130 lines
73 KiB
HTML
130 lines
73 KiB
HTML
<!--
|
|
title: 5
|
|
description:
|
|
published: true
|
|
date: 2026-02-11T14:43:25.309Z
|
|
tags:
|
|
editor: ckeditor
|
|
dateCreated: 2026-02-11T14:42:59.270Z
|
|
-->
|
|
|
|
<h2><span style="font-family:Arial, Helvetica, sans-serif;">General</span></h2>
|
|
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Simple Linear Regression</span></h3>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Normal equations</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAN8AAAApCAMAAACC7AwaAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjpmOjqQOmaQOma2OpDbZgAAZjoAZjo6ZjpmZjqQZma2ZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kGZmkJBmkNvbkNv/tmYAtmY6tpA6trZmtraQttv/tv//25A625Bm27Zm27aQ29uQ2//b2////7Zm/9uQ/9u2//+2///bHPl2IgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADXUlEQVRoQ+2ZW3ObMBCFJadpaHPBTdvYNL3gpglpWgvD//9xlTABtHsMQt7M9CF6yEwS/LFndXa1YKVe12sG/uMMGA3X4odEzNLwGF6u9cmDL6b+qWX0KWl4BK9KtT6jm5UL6ZOGx/DKROs1EWiE9ClpeAyv0MyO5TuR+rNZk4ZH8OpM69OtRD8BDGl4DM+5+uqF9ClpeAzP9V1agmJ6peExPOtqekiI6XMlKAqP4DlXs0NCSqE0PIS3u9X6zeBYj3F1sH5p+DSvzm7ULh3umHW11JnHdR8Bt2bkrS+Ml3uOjHB18AYeU4KPqPOFBFulXssMcXW4IHLlDDgdLQrUm0J4G7LvaPSJFkQ/GA6n+nI4ekzzNpc0hjBXR0oOhhN9dYb7+hSPy1PuaYYla+PabJ3Z3vM7WayUG0fGZ7ndB63P787ZvDcO77NG9JXJulx6rb69FPD6WJWxQVYfSRDW1bSHPq7K5Kr+Yqft8tPfzCmzv7d3sEXerc7rJjnb2nbCe94ofGAKos8svn3emu6e/YWc18faDIVgs0zCi7nO3m7aRlQ49WZ0FqlSlwODet4E/Dlyoi/Xto4q7yhrrwS8QayojBobstXcoVlN2MXoJF40yppEsBY6Dncf44aoM5dOpA8G28eK9CFbWVVdXM6a1TV5meGB9uEo1POm4Hj/qtSls6+J/m6QN/pcbuAIWi07s7k0Fv2hCdK9t2eZ8J43Ccf69k4HfoC8Qax8/6oUVtbme9+h89M/7FTxQI2++jZhD1sB8Bbk11+jbJ81ciMU7DBWXmdw/rTllp88tLtWLN6PuVPZg+Tkvv56p9dPJA/4hZUHR/psk1yp3ZJrgTyE62RCPxeLG2c397NrMKhyu7/Zs+ri3trk0k94CBzpq65/LbW+YIcp4pFYSZioZpgSM+7Og8qD4NCfGDmHtyccqA8fX/KpZHQzn/8ZBA8izQjW5+WT71/y9VOkPDv3yb7cmc/Dh9MwBbbSSU0FJ3waHoxqLpzPK5MXe//p2pMsfD5Puj4CTqp5Oza8OiJY7udDT10RYUnD5/OAn+HAHiEOFstR8PnBIj/jaTFCoDR8Pg/5ebcU+j5CGh7Bs8/5aMl83yINn88bPuQMdYqcyNLwCJ794gEuCX3uLaUkPIL3D8KzV9UAmPpuAAAAAElFTkSuQmCC"></figure>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Least-squares calculations</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Solution for normal equations</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Standard error of estimate</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Test Statistic for inferences concerning β</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Or it can be written as</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Confidence interval for regression coefficient β</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Confidence interval for the mean of y when x = x0</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARMAAABHCAYAAAAkwaPtAAAAAXNSR0IArs4c6QAAAAlwSFlzAAASdAAAEnQB3mYfeAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABKqSURBVHhe7V2/bypZlj6FJnfnhEuxksepW3pFx+uhHAwTDAEJmzzYzNVSkyH87GEiRmo80cAEKxJa42QdtKEdb0MwpIylBm/48vYf8Lj7nVsUxvwwVUAVBb5IM+pnqm6de+6tj3PPj+/85urqitRHaUBpQGlgUw38ZtMB1P1KA0oDSgOsAQUmah8oDSgNbEUDCky2okY1iNKA0oACE7UHlAaUBraiAQUmW1GjGsSLBkqlU5HXTKp7uUldG3oNKDAJ/RIdoIBPA+pTjlqiRr3ra+0AZ/gup6TA5F0uu5q00sD2NaDAZPs6VSO60YBxTDqu67m5Vl2zFxpQYLIXy3RgQg4fqUvHBzYpNR0FJmoPKA0oDWxFAwpMtqJGNYgXDTwN+kQnKWoq56sXtYX+WgUmoV8iJaDSwH5oQIHJfqzTwUlpHMP9+qzcr4e0sApMDmk192Quw8cuKf/rniyWBzEVmHhQlrr0/WmglDkVN5Uy3VKaGrWLg/XzZL56GGX/caIVGwVKxmKR6+trMbva0MUIutCsOn4M+GPk6P7nGpkayesVmLy/92OnMy6VMuImcQn/ayz0SSal088ioT/QSatBZ72mBofxTnXn58Obv55FOo2vR/lsXCuf/Djq1kuRq6sXQMG6jW6+iWuPf/wFYugRMWx/ycfPtfP/+j1R3SSmRVJg4ucKqbE9a8CxBCwq0lW0t7NUewYSzaxTriUo2tvvlH+2OuIXXW3O1JDWRZUGnQtOIGTrIlLr3I/ykXONqr+MLq0XQLm+bkboPz5R9PkHCRzXTYqkPorR34km4yow8bzd1Q2ba8CgWf+rAyKafmkPn9v8KeuOYBciXuI9G+49kLAO2Or4dHW2RB3P9MOUxXV93YvU7j+OIuf/qVUHP48sHYCy6MhTOgXoaNrHH5NUr2FoGG0KTNbdceq+NTUwpFn/aylzJBLZOyo2GiRqQ9p1RfHTTRkVzQZVz2P03Fxzmvt8W7JA3xtxsv7SlkcYWsDs2s6Xqf/9gLrn2uQ4pMBknxf9QGS/bj5rZ2dR6jWblIRVsMtpOT4dNv+BJfQesYSPNJn0h9G3F3/Wvh8k56yT088PozIVta4Ve+VXUWCyy537Hp8t6QdOKLz+V9tyolx8aeQGL5MwOaKBaEarY9Mo2CCkk9WFRTPswKIJh5/la7z4yXpXc2SFnRER9PTlJhHXrO4Hqg46ZOk0d5SJ6SfwhtTpccj+1peNOgGSevIVkPAVCkze4wut5rxcAxLsgBNLkuoyR59F5RTHscI9JXSLyjcF6kggyRI1BF0BRAAkodBw5qvPI8iqSVnjLOt3JC60kS3riChGkWf4Qxb2p9B/i4MeUX/4BFABmuAiOKVHkYe09svPSdLZT0Lwm3wz0Ar/e0ExhIcVmIRi2ZUQ+6KB5nNUi/Zw+ElmRNqwyHq8p3b+lh6LHYqGxBpxdNn8NRoZyzpKf/hWsx5bE1nrbI1MhX5X6R9OaThcP2lCCIpHLL4caMSoW6XvxjcrMFmlRfX9djXA9AMHwGUCv4J2ekKC6vjFz7WQh7KdY03m6EHo1jgpzIXmjSqcoJb+JjCwD+TrEzGCrBrL2jXZaXrlyTfFUZ7op08LfLGIBv3JtsQUmLhYMHWJ0sAiDSRTiF/X+5QuJOEjWVxnxMeirFUHfwu7WKors2ibz2fa1dIw7gIpkPdx5qKP3u/+kIMLBLJ+l6RuDTjiQwKeAhP1ngSqgdDTD8TicA8DI+B5RIBp6UfmoiCTlz/spFx0qZ34RtQaCkpSm/K6CV9mHMl4gaqcSiVktiaSMrns8Qn/H0cu4CoAGv5LAuBHPUZdvtGFG0iBSbDrqp4Weg3odCw9jwPK1EpiGecK51kcN4ZUzSKCc9eeAwgnusOJbz34UthuKVQNUbfu6FTURJBE2j/l/zSWFbkjdz9BEiDcCjR5GsINLezkQrcfBSZuNaWuC0YD42jKqpfZL2HYF5JJG8Kybun+6WLhY9ivkT1CvU7T8ZvYAKHfJKgShyNW+k/GIeb0yxCxONs8fRogQBLURxbwHTW0rh6LtHPiC9XvtNZIjPS/2rIiJ23O32LX4cDZmvuRrPhLUtoqmRWYrNKQ+n6rGmD6gdmwq/wVz2fptt+ly3E2PbyKpGsWGYYhTtIN1IQ0A6vTiV0UKWeZZFVeWxy2c5TocxVAMpYnWaiSASesqaF5B/4+W8dzEt9NQaNdj0May+okl/0uc0PG3y/IjNiyLgISudjtCn3LOSj/nSRrnCrvZhMoMHGjJXWNrxpga4CiZ/BR4H+LSkgCzmlH5EKrtXKibpr0uSWEAxC2cxSqmJJHZu/ij1LsBXL2YYa8dpGcUBD4Ytfj2DJJmfG5bv4aOcMfHVmdv08vrhMC/vDRm1XCYywEk33gcJgOofG51Pml8HPXS/P29gQ1JAVO/Q7sl9LPOQU59j7RD1z3opoAoCTMBDyoDQCK1/W2fS/TjlzpfDbSoW3xUcqwoxY2FoCkWzc95aEsBJN94XDgX4lh9QRmZ52CMiX5mZ0GvPhwuvVPWuJszRJ5Wdimg24nJGnX/JK3bypUvkUIc5LiYOCIwcCJdPGQJWMFBYAMKJ1hQbQrWSpTWnghR3rxvcCfMqyJZOyJmMfFwJEtjETanC2byP4PyJEGVGNypOg8OdIqvb+yTILkcNjOC8WJzzlKJcGzExCd6HUTJnCnJXvlPlSHIgiLaNUibvL9q5qSFiw8/AJLcMnrZNbhMMSRf98+29lbztFgfASjZwYBT6qIXTSo9ZglU7eNWAMJY42LGMbxNEwgF3O2LB8xudhy3VdpAib7yOEguUR3YDY6Z2rNzLJ1IXZR1DXJYdi0Xy+cbZxwmWuhOG2cxcm/qqVCVRjA6u123eMIxzyXSSBvyw4e4viCXpLQegCSdV/VHUzA4yMnYLJvHA6TUvGT5dWdHnXh7XJwPlQN5BjMePy9DbLe1ezTyjOJEOoiNn3Z5TkeJV2zdW02LQBK8D3+Gq83I3XXIWhAgolbDge5ibMgjhkfrA1s5mLxkcrlY2qA+i3Qs+DTPd3yL2oxSSV9ALksyCVtyUlZuLNAfpSMv5yJy3QUkHXiHElAAmZ/xuFT/JfYzAndDRAUg4lmHMLLuW9zGFsmqzkcbMfsJXVx7ht2khI4Mke3QjeRN4BoSqBAwlqW/WoNSg/ylB+kqNARVGvnKQHeTi4LdyKMfpaM20lINudDEBnS0mxGIYYoLuAnnQpLymgcQN9i0Ae4VuFEjVc0MvtVrN1r0HdyKupIOnjIVT05GT1v9nFCWsrzjeqGfdCADSYrOBwcf0oXlsiwZgMJ32a/TN3AoinTCm3f1eU/bx+LyE/ogTm8BwsrJU7wck+H43wtGdePbc6HuVyCF0kXVYE6iVld2zH3qnrTjYVhH00WO57ttTKpX7VBn27ylK3kgXmw2MS89Sj9P2IojpnYB8lXev2WyX124gfahxdGybhcA66S1mx/Ch8pXm/GZeft2cdt+4WaHMvwQhUBbj0XTi2/SsZXba5FVaBvRhtWJGi9HEkX5yu08ybVGfQvbNAvnZLoInzOLOvL6kEci2cIi0eHZWfpeQCPD/UjC+gHLi8vPZXCo3T+VX7PNveWV1lWrf17+34lmEy/uLMhWDuasporc9svlFP3YFSRPDbd/HqFheVHyXjwG8Y+khrV87mjpW2VcGRmxgLB0dRNu4Ym8iqGKEbj3J3po6Kfc5wFB6/P2ube2lQWr7If2vUrwWRSsDRDaGP/urK5soNoSvvOtpRm8pKf7m+lH2URq/g+lYy/ucmWzP3luAo/0riNr+OwRccr1/s2dp4mwwM5j+uBnQt3FX3zLKi6wasGbDBxyeHgDO4UZvG/c0FmjI0FWHS8cvw6yywlX0rGpRN4HtS8LoKX6988Wsp17EqHcE0mnlWI0vDqPCJiB/C/GZ4jl8ROC5d5Knep+UZXS+bkrLnTGtKAT+bs2VuTLFt298DmRS/q2t1rYGyZvMXhMP6u+0jMLWtvqgrFU9i2iMWyCzZzeiSyd3HpCPV7Si/HLialsYuoZMg6AV8BfCitBSFqv0rG3fqMtq+TKcDgNHhC9ApVrOxMTeGYYqL5a51D5IjiXAzzZKECNkHM8oXsy3HOlHRgg3nrCHUnDsDwOiZMxJ1njkU2UKOEgJ26IkkxRM00E31u/PCrbF9ZasSANCDB5C0OB5kN2aiKR+RxmDpaE4F6rliooblxm3IGIifYuH1OE5ZRniCy++AzYNBoHdNdWafLLgmOjrBcs2FPP0vGJ6CGuQeZAStDubcATgYMHOmMXNEGiXGKdm+K9g81NUiNjqJqVJaPvk5AO86h9qZPlinZb6QT9NIwgCN2Sv30/pNOXczzii2RJxI3ZQAR/u2V4GcR/UBA+1w9JgANTHwmyzgcJNggGzKK/AabmvKZC79k/v7L34JLE+Zf3yg3bOo9Tz3flms2W9PXknGZhg7/TGM5/+ey9bPL1s8YhDwvsT1/Zy349vV03wPLOje+Oput+Wfm9amP49Rldi5gtrh8AOCkYaHIaFEQPx6eVbRXN6wqsjTRjmJRe84wTnICJss4HPwSepMXyh+Z3JeMT+qYXFgl3tnGg6FTcK1DGSGbaSz1vB6A8TODqPAO395arO2VRZb/5nqVQnHhq2jO5hwOoZjTWkK4LRl3/DN8tHPjI/LONh6yhpQTp+6UfwrZtccNb13rJsfC1FrLc5g3rSqyxGHTJZdzKPQzFxrehMMhFDPaQIhVJeOcmp/IfgbHxxANl7yS5WwgmMtb3SZdecmnYIu1UM2JLHwr8JSIhwf4zAAk75XjxOVSuLrs0IosF+aZXPOLwhR6a3A4uNJiSC9aVTLOqfkO50MYp+AFJLzIL+ftUBOOfWZe7revXUw/MPEZyN4y9nHqAkRCbXDCyn6+/LcpegTvzw37HUEWWfqrCxdJa/4KoEZ/3xp4usnSXbxBneGx7N3L4f6bClIPCh0SNfSaQZ2RVb5BpG5524l91WCgRZYBKEmBSQBKVo9wNDBPP8A+JdkPVz+S4el+uUKpDqgiUSaRRH6LvPNAs2YPrchSgckBvukOIbiTrbqI4yXwaa+gH7BLIbiY1AYSKd+KWqvA5+DDAwMrsvRB9tkhFZgEoOQgH+GEGx/TQySrIeFQsrKZZOY5dT5ISbw9SxaNztIqjDlrFtVaeRs9/Ffvoshy21pRYLJtje54POeXDk2rpCRMgI3+2sJmf9nhZwH9gCPNSzZx6lVWrc1Zkwukz8wONTN5tO9Flj5PUoGJzwre9fAvtAQBUvh7nfSYgtNwyp1x/zKA8Tp0GK/3UmRZynw1SsQvtO