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Updating book (30)
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@daviddalpiaz
daviddalpiaz committed Jun 6, 2016
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75 changes: 42 additions & 33 deletions intro-to-r.html
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Expand Up @@ -299,26 +299,8 @@ <h3><span class="header-section-number">2.1.3</span> Installing Packages</h3>
<p><code>R</code> comes with a number of built-in functions and datasets, but one of the main strengths of <code>R</code> as an open-source project is its package system. Packages add additional functions and data. Frequently if you want to do something in <code>R</code>, and it isn’t availible by default, there is a good chance that there is a package that will fufill your needs.</p>
<p>To install a package, use the <code>install.packages()</code> function.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">install.packages</span>(<span class="st">&quot;UsingR&quot;</span>)</code></pre></div>
<pre><code>## Installing package into &#39;/home/travis/R/Library&#39;
## (as &#39;lib&#39; is unspecified)</code></pre>
<p>Once a package is install, it must be loaded in your current <code>R</code> session before being used.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(UsingR)</code></pre></div>
<pre><code>## Loading required package: MASS</code></pre>
<pre><code>## Loading required package: HistData</code></pre>
<pre><code>## Loading required package: Hmisc</code></pre>
<pre><code>## Loading required package: lattice</code></pre>
<pre><code>## Loading required package: survival</code></pre>
<pre><code>## Loading required package: Formula</code></pre>
<pre><code>##
## Attaching package: &#39;Hmisc&#39;</code></pre>
<pre><code>## The following objects are masked from &#39;package:base&#39;:
##
## format.pval, round.POSIXt, trunc.POSIXt, units</code></pre>
<pre><code>##
## Attaching package: &#39;UsingR&#39;</code></pre>
<pre><code>## The following object is masked from &#39;package:survival&#39;:
##
## cancer</code></pre>
</div>
<div id="data-types" class="section level3">
<h3><span class="header-section-number">2.1.4</span> Data Types</h3>
Expand Down Expand Up @@ -442,6 +424,9 @@ <h3><span class="header-section-number">2.1.6</span> Functions</h3>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">rep</span>(x, <span class="dv">3</span>)</code></pre></div>
<pre><code>## [1] 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
## [21] 1 2 3 4 5 6 7 8 9 10</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">c</span>(x, <span class="kw">c</span>(x, x), <span class="dv">42</span>, <span class="dv">42</span>, <span class="dv">42</span>)</code></pre></div>
<pre><code>## [1] 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
## [21] 1 2 3 4 5 6 7 8 9 10 42 42 42</code></pre>
<p>TODO: Basic stat functions. Mean. SD. Etc.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">y</code></pre></div>
<pre><code>## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Expand Down Expand Up @@ -648,8 +633,8 @@ <h3><span class="header-section-number">2.1.8</span> Distributions</h3>
<pre><code>## [1] 11.79982</code></pre>
<p>Lastly, to generate a random sample of size <code>n = 10</code>, use:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">rnorm</span>(<span class="dv">10</span>, <span class="dt">mean =</span> <span class="dv">2</span>, <span class="dt">sd =</span> <span class="dv">5</span>)</code></pre></div>
<pre><code>## [1] -4.1362715 2.9901554 5.5123603 0.7225186 5.3737812
## [6] 2.4657209 2.5275511 7.3373097 1.0427288 -0.2397438</code></pre>
<pre><code>## [1] -4.7325397 -1.3031095 3.7843217 -1.5098816 -0.7039219
## [6] 6.7456606 4.2253388 -2.2042964 11.3596755 -3.5841880</code></pre>
<p>These functions exist for many other distributions, including but not limited to:</p>
<table>
<thead>
Expand Down Expand Up @@ -695,44 +680,64 @@ <h3><span class="header-section-number">2.2.1</span> Logical Operators</h3>
<tr class="header">
<th align="left">Operator</th>
<th align="left">Summary</th>
<th align="left">Example</th>
<th align="left">Result</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><code>x &lt; y</code></td>
<td align="left"><code>x</code> less than <code>y</code></td>
<td align="left"><code>3 &lt; 42</code></td>
<td align="left">TRUE</td>
</tr>
<tr class="even">
<td align="left"><code>x &gt; y</code></td>
<td align="left"><code>x</code> greater than <code>y</code></td>
<td align="left"><code>3 &gt; 42</code></td>
<td align="left">FALSE</td>
</tr>
<tr class="odd">
<td align="left"><code>x &lt;= y</code></td>
<td align="left"><code>x</code> less than or equal to <code>y</code></td>
<td align="left"></td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left"><code>x &gt;= y</code></td>
<td align="left"><code>x</code> greater than or equal to <code>y</code></td>
<td align="left"></td>
<td align="left"></td>
</tr>
<tr class="odd">
<td align="left"><code>x == y</code></td>
<td align="left"><code>x</code>equal to <code>y</code></td>
<td align="left"></td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left"><code>x != y</code></td>
<td align="left"><code>x</code> not equal to <code>y</code></td>
