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Tutorial5_BasicAnalytics.html
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Tutorial5_BasicAnalytics.html
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<?xml version="1.0" encoding="utf-8" ?>
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<meta name="generator" content="pandoc" />
<meta name="author" content="DPI R Bootcamp" />
<title>Tutorial 5: Analytics</title>
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</head>
<body>
<div class="slide titlepage">
<h1 class="title">Tutorial 5: Analytics</h1>
<p class="author">
DPI R Bootcamp
</p>
<p class="date">Jared Knowles</p>
</div>
<div class="section slide level1" id="overview">
<h1>Overview</h1>
<p>In this lesson we hope to learn:</p>
<ul class="incremental">
<li>How to use summary statistics to look at data</li>
<li>How to run basic statistical tests on a dataset</li>
<li>How to use formulas to build a statistical model</li>
<li>Analyze subsets of data</li>
</ul>
<p align="center">
<img src="data:image/png;base64,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" height="81" width="138">
</p>
</div>
<div class="section slide level1" id="datasets">
<h1>Datasets</h1>
<p>In this tutorial we will use a number of datasets of different types:</p>
<ul class="incremental">
<li><code>stulong</code>: student-level assessment and demographics data (simulated and research ready)</li>
<li><code>midwest_schools.csv</code>: aggregate school level test score averages from a large Midwest state</li>
</ul>
</div>
<div class="section slide level1" id="reading-data-in">
<h1>Reading Data In</h1>
<ul class="incremental">
<li>We start with the aggregate school level data</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">load</span>(<span class="st">"data/midwest_schools.rda"</span>)
<span class="kw">head</span>(midsch[, <span class="dv">1</span>:<span class="dv">12</span>])</code></pre>
<pre><code>## district_id school_id subject grade n1 ss1 n2 ss2 predicted
## 1 14 130 math 4 44 433.1 40 463.0 468.7
## 2 70 20 math 4 18 443.0 20 477.2 476.5
## 3 112 80 math 4 86 445.4 94 472.6 478.4
## 4 119 50 math 4 95 427.1 94 460.7 464.1
## 5 147 60 math 4 27 424.2 27 458.7 461.8
## 6 147 125 math 4 17 423.5 26 463.1 461.2
## residuals resid_z resid_t
## 1 -5.7446 -0.59190 -0.59171
## 2 0.7235 0.07456 0.07452
## 3 -5.7509 -0.59267 -0.59248
## 4 -3.3586 -0.34606 -0.34591
## 5 -3.0937 -0.31877 -0.31863
## 6 1.8530 0.19094 0.19085</code></pre>
</div>
<div class="section slide level1" id="what-do-we-have-then">
<h1>What do we have then?</h1>
<ul class="incremental">
<li>We have unique identifiers for districts and schools</li>
<li>For each school/district combination we have a row of test scores in year 1 and year 2 by test_year (of year 1); grade; and subject</li>
<li>How can we use R to ask this?</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">table</span>(midsch$test_year, midsch$grade)</code></pre>
<pre><code>##
## 4 5 6 7 8
## 2007 1150 1094 472 638 734
## 2008 1204 1146 462 588 692
## 2009 1173 1092 434 592 668
## 2010 1120 1090 428 610 686
## 2011 1126 1060 420 618 688</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">length</span>(<span class="kw">unique</span>(midsch$district_id))</code></pre>
<pre><code>## [1] 357</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">length</span>(<span class="kw">unique</span>(midsch$school_id))</code></pre>
<pre><code>## [1] 247</code></pre>
<ul class="incremental">
<li>What's wrong with this?</li>
<li>More districts than schools? The IDs must be goofed</li>
<li>We need to create a unique school ID</li>
</ul>
</div>
<div class="section slide level1" id="explore-data-structure-ii">
<h1>Explore Data Structure (II)</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">table</span>(midsch$subject, midsch$grade)</code></pre>
<pre><code>##
## 4 5 6 7 8
## math 2886 2741 1108 1523 1734
## read 2887 2741 1108 1523 1734</code></pre>
<ul class="incremental">
<li>Why don't we want to do <code>table(midsch$district_id,midsch$grade)</code></li>
<li>What else do we want to know?</li>
</ul>
</div>
<div class="section slide level1" id="diagnostic-plots-perhaps">
<h1>Diagnostic Plots Perhaps</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(ggplot2)
<span class="kw">qplot</span>(ss1, ss2, <span class="dt">data =</span> midsch, <span class="dt">alpha =</span> <span class="kw">I</span>(<span class="fl">0.07</span>)) + <span class="kw">theme_dpi</span>() + <span class="kw">geom_smooth</span>() +
<span class="kw">geom_smooth</span>(<span class="dt">method =</span> <span class="st">"lm"</span>, <span class="dt">se =</span> <span class="ot">FALSE</span>, <span class="dt">color =</span> <span class="st">"purple"</span>)</code></pre>
<div class="figure">
<img 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" alt="plot of chunk diag1" /><p class="caption">plot of chunk diag1</p>
</div>
</div>
<div class="section slide level1" id="frequencies-crosstabs-and-t-tests">
<h1>Frequencies, Crosstabs, and t-tests</h1>
<ul class="incremental">
<li>Some of the most basic analyses we can implement in R are sometimes the most useful</li>
<li>Before we dive in to linear regression and evaluating a linear regression, we will first look into tests of differences among groups</li>
<li>This is really useful in an education context or for evaluating experiments quickly when we are interested in whether the difference we observe in groups is real, or due to chance</li>
</ul>
</div>
<div class="section slide level1" id="lets-take-a-simple-example-of-cars">
<h1>Let's take a simple example of cars</h1>
<ul class="incremental">
<li>Sometimes we want to compare groups of data to other groups or a fixed value</li>
<li>We use a t-test for this, but only if we believe the data are normally distributed</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">data</span>(mtcars) <span class="co"># load the data from R</span>
<span class="kw">head</span>(mtcars)</code></pre>
<pre><code>## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1</code></pre>
</div>
<div class="section slide level1" id="check-for-normality">
<h1>Check for normality</h1>
<ul class="incremental">
<li>The Shapiro-Wilk normality test checks this for us:</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">shapiro.test</span>(mtcars$mpg)</code></pre>
<pre><code>##
## Shapiro-Wilk normality test
##
## data: mtcars$mpg
## W = 0.9476, p-value = 0.1229</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">shapiro.test</span>(mtcars$hp)</code></pre>
<pre><code>##
## Shapiro-Wilk normality test
##
## data: mtcars$hp
## W = 0.9334, p-value = 0.04881</code></pre>
<ul class="incremental">
<li>Which of these is normally distributed?</li>
<li>For more on hypothesis testing, see the optional intro to statistics module</li>
</ul>
</div>
<div class="section slide level1" id="t-test">
<h1>T-test</h1>
<ul class="incremental">
<li>We can t-test the <code>mpg</code> variable then</li>
<li>Let's test it against an assumption about the population using a one-sided test</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">mean</span>(mtcars$mpg)</code></pre>
<pre><code>## [1] 20.09</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">t.test</span>(mtcars$mpg, <span class="dt">mu =</span> <span class="dv">18</span>, <span class="dt">alternative =</span> <span class="st">"greater"</span>)</code></pre>
<pre><code>##
