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alexanderthclark · Mar 9, 2024 · c59ee2c · c59ee2c
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diff --git a/_sources/bayes.md b/_sources/bayes.md
@@ -141,11 +141,12 @@ A box contains two tickets, labeled $H$ or $T$. There is a 25% chance the box co
 
 3. Suppose you draw an $H$. What is the chance that the box contained two $H$s?
 
-4. After replacing the $H$, what is the chance of selecting another $H$? 
+4. You draw and replace an $H$, what is the chance of selecting another $H$? 
 
 ```{exercise-end}
 ```
 
+
 ```{exercise-start}
 :label: bayesraredisease
 ```

diff --git a/_sources/solutions.md b/_sources/solutions.md
@@ -148,6 +148,18 @@ Let A have an average of 1000 with an SD of 1. Let school B have an average of 1
 
 ## [Correlation](correlation)
 
+```{solution-start} corrPairing
+:class: dropdown
+```
+The correlation coefficient is $r=0.5$ for the first two tables. The correlation increases to $r=0.866$ for the last table. 
+
+This is a question about the structure of data. There is an ordered pair $(x,y)$ for each day of the week where $x$ first represents Matt Damon and $y$ represents Wahlberg. In the second table, all $x$ and $y$ values are swapped. In a scatter plot, this would be like changing the $x$ and $y$ axis labels, so the correlation does not change. 
+
+In the third table, there is a more substantive change. The list of values for our $x$ and $y$ variables beyond just relabeling. $(x,y)$ points are ordered pairs and the Wednesday pair is reordered without reordering the Monday and Tuesday points. This creates a visible change in the scatter plot and in the correlation coefficient. 
+
+```{solution-end}
+```
+
 ```{solution-start} corrMental
 :class: dropdown
 ```

diff --git a/bayes.html b/bayes.html
@@ -547,7 +547,7 @@ <h2>Exercises<a class="headerlink" href="#exercises" title="Permalink to this he
 <li><p>What is the chance of drawing an <span class="math notranslate nohighlight">\(H\)</span>?</p></li>
 <li><p>Suppose you draw an <span class="math notranslate nohighlight">\(H\)</span>. What is the chance that the box contained two <span class="math notranslate nohighlight">\(T\)</span>s?</p></li>
 <li><p>Suppose you draw an <span class="math notranslate nohighlight">\(H\)</span>. What is the chance that the box contained two <span class="math notranslate nohighlight">\(H\)</span>s?</p></li>
-<li><p>After replacing the <span class="math notranslate nohighlight">\(H\)</span>, what is the chance of selecting another <span class="math notranslate nohighlight">\(H\)</span>?</p></li>
+<li><p>You draw and replace an <span class="math notranslate nohighlight">\(H\)</span>, what is the chance of selecting another <span class="math notranslate nohighlight">\(H\)</span>?</p></li>
 </ol>
 </section>
 </div>

diff --git a/correlation.html b/correlation.html
diff --git a/normal.html b/normal.html
diff --git a/objects.inv b/objects.inv
diff --git a/regression.html b/regression.html
diff --git a/searchindex.js b/searchindex.js
diff --git a/solutions.html b/solutions.html
@@ -558,6 +558,15 @@ <h2><a class="reference internal" href="normal0.html#normal"><span class="std st
 <h2><a class="reference internal" href="regression.html#correlation"><span class="std std-ref">Correlation</span></a><a class="headerlink" href="#correlation" title="Permalink to this heading">#</a></h2>
 <div class="solution dropdown admonition" id="solutions-solution-8">
 
+<p class="admonition-title">Solution to<a class="reference internal" href="correlation.html#corrPairing"> Exercise 21</a></p>
+<section id="solution-content">
+<p>The correlation coefficient is <span class="math notranslate nohighlight">\(r=0.5\)</span> for the first two tables. The correlation increases to <span class="math notranslate nohighlight">\(r=0.866\)</span> for the last table.</p>
+<p>This is a question about the structure of data. There is an ordered pair <span class="math notranslate nohighlight">\((x,y)\)</span> for each day of the week where <span class="math notranslate nohighlight">\(x\)</span> first represents Matt Damon and <span class="math notranslate nohighlight">\(y\)</span> represents Wahlberg. In the second table, all <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> values are swapped. In a scatter plot, this would be like changing the <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> axis labels, so the correlation does not change.</p>
+<p>In the third table, there is a more substantive change. The list of values for our <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> variables beyond just relabeling. <span class="math notranslate nohighlight">\((x,y)\)</span> points are ordered pairs and the Wednesday pair is reordered without reordering the Monday and Tuesday points. This creates a visible change in the scatter plot and in the correlation coefficient.</p>
+</section>
+</div>
+<div class="solution dropdown admonition" id="solutions-solution-9">
+
 <p class="admonition-title">Solution to<a class="reference internal" href="correlation.html#corrMental"> Exercise 22</a></p>
 <section id="solution-content">
 <p>No, the award is not merited because the lack of correlation does not demonstrate that there can be no causal effect. This is a chicken and egg problem like in the case of police funding and crime.</p>
@@ -566,7 +575,7 @@ <h2><a class="reference internal" href="regression.html#correlation"><span class
 </section>
 <section id="regression">
 <h2><a class="reference internal" href="regression.html"><span class="doc std std-doc">Regression</span></a><a class="headerlink" href="#regression" title="Permalink to this heading">#</a></h2>
-<div class="solution dropdown admonition" id="solutions-solution-9">
+<div class="solution dropdown admonition" id="solutions-solution-10">
 
 <p class="admonition-title">Solution to<a class="reference internal" href="regression.html#assortMating"> Exercise 23</a></p>
 <section id="solution-content">
@@ -577,14 +586,14 @@ <h2><a class="reference internal" href="regression.html"><span class="doc std st
 </section>
 <section id="probability">
 <h2><a class="reference internal" href="probability.html#probability"><span class="std std-ref">Probability</span></a><a class="headerlink" href="#probability" title="Permalink to this heading">#</a></h2>
-<div class="solution dropdown admonition" id="solutions-solution-10">
+<div class="solution dropdown admonition" id="solutions-solution-11">
 
 <p class="admonition-title">Solution to<a class="reference internal" href="probability.html#conditional"> Exercise 28</a></p>
 <section id="solution-content">
 <p><span class="math notranslate nohighlight">\(\mathbb{P}(A \mid B) + \mathbb{P}(\text{not }A \mid B)=1\)</span> for any <span class="math notranslate nohighlight">\(A,B\)</span>.</p>
 </section>
 </div>
-<div class="solution dropdown admonition" id="solutions-solution-11">
+<div class="solution dropdown admonition" id="solutions-solution-12">
 
 <p class="admonition-title">Solution to<a class="reference internal" href="probability.html#glee"> Exercise 31</a></p>
 <section id="solution-content">