<td align="left"></td>
<td align="left"></td>
</tr>
<tr class="odd">
<td align="left"><code>!x</code></td>
<td align="left">not <code>x</code></td>
<td align="left"></td>
<td align="left"></td>
</tr>
<tr class="even">
<td align="left"><code>x | y</code></td>
<td align="left"><code>x</code> or <code>y</code></td>
<td align="left"></td>
<td align="left"></td>
</tr>
<tr class="odd">
<td align="left"><code>x &amp; y</code></td>
<td align="left"><code>x</code> and <code>y</code></td>
<td align="left"></td>
<td align="left"></td>
</tr>
</tbody>
</table>
Expand All @@ -753,6 +758,7 @@ <h3><span class="header-section-number">2.2.1</span> Logical Operators</h3>
## shorter object length</code></pre>
<pre><code>## [1] TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE</code></pre>
<p>What happened here? <code>R</code> still performed the operation, but it also gives us a warning. (To perform the operation automatically made <code>b</code> longer by repeating <code>b</code> as needed.)</p>
<p>TODO: add comparison to “scalar”</p>
</div>
<div id="control-flow" class="section level3">
<h3><span class="header-section-number">2.2.2</span> Control Flow</h3>
Expand Down Expand Up @@ -802,9 +808,18 @@ <h3><span class="header-section-number">2.2.3</span> Writing Functions</h3>

x =<span class="st"> </span><span class="kw">rnorm</span>(<span class="dv">10</span>, <span class="dv">2</span>, <span class="dv">25</span>)
<span class="kw">standardize</span>(x)</code></pre></div>
<pre><code>## [1] -1.40307732 0.63459818 -0.72811900 0.75589756 -0.03809855
## [6] 1.49540769 0.18358848 0.50515712 0.30057426 -1.70592842</code></pre>
<pre><code>## [1] 0.3325062 -0.8745846 -0.8723640 -0.9524615 1.3417232
## [6] 0.5992176 0.4274352 1.0139296 0.6260500 -1.6414517</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">standardize =<span class="st"> </span>function(x) {
(x -<span class="st"> </span><span class="kw">mean</span>(x)) /<span class="st"> </span><span class="kw">sd</span>(x)
}</code></pre></div>
<p>TODO: function with arguments, control flow, if based return, how return works. compare these two?</p>
<p><span class="math display">\[
s = \sqrt{\frac{1}{n - 1}\sum_{i=1}^{n}(x - \bar{x})^2}
\]</span></p>
<p><span class="math display">\[
\hat{\sigma} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x - \bar{x})^2}
\]</span></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">get_sd =<span class="st"> </span>function(x, <span class="dt">biased =</span> <span class="ot">FALSE</span>) {
n =<span class="st"> </span><span class="kw">length</span>(x)
if (biased) {
Expand All @@ -818,12 +833,6 @@ <h3><span class="header-section-number">2.2.3</span> Writing Functions</h3>
n =<span class="st"> </span><span class="kw">length</span>(x) -<span class="st"> </span><span class="dv">1</span> *<span class="st"> </span>biased
<span class="kw">sqrt</span>((<span class="dv">1</span> /<span class="st"> </span>n) *<span class="st"> </span><span class="kw">sum</span>((x -<span class="st"> </span><span class="kw">mean</span>(x)) ^<span class="st"> </span><span class="dv">2</span>))
}</code></pre></div>
<p><span class="math display">\[
s = \sqrt{\frac{1}{n - 1}\sum_{i=1}^{n}(x - \bar{x})^2}
\]</span></p>
<p><span class="math display">\[
\hat{\sigma} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x - \bar{x})^2}
\]</span></p>
</div>
</div>
<div id="hypothesis-tests-in-r" class="section level2">
Expand Down Expand Up @@ -863,7 +872,7 @@ <h3><span class="header-section-number">2.3.2</span> One Sample t-Test: Example<
<pre><code>## [1] 15.9</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">sd</span>(x)</code></pre></div>
<pre><code>## [1] 0.25</code></pre>
<p><strong>b)</strong> Construct a <span class="math inline">\(95\%\)</span> confidence interval for the overall average weight of boxes of cereal.</p>
<p><strong>b)</strong> Construct a <span class="math inline">\(95\%\)</span> confidence interval for the overall average weight of boxes of <em>Captain Crisp</em> cereal.</p>
<p><span class="math inline">\(t_{n-1}^{(\alpha/2)}=t_{8}^{(0.025)}=2.306\)</span>, so the 95% CI for the average weight of a cereal box is:</p>
<p><span class="math display">\[
\begin{split}
Expand Down Expand Up @@ -1049,10 +1058,10 @@ <h3><span class="header-section-number">2.4.1</span> Paired Differences</h3>
<span class="kw">mean</span>(<span class="dv">0</span> &lt;<span class="st"> </span>differences &amp;<span class="st"> </span>differences &lt;<span class="st"> </span><span class="dv">2</span>)</code></pre></div>
<pre><code>## [1] 0.9222</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">hist</span>(differences, <span class="dt">breaks =</span> <span class="dv">20</span>, <span class="dt">main =</span> <span class="st">&quot;Empirical Distribution of Differences&quot;</span>)</code></pre></div>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-52-1.png" width="672" /></p>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-54-1.png" width="672" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">qqnorm</span>(differences)
<span class="kw">qqline</span>(differences)</code></pre></div>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-52-2.png" width="672" /></p>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-54-2.png" width="672" /></p>