## One Sample t-test
##
## data: mtcars$mpg
## t = 1.962, df = 31, p-value = 0.02938
## alternative hypothesis: true mean is greater than 18
## 95 percent confidence interval:
## 18.28 Inf
## sample estimates:
## mean of x
## 20.09</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">t.test</span>(mtcars$mpg, <span class="dt">mu =</span> <span class="dv">22</span>, <span class="dt">alternative =</span> <span class="st">"less"</span>)</code></pre>
<pre><code>##
## One Sample t-test
##
## data: mtcars$mpg
## t = -1.792, df = 31, p-value = 0.04144
## alternative hypothesis: true mean is less than 22
## 95 percent confidence interval:
## -Inf 21.9
## sample estimates:
## mean of x
## 20.09</code></pre>
<ul class="incremental">
<li>What does <code>t.test(mtcars$mpg,mu=18)</code> test?</li>
</ul>
</div>
<div class="section slide level1" id="two-sample-t-test">
<h1>Two sample t-test</h1>
<ul class="incremental">
<li>What if we want to compare two groups?</li>
<li>For example cars with and without automatic transmissions</li>
<li>How might we do this?</li>
<li>Look at the documentation?</li>
</ul>
</div>
<div class="section slide level1" id="answer">
<h1>Answer</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">t.test</span>(mpg ~ am, <span class="dt">data =</span> mtcars)</code></pre>
<pre><code>##
## Welch Two Sample t-test
##
## data: mpg by am
## t = -3.767, df = 18.33, p-value = 0.001374
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -11.28 -3.21
## sample estimates:
## mean in group 0 mean in group 1
## 17.15 24.39</code></pre>
</div>
<div class="section slide level1" id="if-data-is-non-normal">
<h1>If data is non-normal</h1>
<ul class="incremental">
<li>You can do <code>wilcox.test(mtcars$hp,mu=102)</code></li>
<li>Or <code>wilcox.test(hp~am,data=mtcars)</code></li>
<li>Just Google it!</li>
</ul>
</div>
<div class="section slide level1" id="chi-square">
<h1>Chi-Square</h1>
<ul class="incremental">
<li>Placebo v. aspirin</li>
<li>Heartattack or no</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">aspirin <- <span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">189</span>, <span class="dv">104</span>, <span class="dv">10845</span>, <span class="dv">10933</span>), <span class="dt">ncol =</span> <span class="dv">2</span>, <span class="dt">dimnames =</span> <span class="kw">list</span>(<span class="kw">c</span>(<span class="st">"Placebo"</span>,
<span class="st">"Aspirin"</span>), <span class="kw">c</span>(<span class="st">"MI"</span>, <span class="st">"No MI"</span>)))
aspirin</code></pre>
<pre><code>## MI No MI
## Placebo 189 10845
## Aspirin 104 10933</code></pre>
<ul class="incremental">
<li>We want to know how independent from one another heart attacks and taking the placebo are. If it is unlikely that they are independent, then we would conclude these two variables have some relationship in our population (assuming the data was collected well)</li>
</ul>
</div>
<div class="section slide level1" id="test-it">
<h1>Test it</h1>
<ul class="incremental">
<li>To test these we use a chi-squared test statistic</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">chisq.test</span>(aspirin, <span class="dt">correct =</span> <span class="ot">FALSE</span>)</code></pre>
<pre><code>##
## Pearson's Chi-squared test
##
## data: aspirin
## X-squared = 25.01, df = 1, p-value = 5.692e-07</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">fisher.test</span>(aspirin)</code></pre>
<pre><code>##
## Fisher's Exact Test for Count Data
##
## data: aspirin
## p-value = 5.033e-07
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
## 1.432 2.354
## sample estimates:
## odds ratio
## 1.832</code></pre>
</div>
<div class="section slide level1" id="back-to-school-data">
<h1>Back to School Data</h1>
<ul class="incremental">
<li>Let's imagine that a journalist has used this dataset to detect testing "irregularities" using publicly available aggregate test data</li>
<li>The journalist's methodology is to regress test scores for a school/grade/subject in one year on a school/grade/subject aggregate test score in the next year</li>
<li>For example, 2005-06, 3rd grade, reading scores are regressed on 2006-07, 4th grade, reading scores</li>
<li>Where the observed gains are higher or lower than predicted by this statistical model, "irregularities" are suspected</li>
</ul>
</div>
<div class="section slide level1" id="regression-101">
<h1>Regression 101</h1>
<ul class="incremental">
<li>What is wrong with this approach?</li>
<li>What are the five assumptions of simple linear regression?</li>
</ul>
<ol class="incremental" style="list-style-type: decimal">
<li>Dependent variable has a linear relationship to a combination of independent variables + a disturbance term (no variables omitted)</li>
<li>The expected value of the disturbance term is zero.</li>
<li>Disturbance terms have the same variance and are not correlated with one another.</li>
<li>The observations of the independent variables are considered fixed in repeated samples.</li>
<li>The number of observations exceeds the number of independent variables and no fixed linear combination exists among the independent variables (perfect collinearity)</li>
</ol>
<ul class="incremental">
<li>What are other concerns?</li>
</ul>
<ol class="incremental" style="list-style-type: decimal">
<li>Sensitivity of the model to outliers</li>
<li>Confidence interval around predictions</li>
<li>Validity of the model on key subsets</li>
</ol>
</div>
<div class="section slide level1" id="how-to-approach-this">
<h1>How to approach this?</h1>
<ul class="incremental">
<li>This is a perfect case for exploring the power of R for doing analysis on data and for checking accuracy of results</li>
<li>Two approaches</li>
</ul>
<ol class="incremental" style="list-style-type: decimal">
<li>Work on one test,grade,school_year combination and validate that</li>
<li>Test model assumptions across all combinations</li>
<li>Build one mega model from full data and control for year, grade, and subject</li>
</ol>
</div>
<div class="section slide level1" id="first-step">
<h1>First Step</h1>
<ul class="incremental">
<li>How many unique combinations are there of <code>test_year</code>, <code>grade</code>, and <code>subject</code>?</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">nrow</span>(<span class="kw">unique</span>(midsch[, <span class="kw">c</span>(<span class="dv">3</span>, <span class="dv">4</span>, <span class="dv">14</span>)]))</code></pre>
<pre><code>## [1] 50</code></pre>
</div>
<div class="section slide level1" id="lets-look-at-one-subset-to-start">
<h1>Let's look at one subset to start</h1>
<p>5th grade, 2011, math scores</p>
<pre class="sourceCode r"><code class="sourceCode r">midsch_sub <- <span class="kw">subset</span>(midsch, midsch$grade == <span class="dv">5</span> & midsch$test_year == <span class="dv">2011</span> &
midsch$subject == <span class="st">"math"</span>)</code></pre>
<ul class="incremental">
<li>How many observations in <code>midsch_sub</code>?</li>
</ul>
</div>
<div class="section slide level1" id="how-to-specify-a-regression-in-r">
<h1>How to specify a regression in R</h1>
<p><code>my_mod<-lm(ss2~ss1,data=midsch_sub)</code></p>
<ul class="incremental">
<li>OLS regression is done by the trusty <code>lm</code> function</li>
<li>The <code>~</code> character divides the dependent variable <code>ss2</code> from the independent variable <code>ss1</code></li>
<li>We want to store the results of our function so we can capture it by <code>my_mod<-</code></li>
<li><code>data</code> means we don't have to write: <code>lm(midsch_sub$ss2~midsch_sub$ss1)</code></li>
</ul>
</div>
<div class="section slide level1" id="run-the-regression">