4Hm440iXoG7n5ooXNAa4R//98NJeIWLfseVReBZdAqMAnjbtuiTFwt3ecmZWPm+S0O7X2oZY7UhZXKYypRVJLaNJR3FB87Zr0/OFx3uC2ylD1/8/daY9SiSsSku/bfiO5QCV5ooGzzHu1TOfJFtPz7YJPeFJiEa59tVRom0i4TaC0D7NO7bAJv0Q84x5lpNgtZAZ0zBHPTan27AtprYeFWlbnNwVwWWeLIGuGyeK6B+sNHGiXNbzSYJ1TXudn4s2he4yj75vfea782maYCk020F+J7J0ASAC3EpmroRa9kD1+AxauhelHu7WtTg3Nx6aF83BZZTs839luDNPSI+g6n1RoC5rMdSFZ9H4TuFJgEoeWAnyHP5A/pcRcBJtpmvpcBGPz9bUfCfCiV8iPqdmpztAyKfmD9TcB+E7hJtA/gFHoCkMQROB/3IpeDrvp+/Sd7u1OBiTd9hf7qCeMcJNU1i+WVfC/MQFfwSXqnn1L2Ab0KuL1GJdxhaJ/UsPVhuf/vvZnS8vAXpTpFIvab/PQ3Gg7+OrrPlOj8Pk/35yla9r0VMH2BApOtb4HdDij5TnBmmP7lsiXy3ivXy0xSKP6rgTCL09/r9cWNyYKgH/Aic9ivffoXOgX8g6S/yASUgOz7S9yMaP3qgLrwm/x7rv7FuiVt2fdXV96bj2+iEwUmm2hP3Ss1wLksTNLEVEm1Vk7UuV1G9qWeRtEPrLdR/hm9inCiIfuL+MehSWeRT+xDev6Be7HRP+nt79d76vp3KTBZX3fqzkUakD2YASZoXVppXwTS6VAtRDg0oMAkHOtwMFJIzuBiTliwTurjal8U2bDTZq45+sFMWk1EakCBidoIW9cAE2y1kMJvot0oWye1pJ2Adrz1J6kBw6QBBSZhWo0DkiVZqJIBMKmbeUqJFGY2Tz9wQNNVU1GWidoDfmmASZ2L0jpBq1H0TecPQ4r6HK4GlGVyuGu785k51kkXgMLVv+pz2BpQYHLY67vT2bF10pCN0LnT+jFxuy/VaWenS+LrwxWY+KpeNfiE51Sp4uA18P9ESkMTTYqihgAAAABJRU5ErkJggg=="></figure>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Coefficient of correlation</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p> </p>
|
|
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Multiple Regression</span></h3>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Estimated Equation</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASAAAAAaCAYAAAAXFYH/AAAAAXNSR0IArs4c6QAAAAlwSFlzAAASdAAAEnQB3mYfeAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAwpSURBVHhe7V0xcxpZEu6ZUi7npAyBVylbpZHjxaBgdcESkLCJwZec5qpMdC5kWG2krTJytOBgTYJrdcHaVSewLj2Bq06prCsLUuXmB2jeff3ejARIwAwegbSaSVyCR093v+6e7q/7jZdKpRKFV6iBUAOhBhahgaVF3DS8Z6iBUAOhBlgDYQAK7SDUQKiBhWkgDEALU31441ADoQbCABTaQKiBUAML08CdCkDFTFzksymqdRx9mTmq1KvUb5S1hWlwzI3vEq9B6+4+yx60LoOmV8x8a+ezSW3Uh6wo6aVyWQR9v2n0rg1AmfiyyKYsYj83K11K9BsLd/Bi/EysGVtElSZ120mKUo9aeYNSBlFTVMVR+fYEobvE6zQD8fv9fZbdr67mvb747Zm9ZiS1YR+KKR+yq3aqWJx7EBoKQMViRrTyWTIOVsBjl9pGl/JZg7aoIrrtTWosyMmLRWQ+2hZ1ck0q9Y+0RvlI7l1xIyeodkynveC2sphZRqDbo3S3PVNmNU9eg5MauvxKueV+zHGfbpvsQfIzSquYeWCvxX7X0p/bZBmzZSrFIjIfPamxD5GV0hv9ksx2in95Ymu1Y036EALRvK+LAMTBZ3ctSyfP69StRmWwYT+PJErUjZ+I7Nou1dtFsYgg1NvdphqZVCkkERRU8OGrd3o8b31Nvd9d4nWqMD4X3GfZfapq7st7r36i1wI+9CxJVhWxp1y+FT50EYDKZZRZiQRFjho04OOSycZRREsk+hyU5q44FRhRepkVWo+CF4cD9cRGkYiIflswoLvEa9AbeZ9lD1qXQdPD3ti7ay80Yb6U5dYmbsCerDKrjibgQ1ZM0zGUvBgMKAN8JZuqAfMx4c91DkIS81EpNUBf/gMBYDFlWJdOGIzKxWRWxobea+2QxIOguG41ic8vs6KgN88fvWB5jZ8diBSjhQDbm+0qMc6lHN0gq4On2Yxloj+ZvK6+z7J71dGi1vXo5CNiy5MYxTRNF6J7Dp/XBn0oiqyo7CPBgG3a6zUEL9jm/mGVUhrpqEnOdx/FNKu9SpXTQ5SLCGpTgO0lziTyO3GqiwLts2Fv7yPQqFKrXD7Sqt2KODYsovT6RAwos3wgDMttT01XtGdwu/VOBsDcRpKKxqlY0wzqsEN2BR2h+3V7