Made minor modifications to lecture 2

bcaffo · bcaffo · commit acb3541e29f1 · 2014-09-02T23:47:03.000-04:00
diff --git a/07_RegressionModels/01_02_notation/index.Rmd b/07_RegressionModels/01_02_notation/index.Rmd
@@ -8,8 +8,8 @@ framework   : io2012        # {io2012, html5slides, shower, dzslides, ...}
 highlighter : highlight.js  # {highlight.js, prettify, highlight}
 hitheme     : tomorrow      # 
 url:
-  lib: ../../libraries
-  assets: ../../assets
+  lib: ../../librariesNew
+  assets: ../../assetsNew
 widgets     : [mathjax]            # {mathjax, quiz, bootstrap}
 mode        : selfcontained # {standalone, draft}
 ---
@@ -30,10 +30,6 @@ mode        : selfcontained # {standalone, draft}
 * We often use a different letter than $X$, such as $Y_1, \ldots , Y_n$.
 * We will typically use Greek letters for things we don't know. 
   Such as, $\mu$ is a mean that we'd like to estimate.
-* We will use capital letters for conceptual values of the variables and lowercase letters for realized values.
-  * So this way we can write $P(X_i > x)$. 
-  * $X_i$ is a conceptual random variable.
-  * $x$ is a number that we plug into.
 
 ---
 ## The empirical mean 
@@ -48,7 +44,6 @@ $$
 $$
 The mean of the $\tilde X_i$ is 0.
 * This process is called "centering" the random variables.
-* The mean is a measure of central tendency of the data.
 * Recall from the previous lecture that the mean is 
   the least squares solution for minimizing
   $$
@@ -67,9 +62,6 @@ $$
 * The empirical standard deviation is defined as
 $S = \sqrt{S^2}$. Notice that the standard deviation has the same units as the data.
 * The data defined by $X_i / s$ have empirical standard deviation 1. This is called "scaling" the data.
-* The empirical standard deviation is a measure of spread.
-* Sometimes people divide by $n$ rather than $n-1$ (the latter
-produces an unbiased estimate.)
 
 ---
 ## Normalization
@@ -93,8 +85,6 @@ Cov(X, Y) =
 \frac{1}{n-1}\sum_{i=1}^n (X_i - \bar X) (Y_i - \bar Y)
 = \frac{1}{n-1}\left( \sum_{i=1}^n X_i Y_i - n \bar X \bar Y\right)
 $$
-* Some people prefer to divide by $n$ rather than $n-1$ (the latter
-produces an unbiased estimate.)
 * The correlation is defined is
 $$
 Cor(X, Y) = \frac{Cov(X, Y)}{S_x S_y}
diff --git a/07_RegressionModels/01_02_notation/index.html b/07_RegressionModels/01_02_notation/index.html
@@ -8,51 +8,46 @@
   <meta name="generator" content="slidify" />
   <meta name="apple-mobile-web-app-capable" content="yes">
   <meta http-equiv="X-UA-Compatible" content="chrome=1">
-  <link rel="stylesheet" href="../../libraries/frameworks/io2012/css/default.css" media="all" >
-  <link rel="stylesheet" href="../../libraries/frameworks/io2012/phone.css" 
+  <link rel="stylesheet" href="../../librariesNew/frameworks/io2012/css/default.css" media="all" >
+  <link rel="stylesheet" href="../../librariesNew/frameworks/io2012/css/phone.css" 
     media="only screen and (max-device-width: 480px)" >
-  <link rel="stylesheet" href="../../libraries/frameworks/io2012/css/slidify.css" >
-  <link rel="stylesheet" href="../../libraries/highlighters/highlight.js/css/tomorrow.css" />
-  <base target="_blank"> <!-- This amazingness opens all links in a new tab. -->
-  <script data-main="../../libraries/frameworks/io2012/js/slides" 
-    src="../../libraries/frameworks/io2012/js/require-1.0.8.min.js">
+  <link rel="stylesheet" href="../../librariesNew/frameworks/io2012/css/slidify.css" >
+  <link rel="stylesheet" href="../../librariesNew/highlighters/highlight.js/css/tomorrow.css" />
+  <base target="_blank"> <!-- This amazingness opens all links in a new tab. -->  
+  
+  <!-- Grab CDN jQuery, fall back to local if offline -->
+  <script src="http://ajax.aspnetcdn.com/ajax/jQuery/jquery-1.7.min.js"></script>
+  <script>window.jQuery || document.write('<script src="../../librariesNew/widgets/quiz/js/jquery.js"><\/script>')</script> 
+  <script data-main="../../librariesNew/frameworks/io2012/js/slides" 
+    src="../../librariesNew/frameworks/io2012/js/require-1.0.8.min.js">
   </script>
   