<h1>Run the regression</h1>
<ul class="incremental">
<li>To implement the regression described above is simple in this framework</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">ss_mod <- <span class="kw">lm</span>(ss2 ~ ss1, <span class="dt">data =</span> midsch_sub)
<span class="kw">summary</span>(ss_mod)</code></pre>
<pre><code>##
## Call:
## lm(formula = ss2 ~ ss1, data = midsch_sub)
##
## Residuals:
## Min 1Q Median 3Q Max
## -46.36 -7.60 -0.42 6.49 58.36
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.1687 11.3446 -0.46 0.65
## ss1 1.0644 0.0242 44.00 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.2 on 528 degrees of freedom
## Multiple R-squared: 0.786, Adjusted R-squared: 0.785
## F-statistic: 1.94e+03 on 1 and 528 DF, p-value: <2e-16</code></pre>
</div>
<div class="section slide level1" id="explore-the-model-output">
<h1>Explore the Model Output</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">objects</span>(ss_mod)</code></pre>
<pre><code>## [1] "assign" "call" "coefficients" "df.residual"
## [5] "effects" "fitted.values" "model" "qr"
## [9] "rank" "residuals" "terms" "xlevels"</code></pre>
<ul class="incremental">
<li>Most of these we can ignore</li>
<li>A few are interesting such as <code>coefficients</code> <code>fitted.values</code> and <code>call</code></li>
<li>Any idea how to access these objects?</li>
</ul>
</div>
<div class="section slide level1" id="omitted-variable">
<h1>Omitted Variable</h1>
<ul class="incremental">
<li>What other data elements do we have available that might be omitted from our model specification?</li>
<li>What about the class size?</li>
<li>Class size is attractive since class size probably correlates with the variability in the change of scores from year 1 to year 2--big classes swing less than small classes</li>
</ul>
</div>
<div class="section slide level1" id="plot-of-class-size">
<h1>Plot of class size</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">qplot</span>(n2, ss2 - ss1, <span class="dt">data =</span> midsch, <span class="dt">alpha =</span> <span class="kw">I</span>(<span class="fl">0.1</span>)) + <span class="kw">theme_dpi</span>() + <span class="kw">geom_smooth</span>()</code></pre>
<div class="figure">
<img 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" alt="plot of chunk diagn" /><p class="caption">plot of chunk diagn</p>
</div>
<ul class="incremental">
<li>Group size might matter</li>
<li>Another type of omitted variable are non-linear terms (polynomials) of the independent variable</li>
</ul>
</div>
<div class="section slide level1" id="how-to-check-formally">
<h1>How to check formally</h1>
<pre class="sourceCode r"><code class="sourceCode r">ssN1_mod <- <span class="kw">lm</span>(ss2 ~ ss1 + n1, <span class="dt">data =</span> midsch_sub)
<span class="kw">summary</span>(ssN1_mod)</code></pre>
<pre><code>##
## Call:
## lm(formula = ss2 ~ ss1 + n1, data = midsch_sub)
##
## Residuals:
## Min 1Q Median 3Q Max
## -45.39 -7.73 -0.52 6.42 59.67
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.6849 11.7688 0.14 0.886
## ss1 1.0450 0.0258 40.49 <2e-16 ***
## n1 0.0406 0.0193 2.10 0.036 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.2 on 527 degrees of freedom
## Multiple R-squared: 0.787, Adjusted R-squared: 0.787
## F-statistic: 976 on 2 and 527 DF, p-value: <2e-16</code></pre>
<pre class="sourceCode r"><code class="sourceCode r">ssN2_mod <- <span class="kw">lm</span>(ss2 ~ ss1 + n2, <span class="dt">data =</span> midsch_sub)
<span class="kw">summary</span>(ssN2_mod)</code></pre>
<pre><code>##
## Call:
## lm(formula = ss2 ~ ss1 + n2, data = midsch_sub)
##
## Residuals:
## Min 1Q Median 3Q Max
## -45.60 -7.62 -0.53 6.52 59.64
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.7971 11.8544 0.15 0.88
## ss1 1.0450 0.0260 40.12 <2e-16 ***
## n2 0.0377 0.0192 1.97 0.05 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.2 on 527 degrees of freedom
## Multiple R-squared: 0.787, Adjusted R-squared: 0.786
## F-statistic: 975 on 2 and 527 DF, p-value: <2e-16</code></pre>
</div>
<div class="section slide level1" id="f-test">
<h1>F Test</h1>
<ul class="incremental">
<li>Both n1 and n2 seemed to matter, or potentially to matter</li>
<li>How can we test this formally?</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">anova</span>(ss_mod, ssN1_mod, ssN2_mod)</code></pre>
<pre><code>## Analysis of Variance Table
##
## Model 1: ss2 ~ ss1
## Model 2: ss2 ~ ss1 + n1
## Model 3: ss2 ~ ss1 + n2
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 528 66239
## 2 527 65688 1 551 4.42 0.036 *
## 3 527 65755 0 -67
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">AIC</span>(ssN2_mod)</code></pre>
<pre><code>## [1] 4067</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">AIC</span>(ssN1_mod)</code></pre>
<pre><code>## [1] 4067</code></pre>
<ul class="incremental">
<li>No difference between <code>n1</code> and <code>n2</code> but either improves model fit over the model without it</li>
</ul>
</div>
<div class="section slide level1" id="diagnostic-check-for-linearity">
<h1>Diagnostic Check for Linearity</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(lmtest)
<span class="kw">resettest</span>(ss_mod, <span class="dt">power =</span> <span class="dv">2</span>:<span class="dv">4</span>)</code></pre>
<pre><code>##
## RESET test
##
## data: ss_mod
## RESET = 2.642, df1 = 3, df2 = 525, p-value = 0.04866</code></pre>
<ul class="incremental">
<li>Statistically significant</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">raintest</span>(ss2 ~ ss1, <span class="dt">fraction =</span> <span class="fl">0.5</span>, <span class="dt">order.by =</span> ~ss1, <span class="dt">data =</span> midsch_sub)</code></pre>
<pre><code>##
## Rainbow test
##
## data: ss2 ~ ss1
## Rain = 1.402, df1 = 265, df2 = 263, p-value = 0.003105</code></pre>
<ul class="incremental">
<li>Statistically significant</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">harvtest</span>(ss2 ~ ss1, <span class="dt">order.by =</span> ~ss1, <span class="dt">data =</span> midsch_sub)</code></pre>
<pre><code>##
## Harvey-Collier test
##
## data: ss2 ~ ss1
## HC = 2.734, df = 527, p-value = 0.006462</code></pre>
<ul class="incremental">
<li>Statistically significant</li>
<li>This is not a good sign for our model.</li>
</ul>
</div>
<div class="section slide level1" id="adjust-for-linearity">
<h1>Adjust for linearity</h1>
<ul class="incremental">
<li>No need to despair, we can quickly test a couple easy adjustments for non-linearity</li>
<li>First, let's just include polynomial terms of our predictor</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">ss_poly <- <span class="kw">lm</span>(ss2 ~ ss1 + <span class="kw">I</span>(ss1^<span class="dv">2</span>) + <span class="kw">I</span>(ss1^<span class="dv">3</span>) + <span class="kw">I</span>(ss1^<span class="dv">4</span>), <span class="dt">data =</span> midsch_sub)
<span class="kw">summary</span>(ss_poly)</code></pre>
<pre><code>##
## Call:
## lm(formula = ss2 ~ ss1 + I(ss1^2) + I(ss1^3) + I(ss1^4), data = midsch_sub)
##
## Residuals:
## Min 1Q Median 3Q Max
## -44.89 -6.92 -0.20 6.76 59.66
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.61e+03 3.61e+04 0.07 0.94
## ss1 -8.72e+00 3.18e+02 -0.03 0.98
## I(ss1^2) -9.51e-03 1.05e+00 -0.01 0.99
## I(ss1^3) 7.21e-05 1.54e-03 0.05 0.96
## I(ss1^4) -6.98e-08 8.42e-07 -0.08 0.93
##
## Residual standard error: 11.1 on 525 degrees of freedom
## Multiple R-squared: 0.789, Adjusted R-squared: 0.787
## F-statistic: 490 on 4 and 525 DF, p-value: <2e-16</code></pre>
<ul class="incremental">