gg+YDJDXzPKZ2InXSRT2EWwt2t4tUNspk7FZVILsyPymK3peK+6z7PPS8az3+fAHyi/2ocdULVTsNR0+tKp8KIXuF3zdV+aTeXBmwzY1G7b5KGbRz6+eUXJTs189yhL9dg4sSdP7oOnlkNdSudHXIpEjmUVk0qawrD3a73GS5lzdE2RGYHYziifweA00+gmtVEp4V1HfLaYm/0ThPCY9ROrIvLZFF0A5ul+QFVnBrep+Bclrox/RuBymZEakTYusk310/faA0bUpcgvHDu6r7LLrh+oB6ehQt3jS5xrW55oClcZ8OrcXexPVSItu6sJeP2/lY5rjQ767X40vEd2xTfsH8++addJUtvmPQ6p5yHoGPX6oCxaNreC7Gp10AT47q5h5s1KX6b/36BLcyq6qvygG/IcLLcaqitWmyKE0TOU3qOQyOsMtr8vatlDZ8dUxpLhDT4ZpWdtN8MryxlfARw1ZEErORABGG7TcrKj7Kjv7h8z79/aHmjStdwxp4IIzJQZslD/nq/auda3tTtybmLRJ2zFRScesnFLHMoDfjM9iep86MCDlQ3zBpnT4kJ1DV4x9iGopohkOpTOd+DcCXTRL+zm3T50U40j+sqnhOSDjIXINomP05FhnEgNaO6Pn7cnZzwy+7+knCoPi+LMxEgANeqgYpUz1sjPHZUvWUhtv5ipUr04eHbgua5vYjp6QtfnllRWgsDei50LhO+OUktzIwUiOKT3SBRxd75VekHIzD35k5yHF3Z1tstxJuAF86zr5p8nul17QsvND22SLG4EomG+zhmDDqXv/EqNU8iADAqRAR1exy+v5m9CG778lNKrHXqr9Thr7UEofBJqj9HAVJgcfOhXCBpc6MCBfpRjfVMrzGraJ7lqnytHNk2tfLBoOQNEYyRzIidrcVkX08ZT93AgG1DslWYCNbCKetwqY5iDkXJzyIimSdW2SWpQ3UhhriH1VhuRLlX54Zdwtu0fZg44sbydd6iGgnnmDmengbySO55GeL5m8LvYouwugn6S7eOAik+XJduzTuEx2mux+6XkVx8+6MneIOXsYeThN+ly+AmcSnuGHgWlrL/YmClvj+OJGCAeYXp1GYFJwi9v5R+iuCSFtc5Y5oqEAxKAzApqocWZRwDT0znPUtd5KrxvBgCT+hG4P+u9D++sAnqbz1HENkUskBqb5uVKomKJmvaP4vKakPfKqtnOdChjsjLbyxEFz0tXKb9PDepcqGAi1xqTtfujNbm4TfulHdjyuI85mlhuOvY0hPU12NTrind6NyH7bifY+0UfM/7xE/73j9t+ZZweYNtMpdMYInbHe+fLZgcaZaW7/lKqxJoaQLRx7Qmd8v44qLXqloyX3580pbDNG1vsWzJBLuUuFyPb/0x81q9qWNH8Fzb/+aFG1zTTfgKahXzmKYXBtU8PTObuC5GcTgXpxLW63Xt7baaGcUqUWHxNZS6m5oDqAcdUIcjKi9KXwCs8Kdkp6YqBwavvpvDKY7ow5xIcxplH6nFVml+uUwHqFA6mAauyu0U4MYLSDB3mld1O+4n2fhjlwS7dc82o54lX2QYqT6N2U7Led7oc/atLI9n5p8ciKHcVxi96HV+dryS200Cv0ZtMgA4Gp9wET0oU2NdFN337/C+UfbuBPQYXdRxT7eZ9Ok5u2gd+6ZVrmwYEN29Q6RlRv5sS5Vnuv/ctO2bFX/4Zt/odqSU3PtF4RPTvEUSlF8ynTPBT0TNJsSppXApALRK94LL1uagMuB9tylKZtdPZkqiC2kBGZF/M/w9nZiotU3xRTY+jOwuskFlU5S3QG8N89h5csVIApWJi3OKYcPp9XB2WaKr9Gdn6CHnP3aABY/xrZr6M3jf8/8/fuACKZTwZ9yGbswvUh4NJuUNGLj3v27ifSOt98D2A7qUf6ZZF5IGzqnGhuhcWBJ7ZJGttmx0JWBNA5mdkl8/Umretsm5zZKDAaPVy9mJxEU1z/QjJmbvEGrrIas1KgPg7DDrf41djA6OWC55efr1x0z27W0PzzOokfVc5ixUDdySMIjDXIQQePIww3K7NLfTbZechym7jEHz7oPKvs4+jNRwe39S4K5zFfPiPrSqfsOh/C+g6GCH/j4xqQCdVFFx00MtMX8E7jS0J/4dim2zgrN77o3+HD76Rtvh1pqHXpf2NpasMBSHaAsstoJ96C6WJ3sM1TVqO6Yi54znqQsw+O4vwUkcrRE3y8w7tV+eLVO9l5rpxJbmZwBtkvgkXkKJDRjq+lN7Psc9ogdvDEC9jk2/IgxDL97g7O8wQ+5GlEGID1J7ShNjAvpE6qAmTWNW31JXAiHYdgfbbYJYO9LoCQFfoeqZZL8+kAzaX42ZZ4t4Faj3YJZ1ERfBZ36n1Qo2p4KkdjupVDymcwUg1RAiPpVkUy2iM+P2am63M5we+H16syUmCn+d3DuUG+HWCalfuVXXYrD9LylSqcxapO16kE5Wc56Bw0vWny3qXvL/bmsUa1wQbYGCF6zd+pIxhslJHDbuXX6fXqS/r8N4UT+TipcXGHKzSfrlNtgOYS+3mtptExyi6V+Xjret30RsjBNh8ZTHSzTs2TLA7bqYcql5GXIPXNcuuXVzUyUMNrTtSFMzMcbAXea+Rp5GFUmqDp+dGWH9nd13UwfUOz+B8hBz8Bhhb83NRZGzS9GVi41T+RA4jwISQ0Qw34cUzzeh5tWdddH6rQKXdrZ5wR4vuoEo5p4qiY9MsKfT7cxP4r7Gmpnyhp6gTF9bjKojR8FAFfEe8n8GVLNpJA/ekeB5mfPL55xezIdf8dEoYRZ1I3z5wESc8PE35k5zGPCICDq3Nz3vd5kLeg6fmR+y6s/W+kpLMPvfVgVy5g/eQ5jlOgg6UOkc62L65uJE3MCY3SfPvTpZ3fqVey3oVND3kMNXAnNdBr0t7HVUo7xzUCkQE0/wkA+ocJNMMAFIimQyKhBu64BuTAIibzY09p33k96yxHM4a00P0E8LtDbUnzV3nodZTm/wEaIEA2FZXIfQAAAABJRU5ErkJggg=="></figure>