-    <link rel="stylesheet" href = "../../assets/css/custom.css">
-<link rel="stylesheet" href = "../../assets/css/custom.css.BACKUP.546.css">
-<link rel="stylesheet" href = "../../assets/css/custom.css.BASE.546.css">
-<link rel="stylesheet" href = "../../assets/css/custom.css.LOCAL.546.css">
-<link rel="stylesheet" href = "../../assets/css/custom.css.orig">
-<link rel="stylesheet" href = "../../assets/css/custom.css.REMOTE.546.css">
-<link rel="stylesheet" href = "../../assets/css/ribbons.css">
+  
 
 </head>
 <body style="opacity: 0">
   <slides class="layout-widescreen">
     
     <!-- LOGO SLIDE -->
-    <!-- END LOGO SLIDE -->
+        <slide class="title-slide segue nobackground">
+  <aside class="gdbar">
+    <img src="../../assetsNew/img/bloomberg_shield.png">
+  </aside>
+  <hgroup class="auto-fadein">
+    <h1>Some basic notation and background</h1>
+    <h2>Regression</h2>
+    <p>Brian Caffo, PhD<br/>Johns Hopkins Bloomberg School of Public Health</p>
+  </hgroup>
+  <article></article>  
+</slide>
     
 
-    <!-- TITLE SLIDE -->
-    <!-- Should I move this to a Local Layout File? -->
-    <slide class="title-slide segue nobackground">
-      <aside class="gdbar">
-        <img src="../../assets/img/bloomberg_shield.png">
-      </aside>
-      <hgroup class="auto-fadein">
-        <h1>Some basic notation and background</h1>
-        <h2>Regression</h2>
-        <p>Brian Caffo, PhD<br/>Johns Hopkins Bloomberg School of Public Health</p>
-      </hgroup>
-          </slide>
-
     <!-- SLIDES -->
-      <slide class="" id="slide-1" style="background:;">
+    <slide class="" id="slide-1" style="background:;">
   <hgroup>
     <h2>Some basic definitions</h2>
   </hgroup>
-  <article>
+  <article data-timings="">
     <ul>
 <li>In this module, we&#39;ll cover some basic definitions and notation used throughout the class.</li>
 <li>We will try to minimize the amount of mathematics required for this class.</li>
@@ -63,11 +58,11 @@ <h2>Some basic definitions</h2>
   <!-- Presenter Notes -->
 </slide>
 
-      <slide class="" id="slide-2" style="background:;">
+<slide class="" id="slide-2" style="background:;">
   <hgroup>
     <h2>Notation for data</h2>
   </hgroup>
-  <article>
+  <article data-timings="">
     <ul>
 <li>We write \(X_1, X_2, \ldots, X_n\) to describe \(n\) data points.</li>
 <li>As an example, consider the data set \(\{1, 2, 5\}\) then 
@@ -78,24 +73,17 @@ <h2>Notation for data</h2>
 <li>We often use a different letter than \(X\), such as \(Y_1, \ldots , Y_n\).</li>
 <li>We will typically use Greek letters for things we don&#39;t know. 
 Such as, \(\mu\) is a mean that we&#39;d like to estimate.</li>
-<li>We will use capital letters for conceptual values of the variables and lowercase letters for realized values.
-
-<ul>
-<li>So this way we can write \(P(X_i > x)\). </li>
-<li>\(X_i\) is a conceptual random variable.</li>
-<li>\(x\) is a number that we plug into.</li>
-</ul></li>
 </ul>
 