<li>Ok, now what?</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">anova</span>(ss_mod, ss_poly)</code></pre>
<pre><code>## Analysis of Variance Table
##
## Model 1: ss2 ~ ss1
## Model 2: ss2 ~ ss1 + I(ss1^2) + I(ss1^3) + I(ss1^4)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 528 66239
## 2 525 65253 3 985 2.64 0.049 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
</div>
<div class="section slide level1" id="is-this-polynomial-model-still-nonlinear">
<h1>Is this polynomial model still nonlinear?</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">resettest</span>(ss_poly, <span class="dt">power =</span> <span class="dv">2</span>:<span class="dv">4</span>)</code></pre>
<pre><code>##
## RESET test
##
## data: ss_poly
## RESET = 1.562, df1 = 3, df2 = 522, p-value = 0.1976</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">raintest</span>(ss2 ~ ss1 + <span class="kw">I</span>(ss1^<span class="dv">2</span>) + <span class="kw">I</span>(ss1^<span class="dv">3</span>) + <span class="kw">I</span>(ss1^<span class="dv">4</span>), <span class="dt">fraction =</span> <span class="fl">0.5</span>, <span class="dt">order.by =</span> ~ss1,
<span class="dt">data =</span> midsch_sub)</code></pre>
<pre><code>##
## Rainbow test
##
## data: ss2 ~ ss1 + I(ss1^2) + I(ss1^3) + I(ss1^4)
## Rain = 1.392, df1 = 265, df2 = 260, p-value = 0.003804</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">harvtest</span>(ss2 ~ ss1 + <span class="kw">I</span>(ss1^<span class="dv">2</span>) + <span class="kw">I</span>(ss1^<span class="dv">3</span>) + <span class="kw">I</span>(ss1^<span class="dv">4</span>), <span class="dt">order.by =</span> ~ss1, <span class="dt">data =</span> midsch_sub)</code></pre>
<pre><code>##
## Harvey-Collier test
##
## data: ss2 ~ ss1 + I(ss1^2) + I(ss1^3) + I(ss1^4)
## HC = NaN, df = 524, p-value = NA</code></pre>
<ul class="incremental">
<li>We don't eliminate all the problems</li>
</ul>
</div>
<div class="section slide level1" id="what-if-we-include-our-omitted-variable">
<h1>What if we include our omitted variable?</h1>
<pre class="sourceCode r"><code class="sourceCode r">ss_polyn <- <span class="kw">lm</span>(ss2 ~ ss1 + <span class="kw">I</span>(ss1^<span class="dv">2</span>) + <span class="kw">I</span>(ss1^<span class="dv">3</span>) + <span class="kw">I</span>(ss1^<span class="dv">4</span>) + n2, <span class="dt">data =</span> midsch_sub)
<span class="kw">anova</span>(ss_mod, ssN2_mod, ss_poly, ss_polyn)</code></pre>
<pre><code>## Analysis of Variance Table
##
## Model 1: ss2 ~ ss1
## Model 2: ss2 ~ ss1 + n2
## Model 3: ss2 ~ ss1 + I(ss1^2) + I(ss1^3) + I(ss1^4)
## Model 4: ss2 ~ ss1 + I(ss1^2) + I(ss1^3) + I(ss1^4) + n2
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 528 66239
## 2 527 65755 1 483 3.91 0.049 *
## 3 525 65253 2 502 2.03 0.133
## 4 524 64842 1 411 3.32 0.069 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
<ul class="incremental">
<li>Promising</li>
</ul>
</div>
<div class="section slide level1" id="non-linearity-tests">
<h1>Non-linearity tests</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">resettest</span>(ss_polyn, <span class="dt">power =</span> <span class="dv">2</span>:<span class="dv">4</span>)</code></pre>
<pre><code>##
## RESET test
##
## data: ss_polyn
## RESET = 2.485, df1 = 3, df2 = 521, p-value = 0.05991</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">raintest</span>(ss2 ~ ss1 + <span class="kw">I</span>(ss1^<span class="dv">2</span>) + <span class="kw">I</span>(ss1^<span class="dv">3</span>) + <span class="kw">I</span>(ss1^<span class="dv">4</span>) + n2, <span class="dt">fraction =</span> <span class="fl">0.5</span>, <span class="dt">order.by =</span> ~ss1,
<span class="dt">data =</span> midsch_sub)</code></pre>
<pre><code>##
## Rainbow test
##
## data: ss2 ~ ss1 + I(ss1^2) + I(ss1^3) + I(ss1^4) + n2
## Rain = 1.381, df1 = 265, df2 = 259, p-value = 0.004606</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">harvtest</span>(ss2 ~ ss1 + <span class="kw">I</span>(ss1^<span class="dv">2</span>) + <span class="kw">I</span>(ss1^<span class="dv">3</span>) + <span class="kw">I</span>(ss1^<span class="dv">4</span>) + n2, <span class="dt">order.by =</span> ~ss1, <span class="dt">data =</span> midsch_sub)</code></pre>
<pre><code>##
## Harvey-Collier test
##
## data: ss2 ~ ss1 + I(ss1^2) + I(ss1^3) + I(ss1^4) + n2
## HC = NA, df = 523, p-value = NA</code></pre>
<ul class="incremental">
<li>Yipes, nope, this isn't going to fix it.</li>
</ul>
</div>
<div class="section slide level1" id="another-way-to-explore-non-linearity">
<h1>Another way to explore non-linearity</h1>
<ul class="incremental">
<li>Why might student test scores have a non-linear relationship?</li>
<li>Tests are goofy at the low and high end of the scale, partly due to design, partly due to regression toward the mean</li>
<li>How can we check if this is occurring in our data?</li>
<li>We can use quantile regression, to fit different models to different subsets of the data and see if they are different</li>
</ul>
</div>
<div class="section slide level1" id="diagnostic-check-for-quantile-regression">
<h1>Diagnostic Check for Quantile Regression</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(quantreg)
ss_quant <- <span class="kw">rq</span>(ss2 ~ ss1, <span class="dt">tau =</span> <span class="kw">c</span>(<span class="kw">seq</span>(<span class="fl">0.1</span>, <span class="fl">0.9</span>, <span class="fl">0.1</span>)), <span class="dt">data =</span> midsch_sub)
<span class="kw">plot</span>(<span class="kw">summary</span>(ss_quant, <span class="dt">se =</span> <span class="st">"boot"</span>, <span class="dt">method =</span> <span class="st">"wild"</span>))</code></pre>
<div class="figure">
<img src="data:image/png;base64,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" alt="plot of chunk quantileregression" /><p class="caption">plot of chunk quantileregression</p>
</div>
</div>
<div class="section slide level1" id="results">
<h1>Results</h1>
<ul class="incremental">
<li><code>ss_quant</code> shows that in the lower quantiles the coefficients for the intercept and <code>ss1</code> fall outside the confidence interval around the base coefficient</li>
<li>This suggests the relationship may vary in a statistically significant fashion at the high and low end of the scales, evidence of systematic non-linearity</li>
</ul>
</div>
<div class="section slide level1" id="robustness">
<h1>Robustness</h1>
<pre class="sourceCode r"><code class="sourceCode r">ss_quant2 <- <span class="kw">rq</span>(ss2 ~ ss1 + <span class="kw">I</span>(ss1^<span class="dv">2</span>) + <span class="kw">I</span>(ss1^<span class="dv">3</span>) + <span class="kw">I</span>(ss1^<span class="dv">4</span>) + n2, <span class="dt">tau =</span> <span class="kw">c</span>(<span class="kw">seq</span>(<span class="fl">0.1</span>,
<span class="fl">0.9</span>, <span class="fl">0.1</span>)), <span class="dt">data =</span> midsch_sub)
<span class="kw">plot</span>(<span class="kw">summary</span>(ss_quant2, <span class="dt">se =</span> <span class="st">"boot"</span>, <span class="dt">method =</span> <span class="st">"wild"</span>))</code></pre>
<div class="figure">
<img src="data:image/png;base64,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" alt="plot of chunk quantileregression2" /><p class="caption">plot of chunk quantileregression2</p>
</div>
<ul class="incremental">
<li>The polynomials seem to address some of our concern about non-linearity in this manner, but remember, don't eliminate other symptoms of non-linearity</li>
</ul>
</div>
