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Regression Models Notation #4

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sux13 merged 3 commits into from
Apr 14, 2015
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Regression Models Notation #4

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b6991de
Regression Models notation correction
Apr 14, 2015
c7958e0
Regression Models notation correction
Apr 14, 2015
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Regression Models notation correction
Apr 14, 2015
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2 changes: 1 addition & 1 deletion 7_REGMODS/Regression Models Course Notes HTML.Rmd
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Expand Up @@ -133,7 +133,7 @@ g


### Derivation for Least Squares = Empirical Mean (Finding the Minimum)
* Let $X_i = **regressor**/**predictor**, and $Y_i =$ **outcome**/**result** so we want to minimize the the squares: $$\sum_{i=1}^n (Y_i - \mu)^2$$
* Let $X_i =$ **regressor**/**predictor**, and $Y_i =$ **outcome**/**result** so we want to minimize the the squares: $$\sum_{i=1}^n (Y_i - \mu)^2$$
* Proof is as follows $$
\begin{aligned}
\sum_{i=1}^n (Y_i - \mu)^2 & = \sum_{i=1}^n (Y_i - \bar Y + \bar Y - \mu)^2 \Leftarrow \mbox{added} \pm \bar Y \mbox{which is adding 0 to the original equation}\\
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2 changes: 1 addition & 1 deletion 7_REGMODS/Regression Models Course Notes.Rmd
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Expand Up @@ -131,7 +131,7 @@ g
$\pagebreak$

### Derivation for Least Squares = Empirical Mean (Finding the Minimum)
* Let $X_i = **regressor**/**predictor**, and $Y_i =$ **outcome**/**result** so we want to minimize the the squares: $$\sum_{i=1}^n (Y_i - \mu)^2$$
* Let $X_i =$ **regressor**/**predictor**, and $Y_i =$ **outcome**/**result** so we want to minimize the the squares: $$\sum_{i=1}^n (Y_i - \mu)^2$$
* Proof is as follows $$
\begin{aligned}
\sum_{i=1}^n (Y_i - \mu)^2 & = \sum_{i=1}^n (Y_i - \bar Y + \bar Y - \mu)^2 \Leftarrow \mbox{added} \pm \bar Y \mbox{which is adding 0 to the original equation}\\
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2 changes: 1 addition & 1 deletion 7_REGMODS/Regression_Models_Course_Notes_HTML.html
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Expand Up @@ -348,7 +348,7 @@ <h2>Dalton’s Data and Least Squares</h2>
<div id="derivation-for-least-squares-empirical-mean-finding-the-minimum" class="section level3">
<h3>Derivation for Least Squares = Empirical Mean (Finding the Minimum)</h3>
<ul>
<li>Let $X_i = <strong>regressor</strong>/<strong>predictor</strong>, and <span class="math">\(Y_i =\)</span> <strong>outcome</strong>/<strong>result</strong> so we want to minimize the the squares: <span class="math">\[\sum_{i=1}^n (Y_i - \mu)^2\]</span></li>
<li>Let <span class="math">\(X_i =\)</span> <strong>regressor</strong>/<strong>predictor</strong>, and <span class="math">\(Y_i =\)</span> <strong>outcome</strong>/<strong>result</strong> so we want to minimize the the squares: <span class="math">\[\sum_{i=1}^n (Y_i - \mu)^2\]</span></li>
<li>Proof is as follows <span class="math">\[
\begin{aligned}
\sum_{i=1}^n (Y_i - \mu)^2 &amp; = \sum_{i=1}^n (Y_i - \bar Y + \bar Y - \mu)^2 \Leftarrow \mbox{added} \pm \bar Y \mbox{which is adding 0 to the original equation}\\
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