   </article>
   <!-- Presenter Notes -->
 </slide>
 
-      <slide class="" id="slide-3" style="background:;">
+<slide class="" id="slide-3" style="background:;">
   <hgroup>
     <h2>The empirical mean</h2>
   </hgroup>
-  <article>
+  <article data-timings="">
     <ul>
 <li>Define the empirical mean as
 \[
@@ -105,9 +93,8 @@ <h2>The empirical mean</h2>
 \[
 \tilde X_i = X_i - \bar X.
 \]
-The the mean of the \(\tilde X_i\) is 0.</li>
+The mean of the \(\tilde X_i\) is 0.</li>
 <li>This process is called &quot;centering&quot; the random variables.</li>
-<li>The mean is a measure of central tendancy of the data.</li>
 <li>Recall from the previous lecture that the mean is 
 the least squares solution for minimizing
 \[
@@ -119,11 +106,11 @@ <h2>The empirical mean</h2>
   <!-- Presenter Notes -->
 </slide>
 
-      <slide class="" id="slide-4" style="background:;">
+<slide class="" id="slide-4" style="background:;">
   <hgroup>
     <h2>The emprical standard deviation and variance</h2>
   </hgroup>
-  <article>
+  <article data-timings="">
     <ul>
 <li>Define the empirical variance as 
 \[
@@ -133,22 +120,19 @@ <h2>The emprical standard deviation and variance</h2>
 <li>The empirical standard deviation is defined as
 \(S = \sqrt{S^2}\). Notice that the standard deviation has the same units as the data.</li>
 <li>The data defined by \(X_i / s\) have empirical standard deviation 1. This is called &quot;scaling&quot; the data.</li>
-<li>The empirical standard deviation is a measure of spread.</li>
-<li>Sometimes people divide by \(n\) rather than \(n-1\) (the latter
-produces an unbiased estimate.)</li>
 </ul>
 
   </article>
   <!-- Presenter Notes -->
 </slide>
 
-      <slide class="" id="slide-5" style="background:;">
+<slide class="" id="slide-5" style="background:;">
   <hgroup>
     <h2>Normalization</h2>
   </hgroup>
-  <article>
+  <article data-timings="">
     <ul>
-<li>The the data defined by
+<li>The data defined by
 \[
 Z_i = \frac{X_i - \bar X}{s}
 \]
@@ -163,11 +147,11 @@ <h2>Normalization</h2>
   <!-- Presenter Notes -->
 </slide>
 
-      <slide class="" id="slide-6" style="background:;">
+<slide class="" id="slide-6" style="background:;">
   <hgroup>
     <h2>The empirical covariance</h2>
   </hgroup>
-  <article>
+  <article data-timings="">
     <ul>
 <li>Consider now when we have pairs of data, \((X_i, Y_i)\).</li>
 <li>Their empirical covariance is 
@@ -176,8 +160,6 @@ <h2>The empirical covariance</h2>
 \frac{1}{n-1}\sum_{i=1}^n (X_i - \bar X) (Y_i - \bar Y)
 = \frac{1}{n-1}\left( \sum_{i=1}^n X_i Y_i - n \bar X \bar Y\right)
 \]</li>
-<li>Some people prefer to divide by \(n\) rather than \(n-1\) (the latter
-produces an unbiased estimate.)</li>
 <li>The correlation is defined is
 \[
 Cor(X, Y) = \frac{Cov(X, Y)}{S_x S_y}
@@ -190,11 +172,11 @@ <h2>The empirical covariance</h2>
   <!-- Presenter Notes -->
 </slide>
 
-      <slide class="" id="slide-7" style="background:;">
+<slide class="" id="slide-7" style="background:;">
   <hgroup>
     <h2>Some facts about correlation</h2>
   </hgroup>
-  <article>
+  <article data-timings="">
     <ul>
 <li>\(Cor(X, Y) = Cor(Y, X)\)</li>
 <li>\(-1 \leq Cor(X, Y) \leq 1\)</li>
@@ -209,34 +191,77 @@ <h2>Some facts about correlation</h2>
 