<div class="section slide level1" id="showing-off">
<h1>Showing Off</h1>
<pre class="sourceCode r"><code class="sourceCode r">ss_quant3 <- <span class="kw">rq</span>(ss2 ~ ss1, <span class="dt">tau =</span> -<span class="dv">1</span>, <span class="dt">data =</span> midsch_sub)
<span class="kw">qplot</span>(ss_quant3$sol[<span class="dv">1</span>, ], ss_quant3$sol[<span class="dv">5</span>, ], <span class="dt">geom =</span> <span class="st">"line"</span>, <span class="dt">main =</span> <span class="st">"Continuous Quantiles"</span>) +
<span class="kw">theme_dpi</span>() + <span class="kw">xlab</span>(<span class="st">"Quantile"</span>) + <span class="kw">ylab</span>(<span class="kw">expression</span>(beta)) + <span class="kw">geom_hline</span>(<span class="dt">yintercept =</span> <span class="kw">coef</span>(<span class="kw">summary</span>(ss_mod))[<span class="dv">2</span>,
<span class="dv">1</span>]) + <span class="kw">geom_hline</span>(<span class="dt">yintercept =</span> <span class="kw">coef</span>(<span class="kw">summary</span>(ss_mod))[<span class="dv">2</span>, <span class="dv">1</span>] + (<span class="dv">2</span> * <span class="kw">coef</span>(<span class="kw">summary</span>(ss_mod))[<span class="dv">2</span>,
<span class="dv">2</span>]), <span class="dt">linetype =</span> <span class="dv">3</span>) + <span class="kw">geom_hline</span>(<span class="dt">yintercept =</span> <span class="kw">coef</span>(<span class="kw">summary</span>(ss_mod))[<span class="dv">2</span>, <span class="dv">1</span>] -
(<span class="dv">2</span> * <span class="kw">coef</span>(<span class="kw">summary</span>(ss_mod))[<span class="dv">2</span>, <span class="dv">2</span>]), <span class="dt">linetype =</span> <span class="dv">3</span>)</code></pre>
<div class="figure">
<img src="data:image/png;base64,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" alt="plot of chunk betterquantileplot" /><p class="caption">plot of chunk betterquantileplot</p>
</div>
</div>
<div class="section slide level1" id="showing-off-2">
<h1>Showing Off 2</h1>
<pre class="sourceCode r"><code class="sourceCode r">ss_quant4 <- <span class="kw">rq</span>(ss2 ~ ss1 + <span class="kw">I</span>(ss1^<span class="dv">2</span>) + <span class="kw">I</span>(ss1^<span class="dv">3</span>) + <span class="kw">I</span>(ss1^<span class="dv">4</span>) + n2, <span class="dt">tau =</span> -<span class="dv">1</span>, <span class="dt">data =</span> midsch_sub)
<span class="kw">qplot</span>(ss_quant4$sol[<span class="dv">1</span>, ], ss_quant4$sol[<span class="dv">5</span>, ], <span class="dt">geom =</span> <span class="st">"line"</span>, <span class="dt">main =</span> <span class="st">"Continuous Quantiles"</span>) +
<span class="kw">theme_dpi</span>() + <span class="kw">xlab</span>(<span class="st">"Quantile"</span>) + <span class="kw">ylab</span>(<span class="kw">expression</span>(beta)) + <span class="kw">geom_hline</span>(<span class="dt">yintercept =</span> <span class="kw">coef</span>(<span class="kw">summary</span>(ss_mod))[<span class="dv">2</span>,
<span class="dv">1</span>]) + <span class="kw">geom_hline</span>(<span class="dt">yintercept =</span> <span class="kw">coef</span>(<span class="kw">summary</span>(ss_mod))[<span class="dv">2</span>, <span class="dv">1</span>] + (<span class="dv">2</span> * <span class="kw">coef</span>(<span class="kw">summary</span>(ss_mod))[<span class="dv">2</span>,
<span class="dv">2</span>]), <span class="dt">linetype =</span> <span class="dv">3</span>) + <span class="kw">geom_hline</span>(<span class="dt">yintercept =</span> <span class="kw">coef</span>(<span class="kw">summary</span>(ss_mod))[<span class="dv">2</span>, <span class="dv">1</span>] -
(<span class="dv">2</span> * <span class="kw">coef</span>(<span class="kw">summary</span>(ss_mod))[<span class="dv">2</span>, <span class="dv">2</span>]), <span class="dt">linetype =</span> <span class="dv">3</span>)</code></pre>
<div class="figure">
<img src="data:image/png;base64,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" alt="plot of chunk betterquantileplot2" /><p class="caption">plot of chunk betterquantileplot2</p>
</div>
</div>
<div class="section slide level1" id="test-all-50-models">
<h1>Test all 50 models</h1>
<ul class="incremental">
<li>This is just one of the fifty models we identified at the start</li>
<li>How do we test them all?</li>
<li>With a function and <code>dlply</code></li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(plyr)
midsch$id <- <span class="kw">interaction</span>(midsch$test_year, midsch$grade, midsch$subject)
mods <- <span class="kw">dlply</span>(midsch, .(id), lm, <span class="dt">formula =</span> ss2 ~ ss1)
<span class="kw">objects</span>(mods)[<span class="dv">1</span>:<span class="dv">10</span>]</code></pre>
<pre><code>## [1] "2007.4.math" "2007.4.read" "2007.5.math" "2007.5.read" "2007.6.math"
## [6] "2007.6.read" "2007.7.math" "2007.7.read" "2007.8.math" "2007.8.read"</code></pre>
</div>
<div class="section slide level1" id="now-we-have-fifty-models-in-an-object">
<h1>Now we have fifty models in an object</h1>
<ul class="incremental">
<li>We need to test each one of them</li>
<li>Sound tedious?</li>
<li>R can easily do this as well</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">mytest <- <span class="kw">llply</span>(mods, function(x) <span class="kw">resettest</span>(x, <span class="dt">power =</span> <span class="dv">2</span>:<span class="dv">4</span>))
mytest[[<span class="dv">1</span>]]</code></pre>
<pre><code>##
## RESET test
##
## data: x
## RESET = 2.499, df1 = 3, df2 = 570, p-value = 0.05876</code></pre>
<pre class="sourceCode r"><code class="sourceCode r">mytest[[<span class="dv">2</span>]]</code></pre>
<pre><code>##
## RESET test
##
## data: x
## RESET = 0.8864, df1 = 3, df2 = 597, p-value = 0.4478</code></pre>
<ul class="incremental">
<li>OK, not that easy!</li>
</ul>
</div>
<div class="section slide level1" id="test-residuals">
<h1>Test Residuals</h1>
<pre class="sourceCode r"><code class="sourceCode r">a1 <- <span class="kw">qplot</span>(id, residmean, <span class="dt">data =</span> <span class="kw">ddply</span>(midsch, .(id), summarize, <span class="dt">residmean =</span> <span class="kw">mean</span>(residuals)),
<span class="dt">geom =</span> <span class="st">"bar"</span>, <span class="dt">main =</span> <span class="st">"Provided Residuals"</span>) + <span class="kw">theme_dpi</span>() + <span class="kw">opts</span>(<span class="dt">axis.text.x =</span> <span class="kw">theme_blank</span>(),
<span class="dt">axis.ticks =</span> <span class="kw">theme_blank</span>()) + <span class="kw">ylab</span>(<span class="st">"Mean of Residuals"</span>) + <span class="kw">xlab</span>(<span class="st">"Model"</span>) +
<span class="kw">geom_text</span>(<span class="kw">aes</span>(<span class="dt">x =</span> <span class="dv">12</span>, <span class="dt">y =</span> <span class="fl">0.3</span>), <span class="dt">label =</span> <span class="st">"SD of Residuals = 9"</span>)
a2 <- <span class="kw">qplot</span>(id, V1, <span class="dt">data =</span> <span class="kw">ldply</span>(mods, function(x) <span class="kw">mean</span>(x$residuals)), <span class="dt">geom =</span> <span class="st">"bar"</span>,
<span class="dt">main =</span> <span class="st">"Replication Models"</span>) + <span class="kw">theme_dpi</span>() + <span class="kw">opts</span>(<span class="dt">axis.text.x =</span> <span class="kw">theme_blank</span>(),
<span class="dt">axis.ticks =</span> <span class="kw">theme_blank</span>()) + <span class="kw">ylab</span>(<span class="st">"Mean of Residuals"</span>) + <span class="kw">xlab</span>(<span class="st">"Model"</span>) +
