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Lecture_Materials_2023/Lecture_16_OLS_Regression/lecture_16_ols_regression.html

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<meta name="author" content="Tom Hanna">
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<meta name="dcterms.date" content="2023-11-14">
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<title>quarto-input3a4dad63</title>
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<title>quarto-inputa04e0acb</title>
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<meta name="apple-mobile-web-app-capable" content="yes">
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<meta name="apple-mobile-web-app-status-bar-style" content="black-translucent">
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<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no, minimal-ui">
@@ -1289,9 +1289,10 @@ <h3 id="the-assumptions-of-linear-regression">The Assumptions of Linear Regressi
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<ol type="1">
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<li><p>Linearity - X and Y have a linear relationship.</p></li>
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<li><p>Normality - For any value of X, Y is normally distributed.</p>
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<pre><code> + We&#39;re in a random world
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+ So, X won&#39;t predict Y with precision
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+ X should predict Y according to a random, normal distribution</code></pre></li>
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<pre><code> - We&#39;re in a random world
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- So, X won&#39;t predict Y with precision
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- X should predict Y according to a random, normal distribution
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- The residuals are normally distributed</code></pre></li>
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</ol>
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</section>
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<section id="the-assumptions-of-linear-regression-1" class="slide level2">
@@ -1387,6 +1388,13 @@ <h2>Don’t Panic</h2>
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<figcaption>correlation coefficient formula</figcaption>
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</figure>
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</div>
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<p>## Authorship, License, Credits</p>
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<ul>
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<li><p>Author: Tom Hanna</p></li>
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<li><p>Website: <a href="https://tom-hanna.org/">tomhanna.me</a></p></li>
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<li><p>License: This work is licensed under a <a href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.</a></p></li>
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</ul>
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<p><a href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img data-src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAfCAMAAABUFvrSAAAAIGNIUk0AAHolAACAgwAA+f8AAIDpAAB1MAAA6mAAADqYAAAXb5JfxUYAAAAEZ0FNQQAAsY58+1GTAAAAAXNSR0IB2cksfwAAAf5QTFRF////////////////8fHx7+/v6Ofn4+Pj4N/g39/f1tXV09bS0tXS0tXR0dTR0dTQ0NTQ0NPPz9PPztLOztHNzdHNzdHMz8/PzdDMzNDMzNDLzM/Ly8/Ly8/Ky87Kys3Jyc3Jyc3Iy8rLyMzIyMzHx8vHxsrGycjIxsrFxcnFyMfHxcnExMnExMjDw8jDxMfDw8fCwsfCwcXAwMXAwMW/wMS/v8S+v8O+vsO+vsK9vcK9vcK8v7+/vMG8vMG7vMC8u8C7u8C6ur+6ur+5ub65ub64uL23t7y2urm5tru1tbq0tLqztLmzs7iysrixtbW1srexsbewsLavsLWvr7Wur7SusLOvrrStrrOtr7KvrbOsrLKrr6+vq7GqrKurpqqmo6ijoqaho6Ghn6OenqCdn5+fnp2dn5aampiZlpmWlZmUmJaXk5iTkZSRkZORkY+Pj4+PiYyJjIqLjoeLh4aHhIaEhIWEgoWChIGCf4F+gICAfX98fH98fnt8en15eXx5eHV2dnN0dXJzcHJvcHBwbmxsaGVmY19hYGBgXV5dWldYUFFQUFBQQ0RDQEBAPj8+Pzs8Pzc5NTY1MjMxMjExMDAwMS0uLS0tKioqKSopKSkpKCkoKCgoKicnKCUmJCQkIx8gICAgHxscGxsbGRkZEBAQDg4ODQ4NDQwNAAAA4LK4NQAAAAN0Uk5TAAoO5yEBUwAAA+1JREFUeNq1lot3GkUUxlcviEDS7bYbKxC2oaWKSUmRpkkrSBvzIMGkJjGamoSobROtNqRVWyOppli0NBBSHxst+JiYUvr9l57dheVx8ESpncOeOfvbnW92vjv3DtyzeCqN44BIeCh02t/tcXdIDpvN4Tzs9nj9faHBcGR88u2Z2dm56H9vAIdIeCBwyudxOUWBb7FaW/YJYrvL4+sJDCjK0zOzc00pcwgPBE56j0kif3OzqCyiuHmDP+h0H/e/NhCOnJ+avjA7t55THuTWK+P2JOAwFDjpdduF2G7FoN1lwebq8gcGw2MTUzOf5IFsMpkF8le1UVf3JuAQOuV12/g0gEIqHgzGUwUA6RMvuI73hIZGxyc/fISMmYjInMEjddSlf0HA4bTvmF3RLcSNpLXFApA/YXP7+vqHIxM5pIgIUB4grwzKq2Rlo46YOjtNOgEHv0cS0oBsJr0ZZSAtOD3+wNDoGjKWsjBlsB6NruPnj4lWHj5OmHSSsdBFxhgbKRFFuPuoGANkI1Gt8vJBl7e3P/wAVTOakYtGc/iD3f8e8S+woBMzdbIf7iYYW9GIIuxx8rsoHKKaZixgl2/3+F8fQla5T0FdPmURjSL77W3GWMJkqRAyfMQ+J1pi2xpRhN1tN4E41bVF4Ibo9p0ZQJJUJzQvkopMkqgzASBhqRDDn+w3IhNjz6lEEe44sImCkSiYyWbjWneNiArYFA57e/sbCxOZEtuMbYzo5K1fgqrw87qwxBeVZQbVHZydV7uUsvjiPmdXz7lGVhCRYYksSrTul8nIxZeJFhirWOFoBa4RydgxB3cWZcjm+Z1F1YsWh8cf+lULnvbBeqhog21vI7Hw9V9lssTY6urv7NNK8OxWIKiMjGsCJbuDgNX2kj/0FTJUv90yRKbVh49XDNVkVVnAd4bKdttDePhBJUGS1Qny2UYdObKwYNFJjRXGQztxGbLSVawYfr/ZlC4FrxQ1PXhJFHmpq+fc8Jsf5AA5lZQrJedSfk+ibrc0CqRvt/ms2tEONoUOb+8b4bHJd75pqmy622KqF40S5NUzg6PjUzNNHCLg8Iqa0uZ/SunI+WaFu4+KlxsVoZjo6u7rD49NTF+Ya0oYtyThHiBXlSGzWjalL5/omAZwx7G/utAb4wXgR95+C08qjDXb/nt1RxP/4hX9HS0/oF0a0S4i1L1EtcJYcwiXqw/TmGC/UjWm9KMqldJ9zVQ1QBPGHUnkY+Xjf5kXpWofymWzeiqqmag8F1G9MH56z9l2gG+1Wlt5QWx/d6tmTJ0RZRuohtUtgdP51vWzksNud0hnr2/VxqHRF9d7XI5DA+H/+1/hM09J92+7pmyRGJsTpgAAAABJRU5ErkJggg==" alt="Creative Commons License"></a></p>
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<p><img 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" 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<p>POLS3316, Fall 2023, Instructor: Tom Hanna</p>
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rsconnect

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