|
|
<p> </p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Where</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">SST is the total sum of squares,</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">SSR is the sum of squares due to regression,</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">SSE is the sum of squares due to error.</span></p>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Multiple Coefficient of Determination</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Which is the % of variation of y can be explained by the sample regression line.</span></p>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Adjusted Multiple Coefficient of Determination</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">R<sub>a</sub><sup>2</sup> will always be smaller than R<sup>2</sup>.</span></p>
|
|
<p> </p>
|
|
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Assumptions</span></h3>
|
|
<h4><span style="font-family:Arial, Helvetica, sans-serif;">Linearity</span></h4>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">The relationship between the explanatory X and the response variable Y should be linear.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Methods for fitting a model to non-linear relationships exist but are beyond the scope of this course.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Check using a scatterplot of the data, or a residuals plot.</span></p>
|
|
<p> </p>
|
|
<h4><span style="font-family:Arial, Helvetica, sans-serif;">Nearly Normal Residuals</span></h4>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">The residuals should be nearly normal.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">This condition may not be satisfied when there are unusual observations that do not follow the trend of the rest of the data.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Check using histogram or normal probability plot of residuals.</span></p>
|
|
<p> </p>
|
|
<h4><span style="font-family:Arial, Helvetica, sans-serif;">Constant variability</span></h4>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">The variability of points around the least squares line should be roughly constant.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">This implies that the variability of residuals around the 0 line should be roughly constant as well.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">It is also called homoscedasticity.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Check using histogram or normal probability plot of residuals.</span></p>
|
|
<p> </p>
|
|
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Testing for Significance</span></h3>
|
|
<h4><span style="font-family:Arial, Helvetica, sans-serif;">Whole Model</span></h4>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">To determine whether a significant relationship exists between the dependent variable y and the set of all the independent variables x.</span></p>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Setting H0 and H1:</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;"> </span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJYAAAAXCAMAAADeM0atAAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjo6OjpmOmZmOmaQOma2OpDbZgAAZjoAZjo6ZpDbZrbbZrb/kDoAkDpmkGY6kGZmkLbbkLb/kNv/tmYAtmY6tpA6tpBmtrZmttvbttv/tv//25A627aQ2////7Zm/9uQ/9u2//+2///buCxbAAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABwElEQVRIS+1V0ULDIAws0zp0OjvdZqfrpla0tPz/9xkgbaGjgC/dg+PFDnPJ5XJAklzWRYF/qQCn5OZHd14/ETLH77Nrwemj5iA/Dvg9Pas6n1tFOd2o32LbqjY9p6TOYVBW3Wq2R7Hs/SnJ8cVnk9nlGYp0JFq1My2DlvT4/UqxBOfD8uol3ulsLw5k1tPvtt7Gm3HAXME9rYrCuWMEXV5cfRnhTLLEhQFszel6V4ptH4hbTeaxpQPmpaWTtdYaztYF5XQB1As0IzoStgJYB+w0e5eDKTMx7L27Jzze0giLltrqsQ6RoYQNc8Z0relhdNcCMzUYoVZIec0hAkeZpFU8Hjaulp5h16htLejwxFtASB4JTo2DobcG2EFNB8zBvx2ioiVyvEy9rsUsuoWBtWBL1x1dDpiHFgyjFLsPsvleKg3Cz04FL6bA6w0FqqRtoNH6xTzGdlUT5iOPp5mvyEPZrMhSvs4qf2AVKTwRqX4TkJb+cyBpOY41YSNRIr+Vnrl7Hv7fGo0bbM1KuT9qBUbszRFjrSbr59xkYXGxoAmL6sMIirkezDmzdXSFGHu4kzXZ9Wu4DGt9FQ41I/4G+wU91yeZhiY4NwAAAABJRU5ErkJggg=="></figure>
|
|
<p> </p>
|
|
<h4><span style="font-family:Arial, Helvetica, sans-serif;">Coefficient of Individual X</span></h4>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Setting H0 and H1:</span></p>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<figure class="image"><img src="data:image/png;base64,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"></figure>
|
|
<p> </p>
|
|
<h4><span style="font-family:Arial, Helvetica, sans-serif;">Multicollinearity</span></h4>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">The correlation among the independent variables.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">When the independent variables are highly correlated, say |r| > 0.7, it is not possible to determine the separate effect on the dependent variable.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Every attempt should be made to avoid including independent variables that are highly correlated.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Two predictor variables are said to be collinear when they are correlated, and this collinearity complicates model estimation.