<span class="kw">geom_text</span>(<span class="kw">aes</span>(<span class="dt">x =</span> <span class="dv">7</span>, <span class="dt">y =</span> <span class="fl">0.3</span>), <span class="dt">label =</span> <span class="kw">paste</span>(<span class="st">"SD ="</span>, <span class="kw">round</span>(<span class="kw">mean</span>(<span class="kw">ldply</span>(mods,
function(x) <span class="kw">sd</span>(x$residuals))$V1), <span class="dv">2</span>)))
<span class="kw">grid.arrange</span>(a1, a2, <span class="dt">main =</span> <span class="st">"Comparing Replication and Provided Residual Means by Model"</span>)</code></pre>
<div class="figure">
<img src="data:image/png;base64,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" alt="plot of chunk residplot1" /><p class="caption">plot of chunk residplot1</p>
</div>
</div>
<div class="section slide level1" id="test-expected-value-of-residuals">
<h1>Test Expected Value of Residuals</h1>
<ul class="incremental">
<li>A key thing is that the residuals sum to 0</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">qplot</span>(residuals, <span class="dt">data =</span> midsch, <span class="dt">geom =</span> <span class="st">"density"</span>) + <span class="kw">stat_function</span>(<span class="dt">fun =</span> dnorm,
<span class="kw">aes</span>(<span class="dt">colour =</span> <span class="st">"Normal"</span>)) + <span class="kw">geom_histogram</span>(<span class="kw">aes</span>(<span class="dt">y =</span> ..density..), <span class="dt">alpha =</span> <span class="kw">I</span>(<span class="fl">0.4</span>)) +
<span class="kw">geom_line</span>(<span class="kw">aes</span>(<span class="dt">y =</span> ..density.., <span class="dt">colour =</span> <span class="st">"Empirical"</span>), <span class="dt">stat =</span> <span class="st">"density"</span>) +
<span class="kw">scale_colour_manual</span>(<span class="dt">name =</span> <span class="st">"Density"</span>, <span class="dt">values =</span> <span class="kw">c</span>(<span class="st">"red"</span>, <span class="st">"blue"</span>)) + <span class="kw">opts</span>(<span class="dt">legend.position =</span> <span class="kw">c</span>(<span class="fl">0.85</span>,
<span class="fl">0.85</span>)) + <span class="kw">theme_dpi</span>()</code></pre>
<div class="figure">
<img src="data:image/png;base64,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" alt="plot of chunk residplot" /><p class="caption">plot of chunk residplot</p>
</div>
</div>
<div class="section slide level1" id="residuals-have-uniform-variance">
<h1>Residuals Have Uniform Variance</h1>
<pre class="sourceCode r"><code class="sourceCode r">b <- <span class="dv">2</span> * <span class="kw">rnorm</span>(<span class="dv">5000</span>)
c <- b + <span class="kw">runif</span>(<span class="dv">5000</span>)
dem <- <span class="kw">lm</span>(c ~ b)
a1 <- <span class="kw">qplot</span>(midsch$ss1, <span class="kw">abs</span>(midsch$residuals), <span class="dt">main =</span> <span class="st">"Residual Plot of Replication Data"</span>,
<span class="dt">geom =</span> <span class="st">"point"</span>, <span class="dt">alpha =</span> <span class="kw">I</span>(<span class="fl">0.1</span>)) + <span class="kw">geom_smooth</span>(<span class="dt">method =</span> <span class="st">"lm"</span>, <span class="dt">se =</span> <span class="ot">TRUE</span>) +
<span class="kw">xlab</span>(<span class="st">"SS1"</span>) + <span class="kw">ylab</span>(<span class="st">"Residuals"</span>) + <span class="kw">geom_smooth</span>(<span class="dt">se =</span> <span class="ot">FALSE</span>) + <span class="kw">ylim</span>(<span class="kw">c</span>(<span class="dv">0</span>, <span class="dv">50</span>)) +
<span class="kw">theme_dpi</span>()
a2 <- <span class="kw">qplot</span>(b, <span class="kw">abs</span>(<span class="kw">lm</span>(c ~ b)$residuals), <span class="dt">main =</span> <span class="st">"Well Specified OLS"</span>, <span class="dt">alpha =</span> <span class="kw">I</span>(<span class="fl">0.3</span>)) +
<span class="kw">theme_dpi</span>() + <span class="kw">geom_smooth</span>()
<span class="kw">grid.arrange</span>(a1, a2, <span class="dt">ncol =</span> <span class="dv">2</span>)</code></pre>
<div class="figure">
<img 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PxYXBk0RYKaAo3rmgFofHxFKqAsNdQvXQrRQAsQi0XoPFUBsaseidXsh1eMKToOJaZWnkPpDdcYQCkIzDKFhZprD6BioYNWkQppjePkXSvvxHXZyEwyjnhWFalfnk9mw4BlI6WlIRKz0QAZBAVXLEoCsVc5Yd/VAyiNgTkBdO1ZWAGADE9JguqNJwM3ABbeR1+XCNmhgIIEaqBMPsElICM0bhMxiJjdY1TwU0Gusb7EjwlAjBo5q4gCXSdDYgF+Mpmp4gELtIkGKUnAlh7yiFFcNB7l0fBJNwsFVAFDB6ODlOe8L2EdOsMjTrLNri+A5mdhcpbAKIuWyNq2Ij3u0oRoK3fQXgUDyBgUg+A80AZBApDrugG64F0HwNUk6yL7WVlL81xnh+LOvBOQi9xAgmENWaNvkbWEKatMjTUAUG49M00xC4CKnRrrCyArciO9CqZAyasdsFbOmwKFZmbAkeM4wNhIiDYCEBIf5WG8GR49MA7ZgNMxCGukoEX2EiauMj2uLYCKWBhDKtl2PQEkn3spa7FwMBGLWowD8rJyaBn+AjrjKjwP8eN55CrzSOpBJQ3PHsRJxo+OThOv/I8PQAXnEl4uwBR5qSxMf2oG9rdAS8rEelqsnYuUw2IxYMrdAbREJFYj3SGyhPYhNhHFCCCTeq/jjGJxql4hCzs3IzpfeiwzxRmMVSwiN8OVuDKamuLotx2ahMHgsWfoCCdjkLUQ5BvHU72YN7LbyzjK6NxBECQOkjRUokLoTFll/GZRIMPCllzE5VOg3LuD197Ucq52NojbAQXjE4WiCx3oekKIkFM5Ox6cR3yKyA7li5Hcg0K1F7RUkFfieUTJ5h9DavPlznDRAMq90lByjUOx7wjJCAQP7mP2wYfknyfpBpN3nPfeAxLUU55EebC3FYUcjHDFI09IXMoagQgxkQFqHmDXDUCW5JIXYn4cAMLsCv6AWpaOKAvERqgee5IyiLGHxOoC0LN2dgBB6hiFH48yMjwlMjaGA6E6NgjRP5a5FFuFIuOXv/YAmuypyE4RZSB3HQFUZE20DYkkAIemkEYQnCBPQvOO47FTI0QjtHJ3HKUegjDtupxlGLCu5aGhCL+ex7QxfSUNoDHCUfxmA4iOEPUrWtEi1sIbT6tIXijLOSwLU1A9cKad90Dmodz3MKboaM8Fdb2HW3YcnaZBJ7gsdKPh2wTIWqFqxMLiAuTkV5k7ZB0BNLLQMI2FJQDSYHuDAGQxk1CrXZSjc8LZGI6DKryLZmasoIBECYRoFJIo9tXzMO6MFbKA5jiPtSEol5s6mysjz97WD0ApNEyfwrCwNxtARqEnHf19j7gTiMsgIgFYEC+AIheh0iR93uVkVMXCs2hqYUvyO8R4lLlc0aBLvtEAsk5dYxa2oDVqMCjYMWi1Tt5/vzWA37h/0Hr8y8fw7/3HJ48fnwwGPdjxGL61Hp/ggG0neOBgAL9OTt4/GbTgRPxIJw/0RYrNZ3heZkPBMtcLQJZYPJsjIhs5vfQi1oYCjRvhCSnvkkoo2akBiUEYS63zDBXFB/FRrP+fOA5K1+Kq11HU9KlXfCXaec2E6ORzERnKTZFL3lh6EWsMIGEgrSRqnv1haIoOKGMDZSB2jmG0ouNhTgadiVA5cUg9M6bJgMOmQyuxsOiCNwCabxHrBSAjdFCShZCEMBRpOJAim1zKBaWeY5KZ6UBKb9ZWJJxoQPGLSWmFkN1o8RgA6UtfVwD92FmYmPVYXQoVh2LQCz+XeEMqo0C2ZgqHVi5QFJ9SwGJS1zB6LNCBQ+hMZZ6VyMKBFqVTzn8rFnLaKtcbQAtN8cYAyIgpOu5QKdHB4xYmLpNwg9IOUhQiPpTP3HS1sZlzCrUTFucYsPijhZ/kN6bUJ7FIYcYkfQOgJWe4mrQeEU7kjUt4M7/jFkZucMKgVGuhJDDyc/hAjNg8qDwt8BCIMLVZiz+BRHiEpt5Lz6JMWZP0DYCWnOGKEguNO543xOSAZ6nWc3fuKhabJaiHKgAhKJoSdRhgRjwXWaAUaCzQ0dIkJjCp9NqkGJHbLUgjZ9oq4xsAzTTDlQCoycZjy5SoY8qC4Fzt7Oy4XEWB6JAEqCINakqCIdAYKZ1IuENjYzAQgYdSyjgrWgfGsiujKDP+egDIRKHOPUU+JnrhRYyb4SpYGMUDpWgBmpUVZbkHj4Od91wvxOKZDIOQg8ZCiiMKJMcQq8FQ2Q7U8gFNSupEh7q9Bp0UJzH8lII41yrXBkBJHPy8U+RLMCy8iLEzXJEMlPY1UGWpgBKWvccYSM+hHR45UxWwK8UBzj1S6BXRJuUF2lhIUdGD0NbBpMq0FcNvIkdmXeUNgAoXk91wmQAyJKeXTiENBS8ULT+gqCCSghWaehA/5JgHBDWp9B3XbNUSMYngKERLtURTcShJVGXXW3BdAWSxsALjj73pDWdhidBjxZjGoo4FpKsDVTlR+mWHVEFcgUyE/lT0wft4jKLD9IRsMALADThjXluRYvOBzU6at13reKCibHd7U3Fyq/1l6UWsCYDMixSbIRVM4FT4lsnxCQPCj6KEDA89FQ9dpaQeUChpP2SxZgARaaKaMDo/zLCwhLNd64jEBQC0QHL05DVkN1wJC4uSLeL7ZLUdJeYT0ZY46SKIFRUWR2uico8peoyqAwW6lZhCmHloSOTK9om3w0AlMpe+5gCawsLsSvXZ/ME3Jh4o1Hq1fNNNvwL92rFKa6zlIhKRPQ4ZA0H7oSeGH6I0BCAkTq6LPjRqnkGnse6fBAVFmctPX2Vy3noBaPJuq1dGNgVeJzsvvYirBhCTgCiRgLQLTIQh3a0n1DIwicayhVgY17QLHJeLmFGQPZKo85BS441fNkjCyiY9tjcZQHYw9JsFoJ4tQ4cp/FCGqSQmkyCkK9yhmOQrLUV77EsVl2ogWpgOBXpzADSLCGz6yWdYmO6ZZ010/QEUS4BOOp41lu6UIQXHJ05WoUA6rAMNiQgginDFkgqgmmEXDcrmaCXsMNa+VLlCcUDZpFXyuHoAzSICR6MRIQiOPE9vtwG0xCLSV8tuuHxDYhim4yt4YxBIY9RzcTuEuhCHx4ZDqtLKFEmX5wjUjoO1hOiEAcdDh0Zc1r/GBpRNXCWOawUgPNSeAr5aGRzLLCJ9teyGqwFQfhO9ewKQaPYBNXLyjJCDNMgPYiVg0q2eXMUZiugL0w6MOBW1MR5Aqw5ppX5qVnv0S2VhWQABqgpUtoUWMXGGK3GmplehI4EYOQMO48DyPyTruNz0ifCCHQupJQIpWrrYFFujH4dcajo09MtwwZ65cGYdYbhSAL2gflhJe/TLFaLTLAzoz2jeGWZZxDoAKLMKkyBvACRFoon2cNMMKl0fuMfoRN1xXS7bGoTimif6daIti4EX6K6ZaatB1gi0agC9/jNpC8qdHTM90Rd5d0t4sopzf95MAClOSZZXfi49nKSECxXxZSOR8h566Gl1HeFsYpHGSvaBagleuOQLOWiVpYXZwa7myitlYT/87/8egJP0ll28J7oeI5RuFj95qWvPPK4qpDX5ElITb9OiCU/jbB7pnKoLTgFqHlJwNClhXH+BcEX4C1ta50ISRHMo7ROJNC+7UGfqqw+/SwEojpdlYfh+suvRe2acIjvj/IuYNsNVCNGpIOWYojFio3efMx2hLgfoQcXqG4QKEIcekuVZ+mCiC1WxJwwRdK4nN6GHSns0ojz7mrpKHHMB6Pv/6U+rBtBYFpZF1oQpMhMusIgpM1wWgJLg1dAKacVt3PU01j2+ziVBWQDkOO85WGcckLTjNSlNXhdo5WquGHmG0KPL2V4wLUyHmoXNsMr0mAtALz6JVw6ggvXwh+sIoJR6ajUAnw1Alok4pJ4X2l5MQosXiks+NgDi5EEX+1uyNuY4nmpS33iKFKLWu55YqAORhnW5Rb6kkaIvwxL9/cco89z6JN0e/aK0sJlZWNoMMKXb3CyLWBxAKfX0xbxdmxMAxaGuDyQOLyEbVN8u0CxMW4JcRZGtoHq9txMEvQDbXQbS0FCaYor/a2CsSSLsJKboy3JlEHCuTI0vmiKKjJ+Dvyy9iIUBlPrLIoV12gRjWJisQr/jpNFyTE4KokBsG1TSOTXgCneuG0bovCC9nrcnVkNO62GCFFpoTV1u+irTYyEASXt0HhcCoEI6UtxwjpUx8+UqAWTzdlZY45ypY9a1ULsnQyWMxY/Sc4JzEYG4yC/3iHd2gAR5XtxTVN2F9pAZSPsrAEstO51Q25X0Tadk6BSYzvObzLh6V0Z+Paw753dFxS0vySFmHzRlGZcDIFZY40VNHT0czWaPvzT9Zq9H26Lesd9sRrQTB+yAo5q+7z98eAz/46H+Q/jew41wgJkRjj2GWXAmnqgnV+lZl4wi/mptjlK7ZzFzXDWAiCfNAaAMvSo8d65FrAJAorBOm2DsWpTqJcHvWgcLtSJG6TnopJDQ+UAXE8fUZo+bOWOPXi8UOw9J3J7XCk09Dhxh0gIojuLEr2GzNmNIHKPkryEFKiBAVsThuCnMGesBIFFYp00wbi0gwBwbcTrkHjsSAw97Ma6HfRKSNag1KwaQy4IzWYXIJcZWaizzKwVd8BI6tigdw5/o97zZcmVcJxYWp6mKDagxUySHXCELS4RorbBOm2AsgJTyQ23xw3Y7XiA1fkn1Gmhyw3nLJmIREdb0qCYQyNsO+uE9DSCM+RhI9rK2MFmYSPrbpRaycmdqflyMFpYiQvMBaOlFrEiNX5qFxbH2fHLvSvJckRfsxEM/GNp7pEqQKckahBGI2R6J1+6OCpIO8kiuzjV5CTV/NJSmN4bCrDqcIz8uAUA2OZrKwoqY33yLWBxAop6++BC/LAYg643GOiMjUJrMcFp7cMIeMJf6qXBKvCdd5MMeK2ox5hoqCcOnqeCUlq3XBSmOdX0DyvLrybCwNAbme/1FOtn6ujLijGFGS7kW3aAOPMEJV0VAOsTCDyWlcrBYjylWiN2fPN35Es+Hjy0hO5JHb5Uqe5MAZIszcQ4DPyYACX50yAV3VEE3V4tePnd1UrojT8g1DyMUoNAApEiYtgTlEIFndCxqNSdCeVAUQTthldZYZwDxh6UAdMksbNxYMLFQl2wxxmRFgAnJIMgt5TCSg7IKmZbA3maoDYW6zaEhYcFjLylTL+WEQhG07Bj+6atMxhoCKJ0wmKFH6+1MHTcWiQfqhSbuVBuOAwoxtAFE+RfcGSPgwq3YMzXWpaIkfEgrWFjhXmYPRZxiB9sbBKCRPUcGPxPtQCtcxAUCKPuSJrkyrFqqOkBeV7sbsF81oFxV16FkZs9jc2JPkMNCkbAsbteCLIxXkRh9QjFQRm8AC0O82G4t/vkmAShnzZ0IoER2CbQpRwqIDcwsISljIeefUthPj5kS98eQGURoDk+U4CaJ58jERBeOawIgMkCPMnjJaWPZKVLmouUXUTjDigFkgWgiC9OflJQVl54psQ7n4ClZVFYu54d5qhlLwHSQXIyN1J732DS/tKrZ8aLeEAAlLKxIfyqYwjpMPq4zgOJ0CMVsQfWc+R5ibzkdm3EeB6Z+VMAVFKgeEEZy+AEXANINVrTT3XNd58Sj7t/sFlFKr+kNARDnuae+TZ/imgEIx9wAYgnGoxZOktocan8FAygmTYzKlTnHHMzBvTBDKU5Oh3nUa5XdZjFnAckFim7aGtcFQBOmSNB0Fo3bcw1YGI95WRh7rqSHE+nmAypMxhVa2OzsOBJV5j50XPTC09FIiFwmSPgLszKMAGQ5VZMAyOJx/QEUmajD6Gyar/QyAfTDl+QzfWvc/qkTTBaiky/EpFwunamw92nocan6gBMuOBcVv7jHGJDIbQ5IKnJdrrmJFe0HMlmCHGNqLHpsegVvAoB01OE6Aei7D27p8ZOvJ864PICo82AgYfKY4046GSteVDnR3XFJW/OOAykezeV/XQrqCAhGVCc6MSuGUq5hHIAMr73eAKL05STELMvCimaYjLFVAej7j01c7w9fJiG+RWMxQ6L1hesjckJpwKyIAzQofRCBRHQHZWOf6nIY/wYbrIFA4VEtK2SMRKEk5v6NBRCmrtKOaMYpJrU7nHWGzLiy1OakVHSoi4KTZ74V6IBEMh8iODC2g85osgbGdYCp7RyW4OQiUy2ayjjnuTN4crnseCNYmAbQzFNcKoC+/5t/eDWNf02aYDKAQlNATFuh2T2GRTa1WISMDAWgQEojBn5AJiMpHKQIX67juCg8y+VY+oG5LWvjmytEZypwzPL6L4eFxci6fvJ/fHzr1s/+NGXGBQFE/Zq0FqbdoNS6UrE5J2Bpx6NGlpyFGjS5QCtbExlfHipmMan/xrMRSuFp7dB4cwE0ZoqxILlMLez7jz98fevDV5MFoEkTTKNAKNeQKGIskBRbeMJx87r4BnEyji8LgmOiSmxrFgARpQrIh0YUh2PudV16Vuyvb4m7/Hqy6CgK5yiIvF/ZIuYC0IuffH1hAIq5nY54HdgqKE5RIj0S3YEGRMqSJ7g8fG+HqoeHrPSzMVEio1sMmSCJA+KJYTTfnICyrBsj/S0BkChmxa0OJnCxFduBfvb/XoAdSNSiUL9vtv5RcTHc3MLKGyH3KNRZGZTNDEyphI2gQql+J953CtzAxEIRqhJnqr5eMCGgjM1HY8YKAJTuIb7koCnOYOgNZ2fWN/wgX/R2+9jiGRZbgz3GC9HffXDrk9dTRaC5AURCCY7Uvl4AACAASURBVLqsJNhCAGKKbA5IUafKZIathRITXXLI44Gl6XW/DJbBuUVCqjyidcXxAJKy1GPGWlKglAs+GqUcrGeRKQ2diXjVcYxxnKVacy7i6tV4fL89KgpFsgyXe0a5hVsUoDAcku1HSteJi4xsRD3F3Z/ING2sAGwWGljCeHKtGInc+Jjo6wgg67vYoBks8PksHaaYgM3Ef6S2LrKImQ2J2g69ehkI3mrPtKREWYYzwqTKC/X9AsHGofwdgIvj6ohE4EWUiOjA8LTuH7NLH+1Apv9uKnMQy0uPX/1Fs7D0ZBPHAloYizoSHg0AOi+Ik47tbZG1bbFFrAGAcBWhp0S6IVmG9SpWsAZMmBwqWxYG7o4jZmqkXFwiEXMyXLJb6/BVmKUV6sRCAy0BkPInLP/aCdHW18hGB/7kKdLGIQ6eHkX2DOOZ2DVgYbSK0HAlJZXCpVA0lWmJOfkCjwwAMC57NgBfPeRfrudhoVZT/DdkialF5RJjXRuRBv2mPEbD1mYPvF13AGUFHF3mN4MOXSXCnuENARC7rHTyhNCO4ETzNg6ZVw6nogao1/tSuJ5aNgdK6rgSi/NOJIfVCgbiwRX1bKI04yqvDYD093gcC5MUjktkYThez8jCFtIFBwP4dXIyoHF+Pmi16Odg0Do5gc+Dk8cnuOXkcYsOgl3v//Lx+8d4WOvx+++///jxCZ7UOmmd4zmP6bgTGC38f5C62qB3TlehC9Hl5lBZ1xdAVsKy1rgSLSxfwYNBtPQi5jEkXqAMRD91QkWsjUK0qUVOC45wlTJ21MjbBWnI54BVx0E6FOiSiGynPtHN5dmiZJdX6CUlF94gFmaGVsU0gGLWz+SDOfnyAfTh6598/frDaTMuFA/EvxJ2YrXWQW88RXGgwZmj7UnURuXrmJgTFoqmKguMIJazQYjWNV0CVuwC4ybp6ej7LP+auMprAiAuRx4bFqZ1etmWSNTpqOpFFzGPJfpDJEIXQIFMsrptsNHx8ZjWQ7EcCi2HHnfloa6EjuM+JK+84nLjuvoLQssLuTAVDWojpjMWrdRm1vVmXWV8PQDE9eyTKUQCkiDFaDQcRtaxlwmg+Ls///rVrVurp0BhUNAvzASCBVjnR2GWBqc3Uy48NZAHyDzEmHrueKlcxQSGOFjABkjBJVeTjo1O37MIXbb193UFUOLtioaGyCQA0rxrOLRJ0FUW2Rw75gKQRG8kiYUptYj0qBNs6QRgQW/pDiEI++o6VFr8ISjxAAyP6zBIDBpTJGUAFErbeZkyFc6RWB8nrVKPtQUQ+TCGmsgkhOU8zorPlq/jTQAQ85QgjDIA0vwL2dH7Hpf39SScnuvSY3noIGii+h6zJ5Xm4oIe5FttxcaxH4QWnUmHtOaEoOsIIMKPBpCtthdMoQmQyNlLL+JqtTADoLS/KtTmQAxQ3XY5kRlDOgA3BBSsVI+QaVKMEHVsDqhcom4+57jqRHxhBj7JJSY9tmsKILtYawILM4VVAyZpR7eSRVyxGi+aUmR9j8XhTjkWnutsO7qlZRhivgXpUR7XCmpyvKFSmG244yglzlaMOGvpGuOSlWopXW8agMbaAc91noaRj0ZRouSvZBHzsrAXFyBEJzxFPBqhYAD7OHmPPUmXDzjuVdpmEKZ6oXZ4BZ6zQ1yN20KF5I3XlYO0zqUjg944ANnbohQFYpXMAtAoFVp2+QC6uIhEHKEEbIS6Qxim9bBcA7JOEMRMiajpATK1Zmxi5QPpecAYQx+aWAlTrtQFAXSaLHPNAZTiZQZAhoWNonTr1GvPwmJ+yRYLC3VhF2ZAaEgk6Udx5o7YmhWngPW0915KepA3VhoXDuwL2MaB+QF0utYAyrpKR0kU2XnOFT8apatSLb2IuQH0ybj9UycoXgtRhZRaxEEZhucMSCBi9V2Jk5VyVWEDCtGup72wWoLmah4Da8qMz3ROAJ2uCYBMDIYRnvlbBkFWSEf+ZjK9my+fhU0fMwEoY3OO0ru0l4rIzYBVNRKQTci9JCr7gXIDkXMCKZ4YMudLABQI2UoucT0BlLgjjLoVxzkAxXbw6rm1RTR37eVYcBG5cTUASlkL8wV7EkcGAog3kSxMvQwwqszlLJ6mkhKbiqtHh+KewP/15cgcEKRcFvMB6HS9AZR3tCdhrOfJFjYwJiOZ4VIyU1cckZj1YqaLFho3OVGU81jMOVxiAcHhgsZFNummlIam7hiUmEi95iwWpkmS7YyPbbPThFXKWBcAjWFhOVuzNGhOphDrz6g/FHvRyAZQUTBZgSVp3LgaAGVfYKpsaihOT6lbN+ACvuxop9rjHgVBoxTtSyNdDC4DqsQns2BNQrQp+mrVMI/jOMoCeMwqaZyuDYByI7EOprYmRmkTkUiujv5wFOv238kMBQCabMsuWoM1xrMw6ozxYmV5YZZylAUQObSkAWHQCqT/E/vOKYfHfW+HSgj5XIYBXR1ctoyjN6jISytpGa9btJiGc2EYZp2oY1bJ+FljANkMSQa6NSIzhWZpgCo2Cdl6WTELuxgAff8xAWhVarz4vMQwkyIIugw061Yt6QMfinceo8WwZTOSnKbs45ocmtxQ/4ygJUVhRBw3dkSS2XPZhmNWKfhZXwAV4MdymJ4nORpR2ig9eRGrZ2GxqVC2quIKaQDJJr0r0N1UYLSkbS5SH/aKeejS2MGGqk2snolsDEsqOKx9KW5rgG2ixCgZC8HRlwx6BbHQxas8vQ4Aym/Xm8507HPBzst3ZRCCVpeZarOwiDeYCDBSujH0J+Tuy6JLUY9vIiaui1GKQRMt0tLNZ8cUYWDnBVb1CE31cXNJJGK9MJ6Rha0tgMzrn6BDWSGtcTTKkqnosiMSZx0LuzISVwOTCjYpS5mWGNvrKo4fozgP9GyE2LGQg4GUy9nxVEdILNiBlLi3B1E3Kytj8ipP1xVAxa8/G1U/epngB9majaI3EEBa/TIqPGWm6tBUkmxcT0s5xLuCHgKIDM8sG4XSDArPHwQsHQUJ9dHX6I2Jh86u8nQpAL3mcpJAuFff9tt6/ZkwefpAQhD8fKmlIXai2n4MsSguswieJ7thnBr/1oVmZZjXG0hNcTYZIgYGIrlg8UPu7STlWmFrLxDPKRqHqFi0+PJjSXIPpZZZghixW45F0LksBH8uBaDv/vzr+DU8rVRnxxUByArGsHVy/VE8qACgYYKgKOUIu+xwjgsGkFHjxelAvi8JLDsXEZq0c4+TT7F5GFoMm2GYJLSifBTHsZiG2JBIcpQ2LBnEZESu/Cp53+lyFCimxrJJb1nqiZ7sW+LdiWYeR+k009hiWEycXqZ9p9EoS63eFBZmAMQsh0JTlcCJDYLkkceARC49Lw3kehwGrXPqQ63rI8bwPGlHF9okKM4qfQWrpENPlwfQq5/9KeluTQCKVjFGMjDHQn+MtIkw9Umsz4VzjPuy5Liq1Gb+EIjNJ2QChJp4SxeOZvsO0xL2b4XcZ4y4Fuv8oXbnU5VWqsyaqa1AlytcBO80LOx0aQB998FPvrbbo8crZGGxQVJCTaJcCuq57LLOy0wkmy8ltfliq7Ty4MDD0PROCbFQFOXsSC1WJjHUei5gaZgr25n+qGJypDrR1FvDcsSnzU6ZITvNKpcHUIwy0IUAiM6PYl1PimI07NIusYACATQynQ8KgBIZMC62iPkMiekqrZZ28douXz8HgIyLPLI3hTrBgoXfVkBZYJ7ppEKBQRRUHzeDWOr86hg0CWBVjtcyKlmOBEVF/CsDoNP5AZT/CwPkXBiAaAqtr480TjQWomg4xPIu6ERNJOkCAEVR3tY4zyLmcWWkq7Qm2oXWN6ZMkFtLYIIs7FVIGo7nCShaaCYkKNA5FFom+TvkjadeK0KBJMEHnWPO45BFKd2yh+eWyxVJ0DYLy+BnJgAV1EFOCdGZh7MaSzQOFoe04Ky1LhCPojOiUgZARSxsAvWZaRFzAciu0pp+MLacOPNaxgGIEOQpiWwdaNcYMynKQuWAMuUdYzgr6GYOd+NBRU16Z7huK0hKtgZpw3MxgOxVni4AoMxfGP5JfffP/3QhanwcW5ntIgOnY1UZVWdpFlYwy0RT9tRFxPP6wqwqrWnSjPpGPLei0WzqT71eshU+93