</div>
<div id="distribution-of-a-sample-mean" class="section level3">
<h3><span class="header-section-number">2.4.2</span> Distribution of a Sample Mean</h3>
Expand All @@ -1070,7 +1079,7 @@ <h3><span class="header-section-number">2.4.2</span> Distribution of a Sample Me
x_bar_hist =<span class="st"> </span><span class="kw">hist</span>(x_bar, <span class="dt">breaks =</span> <span class="dv">50</span>,
<span class="dt">main =</span> <span class="st">&quot;Histogram of Sample Means&quot;</span>,
<span class="dt">xlab =</span> <span class="st">&quot;Sample Means&quot;</span>)</code></pre></div>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-53-1.png" width="672" /></p>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-55-1.png" width="672" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">c</span>(<span class="kw">mean</span>(x_bar), mu)</code></pre></div>
<pre><code>## [1] 10.00009 10.00000</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">c</span>(<span class="kw">sd</span>(x_bar), <span class="kw">sqrt</span>(mu) /<span class="st"> </span><span class="kw">sqrt</span>(sample_size))</code></pre></div>
Expand All @@ -1085,7 +1094,7 @@ <h3><span class="header-section-number">2.4.2</span> Distribution of a Sample Me
x_bar_hist =<span class="st"> </span><span class="kw">hist</span>(x_bar, <span class="dt">breaks =</span> <span class="dv">50</span>, <span class="dt">col =</span> shading,
<span class="dt">main =</span> <span class="st">&quot;Histogram of Sample Means, Two Standard Deviations&quot;</span>,
<span class="dt">xlab =</span> <span class="st">&quot;Sample Means&quot;</span>)</code></pre></div>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-53-2.png" width="672" /></p>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-55-2.png" width="672" /></p>
<p>THIS is an example of a pull-request.</p>

</div>
Expand Down
2 changes: 1 addition & 1 deletion search_index.json
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8 changes: 4 additions & 4 deletions simple-linear-regression.html
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Expand Up @@ -268,15 +268,15 @@ <h1><span class="header-section-number">Chapter 3</span> Simple Linear Regressio
<p><a href="data/momma_leona.csv">data is csv here</a></p>
<p>TODO: import into R/RStudio</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(momma_leona$students, momma_leona$sales)</code></pre></div>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-60-1.png" width="672" /></p>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-62-1.png" width="672" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(momma_leona$students, momma_leona$sales,
<span class="dt">xlab =</span> <span class="st">&quot;Students (in 1000s)&quot;</span>,
<span class="dt">ylab =</span> <span class="st">&quot;Sales (in $1000s)&quot;</span>,
<span class="dt">main =</span> <span class="st">&quot;Quarterly Sales vs Student Population&quot;</span>,
<span class="dt">pch =</span> <span class="dv">20</span>,
<span class="dt">cex =</span> <span class="dv">2</span>,
<span class="dt">col =</span> <span class="st">&quot;dodgerblue&quot;</span>)</code></pre></div>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-61-1.png" width="672" /></p>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-63-1.png" width="672" /></p>
<p>response, outcome predictor, explanatory</p>
<p>note about “independent”</p>
<p>How can you use this data to:</p>
Expand Down Expand Up @@ -381,7 +381,7 @@ <h2><span class="header-section-number">3.4</span> Least Squares Approach</h2>
<span class="dt">cex =</span> <span class="dv">2</span>,
<span class="dt">col =</span> <span class="st">&quot;dodgerblue&quot;</span>)
<span class="kw">abline</span>(momma_leona_model, <span class="dt">lwd =</span> <span class="dv">2</span>, <span class="dt">col =</span> <span class="st">&quot;darkorange&quot;</span>)</code></pre></div>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-63-1.png" width="672" /></p>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-65-1.png" width="672" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(sales ~<span class="st"> </span>students, <span class="dt">data =</span> momma_leona,
<span class="dt">xlab =</span> <span class="st">&quot;Students (in 1000s)&quot;</span>,
<span class="dt">ylab =</span> <span class="st">&quot;Sales (in $1000s)&quot;</span>,
Expand All @@ -390,7 +390,7 @@ <h2><span class="header-section-number">3.4</span> Least Squares Approach</h2>
<span class="dt">cex =</span> <span class="dv">2</span>,
<span class="dt">col =</span> <span class="st">&quot;dodgerblue&quot;</span>)
<span class="kw">abline</span>(momma_leona_model, <span class="dt">lwd =</span> <span class="dv">2</span>, <span class="dt">col =</span> <span class="st">&quot;darkorange&quot;</span>)</code></pre></div>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-64-1.png" width="672" /></p>
<p><img src="applied_statistics_files/figure-html/unnamed-chunk-66-1.png" width="672" /></p>
<p>TODO: fit in R TODO: extrapolation TODO: interpretation</p>
</div>
<div id="decomposition-of-variation" class="section level2">
Expand Down

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