     <slide class="backdrop"></slide>
   </slides>
-
-  <!--[if IE]>
+  <div class="pagination pagination-small" id='io2012-ptoc' style="display:none;">
+    <ul>
+      <li>
+      <a href="#" target="_self" rel='tooltip' 
+        data-slide=1 title='Some basic definitions'>
+         1
+      </a>
+    </li>
+    <li>
+      <a href="#" target="_self" rel='tooltip' 
+        data-slide=2 title='Notation for data'>
+         2
+      </a>
+    </li>
+    <li>
+      <a href="#" target="_self" rel='tooltip' 
+        data-slide=3 title='The empirical mean'>
+         3
+      </a>
+    </li>
+    <li>
+      <a href="#" target="_self" rel='tooltip' 
+        data-slide=4 title='The emprical standard deviation and variance'>
+         4
+      </a>
+    </li>
+    <li>
+      <a href="#" target="_self" rel='tooltip' 
+        data-slide=5 title='Normalization'>
+         5
+      </a>
+    </li>
+    <li>
+      <a href="#" target="_self" rel='tooltip' 
+        data-slide=6 title='The empirical covariance'>
+         6
+      </a>
+    </li>
+    <li>
+      <a href="#" target="_self" rel='tooltip' 
+        data-slide=7 title='Some facts about correlation'>
+         7
+      </a>
+    </li>
+  </ul>
+  </div>  <!--[if IE]>
     <script 
       src="http://ajax.googleapis.com/ajax/libs/chrome-frame/1/CFInstall.min.js">  
     </script>
     <script>CFInstall.check({mode: 'overlay'});</script>
   <![endif]-->
 </body>
-<!-- Grab CDN jQuery, fall back to local if offline -->
-<script src="http://ajax.aspnetcdn.com/ajax/jQuery/jquery-1.7.min.js"></script>
-<script>window.jQuery || document.write('<script src="../../libraries/widgets/quiz/js/jquery-1.7.min.js"><\/script>')</script>
-<!-- Load Javascripts for Widgets -->
-<!-- MathJax: Fall back to local if CDN offline but local image fonts are not supported (saves >100MB) -->
-<script type="text/x-mathjax-config">
-  MathJax.Hub.Config({
-    tex2jax: {
-      inlineMath: [['$','$'], ['\\(','\\)']],
-      processEscapes: true
-    }
-  });
-</script>
-<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/2.0-latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
-<!-- <script src="https://c328740.ssl.cf1.rackcdn.com/mathjax/2.0-latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
-</script> -->
-<script>window.MathJax || document.write('<script type="text/x-mathjax-config">MathJax.Hub.Config({"HTML-CSS":{imageFont:null}});<\/script><script src="../../libraries/widgets/mathjax/MathJax.js?config=TeX-AMS-MML_HTMLorMML"><\/script>')
+  <!-- Load Javascripts for Widgets -->
+  
+  <!-- MathJax: Fall back to local if CDN offline but local image fonts are not supported (saves >100MB) -->
+  <script type="text/x-mathjax-config">
+    MathJax.Hub.Config({
+      tex2jax: {
+        inlineMath: [['$','$'], ['\\(','\\)']],
+        processEscapes: true
+      }
+    });
+  </script>
+  <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/2.0-latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
+  <!-- <script src="https://c328740.ssl.cf1.rackcdn.com/mathjax/2.0-latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+  </script> -->
+  <script>window.MathJax || document.write('<script type="text/x-mathjax-config">MathJax.Hub.Config({"HTML-CSS":{imageFont:null}});<\/script><script src="../../librariesNew/widgets/mathjax/MathJax.js?config=TeX-AMS-MML_HTMLorMML"><\/script>')
 </script>
 <!-- LOAD HIGHLIGHTER JS FILES -->
-<script src="../../libraries/highlighters/highlight.js/highlight.pack.js"></script>
-<script>hljs.initHighlightingOnLoad();</script>
-<!-- DONE LOADING HIGHLIGHTER JS FILES -->
-</html>
+  <script src="../../librariesNew/highlighters/highlight.js/highlight.pack.js"></script>
+  <script>hljs.initHighlightingOnLoad();</script>
+  <!-- DONE LOADING HIGHLIGHTER JS FILES -->
+   
+  </html>
diff --git a/07_RegressionModels/01_02_notation/index.md b/07_RegressionModels/01_02_notation/index.md