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Predictors that are associated with each other are not preferred to be added into the model, as often the addition of such variables brings nothing to the table. Instead, the simplest model is preferred or say the parsimonious model.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">While it is not possible to avoid collinearity from arising in observational data, experiments are usually designed to prevent correlations among predictors.</span></p>
|
|
<p> </p>
|
|
<h4><span style="font-family:Arial, Helvetica, sans-serif;">Qualitative Independent Variables</span></h4>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Such as genders (male, female), method of payment (cash, check, credit card).</span></p>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">For example, X<sub>1</sub> might represent gender where X<sub>1</sub> = 0 indicates male and X<sub>1</sub> = 1 indicates female.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">In this case, X<sub>1</sub> is called a dummy or indicator variable.</span></p>
|
|
<p> </p>
|
|
<h4><span style="font-family:Arial, Helvetica, sans-serif;">More Complex Qualitative Variables</span></h4>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">If a qualitative variable has k levels, k - 1 dummy variables are required, with each dummy variable being coded as 0 or 1.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">For example, a variable with levels A, B, and C could be represented by X<sub>1</sub> and X<sub>2</sub> values of (0, 0) for A, (1, 0) for B, and (0, 1) for C.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Care must be taken in defining and interpreting the dummy variables.</span></p>
|
|
<p> </p>
|
|
<h4><span style="font-family:Arial, Helvetica, sans-serif;">Residual Analysis</span></h4>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">In multiple regression analysis it is preferable to use the residual plot against ŷ to determine if the model assumptions are satisfied.</span></p>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Standardized residuals are frequently used in residual plots.</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Identifying outliers (typically, standardized residuals < -2 or > 2)</span></p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Providing insight into the assumption that the error term e has a normal distribution.</span></p>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">The computation of the standardized residuals in multiple regression analysis is too complex to be done by hand, Excel regression tool can be used.</span></p>
|