}SS_R= & \sum_{i=1}^n \hat{y}_i^2-\frac{\left(\sum_{i=1}^n y_i\right)^2}{n} \\</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>= & \hat{y}'\hat-\frac{1}{n} y'Jy \\</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>= & \hat{y}'\hat<ins style="font-weight: bold; text-decoration: none;">{y}</ins>-\frac{1}{n} y'Jy \\</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>& y'[H-\frac{1}{n}J]y\end{align}\,\!</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>& y'[H-\frac{1}{n}J]y\end{align}\,\!</math></div></td></tr>
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</table>
Chris Kahn
https://www.reliawiki.com/index.php?title=ANOVA_Calculations_in_Multiple_Linear_Regression&diff=36658&oldid=prev
Chris Kahn at 23:58, 29 October 2012
2012-10-29T23:58:02Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:58, 29 October 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l31">Line 31:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>where '''I''' is the identity matrix of order .</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>where '''I''' is the identity matrix of order <ins style="font-weight: bold; text-decoration: none;"><math>n\,\!</math></ins>.</div></td></tr>
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</table>
Chris Kahn
https://www.reliawiki.com/index.php?title=ANOVA_Calculations_in_Multiple_Linear_Regression&diff=36657&oldid=prev
Chris Kahn at 23:56, 29 October 2012
2012-10-29T23:56:46Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:56, 29 October 2012</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\frac{\left(\sum_{i=1}^n y_i\right)^2}{n}=(\frac{1}{n} y'Jy\,\!</math></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\frac{\left(\sum_{i=1}^n y_i\right)^2}{n}=(\frac{1}{n}<ins style="font-weight: bold; text-decoration: none;">) </ins>y'Jy\,\!</math></div></td></tr>
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</table>
Chris Kahn