q+7x/3+GPPb8KPXtPv4b4m7GnCj55fOj4u4THNhw+bTTgEth77OPDghz5u6OGxfC797kVFF8yPb7JjrJKRBlCqDvIrtnl8//EKDInFERdMcnQMdDaoI8JuPaMoDxBry1hbdtEiCsccQnS6SmsKQKRvTJsgt5aECPRC6bisd6BiTn5RtkSj5q4kLCik9k7ofXcdP2DjM9fDw0APaTsHGx+TDE51qQIuc2+6hk0rNJ6lP7OysOl1kBcEUIHwogEUaQJjxa3GOvb5bDSyRBxzoGW8Lph13CKKxzx2oBe3fvrvDdPKUKAFZKDE8xX3Aq7+Y1xhJDBzZehzcYLqmvQEIC6L6Dz0lLToDaRPGEtHqH89Dig0iHM2uCyDFI4Ox1dppVXm8TObED1DHeSVAciwsChKKe8iE0uNF2Bh/aFR83MhsalFFJGxQgBlKF1294SAMiDJ/24cCytUNCavxfgWwjAKdGi83sE0B3s0n0ucvW5sSdH1GJEIsk9pR0kBKa754nHvOZjFc973GEBcv17ii3jyyQAqwM+VO1OLBRVDeSJDZ4TRou4VoTe+3zcRiFk5G0fWND0DC8uAbC4hGkAzWYieOEERCwt1anNol1PVPzFiA2OiQ52qSkWCiOKgkuY5JanYyoTJk0FOVPeXnmTNh6EERGv8TGZhFmyeP58ZQDPG/K7OkEhvMvnOI05sjDTOh90hxbHyURmBKCKUWVNcBoBeFKjxWt+YMsGY4gqxSesxBkG9l3IMz0NpBRZwnxUqH82tDpyH6KlgixHxLj6ATnV/ySXuQousceOeKT1TbfwYBPG+dQGQ4VPWlrRXVX6CDEQsTB+WygqLWNW3prh4Fmb3TBXtApPlX90qVjQmryUXkWgr9jr5K4xbOt1dGhkiRkJJtWhSJIdiEsRkSRAIMpDStuww1i0U2DM/8d19uxiAZhwXBSDemjvsDAOgDXHK5KVyTaH8xDMuQp+S3TBBiH41S8/dOSISk1QbvYow0OHPJjgoPFHMuLhcNCGIQhAx2pnywqjAJpdeEF8HIeZEGQ4Z61yxib4wGqcWgOZhYTOOC2JhYw4iNV44lTZZpw/IFpi6UDV+xjEXgKxVsClQ6fwbIkb4r8U9m6WEAvIp9GtQhSCQhqlgtMf2wlCSmvn8EyuSLNRB0XyV8Q/+NAWgOYXoGeogX3x1Dmsvh7RGbFNMNPhsVsZyi5hHBpruSJ04QQELs1bBr51zALnfk8dJFi2u+MN8CKiNg54xRBHgphdS2rwX6MpkKnHKD+wKmmFokDSBhSFUFgfQLAFTFwigbDAQbjk3zC4yQs6Qk36okuKllrib1q156gSFa7G8myF7SsVYyA3D2JBomqYAVnYcyushs6HqUWQHlSZzlZL8ZplzQICyr6Rl6AsD0PQ6yKtkYekpTBCZSMYEnXPN7OJEcBoOKUZoiIdNcHJMX0ScWwONyy3vInxMszDzkkNxl4Z8mpaKgtDdcXY8KvZCvTJCcrsq7uSsRAhiTnUe6yYHYhUwMnRy02mH2OlyAJqlDvIKhejYtuKYMFYUjIcs+MA4z0VMI3T6ozyAxslTawugVICFKTSuVa9Qp4XxaUnENIo+CKDQw7D6sIeYwG0kGzEvY2sARSTyDKyLJYZuS2ZPuVRPlwTQLHWQVwqgKKWUj4TujOQDOuHPojxGNENLsbACU/e0RYy7jcsq7xLaIm7PCjnVYdFaaTpPMkrZX4HtlzHCjJutwD7XoYxVxc53jpjGEndWKmFCfeybTgHodGkAzfdwlmdhKQDFGT0rkoZzGBaUbnOQOsmcfF0BxF96YWiC3rnYT6C7HYQnAqiA24AF0riQMsKOqRMm5Z96FDNEkdLUwCcYGGNAkHhJMjedLMJA5VoAiM6P4gIGxMGJGl/nMdKh/lAnNedCE1NmxAUWMTuAvvvgk3imTgfzsTD5kiRqaYqhTIj8iZiAEANUg56jg1DocZtYgJw0t0BYGAGGJKQBX4ZxqbOFxty05f+6LlpY4rxI8BDZaRrkymBz85DZFQcu0g6j108JB1oZgH748md/+uFL0ONfrCo3PrsK44gPhVdxz10sriChiKSxu2xDRLIDapivqLRmGGgztRa2g6Q+kFRcsIpz5G/69HoCaGSAY+tZsQ0gtjf3xUPP0YkEJWZrCQgXWkTRbRS//xe3zJhmDZrPF5ZZRcieUTY5S5FNKYpIXniqA4TtL0kaCpvUuVAqusa6QTyJO7rEnXaVBWFeiNbjdCUA4jG5DvKqWVhKrElTJCQ2XN5lpFN74lF/RFVeTLHWSwPQD1++BSD6EP7KVkmBjCRkSoYZ5T0MtKfsnGUYYVQYC+RiB2cy+fQCLk7GOOIZpNamLvMbGiRmEgvNSENlWQBNroO8YjuQraTHVkVW4lXw7SyKTGnoSMdHU/kpTbQui4URff5wJmPiQgDSVmPRl4zphigQGaJ1hVZAjyOpg4HqcQcxpEquqOwmxXDAcpTW6uJ4DAs7XRWALo+FGZlHf9XcSwpLEYfCnMMz0MFMaXGxQ4sAdMm58XOMCQBK5FhNcAINoECHYWgxxpgOW4GpL4ZwQPKjSQuVuKOcMa6sQHmJSmLIThhJbFcKjFfVumn8koPK0gCaWAf5IgBE1AT96mlxGQH0cjgc2UFAptCmsSsuvohxt3GBAEp0d/1J/45iqU9vbYe3RgAaJC8fv3uOJPggWo7JC0auDDqdsnok8PXE4+BWbSHQw9w0X2R1AJrz4azMlUGIwAKI+IPZExp/kIW9tMLJzLH8SVpmLLGI2FqDNSZmZcwSz7EYgHSPd/p+evr8GUVSPHv69OkX8Om5fvnEoSQ0NVYeAQhNiFTJjltpUBBPjBXKdHUyXd9Mu8ISAD3PQ+VaACg1BanmSHyIDgk5Ynv0WTr+J2NnXMkiZrcDzaqGzcPC7HggYmfPnvELe/YMYfD8yV8+efL75/gF/8e3j31UEEDUiVc95AgzLDyFgaxw/NNTCuOBE1oxT8plgijLQwd18E1b4T7LA+hyQ1rtKZiokAcsYtqUNA+zKpSxc2yo7YxGiF52ETMC6PuPzXOZJkhPEaLT/kvZRAACgqBjAAEvQIKeP3nym988+f3TJ0CI8B+O5xIlRMHO7kPkUSAAOd6OEzx79kSpp88pkBDGHxGHXA6GbYtJmQ50vZ0W4+e6AigTrSqK11mCn2F3BEo8V/NIop/zzo15F3HZroy0/zKWTfhG+bUzCSKK8+y5+o36y6e/f/L0yVP1RP3lM4DQU0HYs6euC/IQdm3GYlNP1W/gqGcKCBZRn2fw41uA4dMnT548I+r1lKxFz4k4Pf8DX2N2CvQoeVgTWNgMdZAvhIVljUD6FwaU6SP7fczPQCHbynROQ3CxRcwBoJUU2cwBiGSbXsycB4DBwg9h6cnTv1TPn31BMABSBFToyTPN456oJ7DhI3X6FMnOEyJSz+B42P38KU7y/Avc8EQhEFGiIng+fUZzfzMXgB49ejSjFja9DvK/OTcjOl9knJ1ZX6L0nrOXZ/TrTI6Tj/jtZa8Xhmcv4VGfheHLl+kZkuMWGLnbmCZEL2tILMIPv1GiLAYhj9LjN+rJU0DG02fy1oFdAcX5KwAZQgm41zMCjhyN9Aso1zOkPxopz5kUGQDNwsJoMvzAi50MoFke0GIUKBvUk5lCOJIU0iRjkAhGL/kANgvBAUCFhiOb2eVZWIYYrTQeaKWFxmWwKmQAhO+YXxtSDQTTMxCinz5Vjww0GEKAjSdPnzaeAvVRLCE9fYpnEQd7yseS2PRckPKcBfGEhY0ZFoAYO6ezAmgWEr0QgCzUaHeXPYX2n0okELEoLrcQnY2sNFVQ1br94TAxLEZRfhFZdrZKFkZentW1OuDBb9cA6PQ5oUDIxnPEELIioDbPmIgwuBAluK3xBInMs+eMGEAUH4Xc7tnvYeMz4Vmnp1oyOp0NQIb0zAOgGcayAEp8pckUWnvnmDKufydhQOEQ/WAjUd4pmhXxNRyO9YNdFIBW3WwFh/V+/qC5Cb41pBXP9SAAASCeaYA9B4HnUW48JX7Fx6HsjPYjID8MN2ZhWryCKf5QyLz0CjLYuXoAZRlX4oPn70Nt9pE6UyP2wIPW1euKaVFOHA05Pmiomx7YizBkyeZj56lvBeMCADSD5PVtevzxD3/8I314hF/++Mcv/ojjW/rxxRd//OL3X/B+2PHtH3//13/917///b/86y/+5V///q/gWDz4Cxy/x+306Qv8BJ/5PMADT/TFF9/SPOZymUHQKdrx7beJwDhWjZ+pjO1KiiuYeFYOgo5ErhFWxUr9cNjt9Ltfdbs6+VSMP6iEDYc6liMuwGUc2cg6zyVEZ8blqvFj/uqBJDwX8kMmROFf7PHC8i7Bc5ZhSAIC6qJA83qGMhBKy8+IusAH3ERxIHDY02dfIEF6zkxLS9ZMjORyp0aOfmSRnYXtQJcHIN6C5Eb/1g6MocljHnW6nU7/8/5wqBGlSyiOJB81a0i0CJvdtjcJPiseFwwg+yUUvxoawFOe8wskKJAtWQISsUprqPvNKS8gGD1Bnez0yV/+1TM6nuVjrmQmlcXD4Iun6gkxwediFcgzvkc2ciauMnlYa1Kdg1+zed2Mn37HpKBG/S6QoHAoYayjrkCJHB1DNldH6bywIgIkZTqL11B8GysEUOYlTADQN4Af0bVZ7tV+eSAoBKBQmu4qHRekUNlS/7VC/es5dQUL5TjpfBkPkEohvWIrEB54+pxJkpbZi0xB6wmg/NCuUB2kiqJQu91HnHBuT7c76oeoug8BP/1+p6sbxnPez8hITkUzW4uwnCFFS75iAMkL/IZVL60rhaF0/0aqM5BvHgUrUlaz9Ll0nV9QiyeP/BrM8FxPhz+fo/PiFBkdKf7A+J48Y/HcshrkpeklADRDHeTVW6KNYg9Ep93twr8+CNMgAbU7/WGIpp8+8jjYrDkRitcEILJKT1nGOEl+/G1cAoCS1yYkgHUv2RJL32Vdd6wlhRH0cB0K2cBIxJ0HWJ5VuZ4j/QywmL0SYzf7boPg6RMWfMiMnQFQwVgmsTBXpXXCw1kQQJZFyAIQbwH9qouSDxao77brjUb/5QhYGapjMIaGE0lq8xDbqE4UkOOMIFa4oOyGiweQxTj44yPbDsT5zYqdnxgthmV+qZO8FHHxKOiHuoK5JTeIleM6Lnd/CgIH0CW5ZlLZDM7SDlpxaZxeEICydZAnP5zFAJRSlcSTlYgoKCAD50J21m3UG+3+Sw4UAhANkRDZU2hbYwYWli4/dhHpE7IbJgDoxUzVFeYB0CnjJ3mjEv0uJX8olL6lAin6IhXGOOyQSpQdwz7XxQ4aUkzK23F1SOOAw8g4xNFcjMaFAShVpXXyw1kGQMZomGySrAsxOgPJ6SILewk6Oyjy/S5IQKCh6Tnopzg+svixYj3GLSJ9xoRbzI7vPpheHWg+FnYquvs3+jXpLBydngqYOAm5665JqkCBmUrVY9NdYGCS2UPlYDC0leN/OJZaxyCmF3NRLOzCqrSac8z7jczrj3TtDbISsj6GHAv9XiFiB4AExKifrW8nin2aM3Gc2UUB6PUM5aXm1cJYhf6GMIXn6DxmScPArjvSWYXT3nXqGLUHC5r4YceVXENqbSCFOEF7C8IkPD+9om8skWt1ALrAKq36FENsWNVmBLC3woSRjYaEniHKz1+h9gVyEfzP0fRJ5obuLm+BhSdLdzZccZnfiQHjuQlmeDVigvnDc4w35LN0frNuU9AKldTw1VUXKMLeA8kn6HF3A5a4CT+UnEop0IOkOlBmoNVAK305BC2jxqfqIE95ODMDyI4TS7yg9FkQwJHzsc497SPTQlbW73/eQaFoiPxMGhbi1tjAME551giTo1Rf+ZUCyIpKnDTmAZA24QGAUn24Q2lzQSyMM3c8TAYLNQkCZctxXLcnde2oDCfaGQFUEq+IFuxkusxNXwyA0nWQpzycWQGU0p5TDo2RNHuicGiTaEpRY0MmR92vMFcDiA/QoCG76FFRG0ZJknxKrxPZ6uIAND2aLJ4LQMYE/M3zRFjBIaXqSZg5cdmE6EmdRByYHAbqvNeMdYtwkqx3dlxpz6MoHShJtQ+F+5mbDrkh2CpZWKYO8pSHsxCA7IEkRgyII53qlXjE6OMwHLGDY8hqPM6EBEkipmO2RBtByPywVLEVF9lcLQtLXAjfxGkyITWCYJvnPsbyP5L9Tm2ZKX1nZwdDWZtWRQ+kP5jzzMU7UIjWGT3M3yyB2tz0BQBoSkRi8nEygKKogIWljxiNxDmBlVhHw5HxpUqH3YhqJHba3T4an/sjE9OhQ+7jSJuxbd6YrAC/XWlM9JRXY7mgMqsw7xoYmftL1+Xiv1RdyvFIMtrZwV/esS6qSWWkXTJSk0GIhG/dciMwTRKyAApXzcKm5T3NCiB8ezNUaU1ohu59ORyJTESZhS+jfqdR74rdWVusOeojSgCkffjGSBDH6w8gy/p8aq1CZ6QKOQLW9b4nee+YVOhijwOPdHi0+jzkJvEs/4CoFGg7ElbnoEqdStcmC60KUwmAwpUK0dPrIK8GQEMpMG8JR7qNKkrQpMH3Udh5Cd9BhR9GWjBiWXs40liRgBC7DYtlq4zXGEBIfowIa1ZhikyZH4FqBdydEPeCII3CD9bX9DCR+dhlUZvKvYgBSXGHMHLCSkWO5BNPm8br6gA0z8OZmYWlN+JANGgAaabDMUEjgs2wP+z2O/V+t38WjQBAQ9LITD4Gx0drQ0Bsi1kZI1C8vgAi9qUBZFZh6iLGOpsUxoALjnHaKrpUXWfHFXNjkxogsI9MElelyhT2Wk2lStudXHI3vUIAff83F2aJmMNC3AAAIABJREFU1q92pK3KCbmgQDGQiYZtULcQQO02KF7Dl9GoA4N0+74uCoSh0VEs2c+pAMQUCxuziNyiJtxiZvzw5SfSV27imAVAIv5wtFeyCl1iIZZcwEBqJOp2zYwaLA9EYArCZkiueE/S5ak8oiehHS0VpMRyT8V66txNWznOiwIIw8neIlPQhQPINgYaTFEhu4gtiPC53cZE+ZcY4gEAIuPiSAeXoWtsRCJ4KkGjsP3lanPjP4TnM0dQ/VgAWeIzGxD1KnRvSoKHqdIq3lURgrmjHCteTVLvQaf3pLZLoEv7xqDG23URQ10zD9lk9qZDK0t+QQBxTs9/8fGFVmnNOq4Sgw6HtWLpVWqOgawMyNGwhz6xNoKlixFlgiBBEyn6KcNkgca30rQefDSTzRzpCcYByI4A5MDDRKoNpHdhYAqrnjNWglCl6s4jv/N86eHjOAQgshQpiecYJAAydabEHZtt98Qi9lIAwqQncoZNptCrjAeKGC5COkSvIumIiwOB/PM5BZIhgProzRh22VyEQOLAs6Qm+Rh705XmhY0BUCqCNLbKZeAw3XVDbp8ShOccHhRK+Q4+AUvQA1KOsZq98nbuOsifqM6dFqipspnMGUozccFkvl8YC+/LAejDWcIVVgIgoyVp5+koacozwgggMh2iDboHhKdL1Kbd4OTmkYCNLEHI6wx20vjR31aaFzZveZdiAKVTZkx5Fw0Nu+kcOUXPA6rNGuoyCSHV5vA8rPTS5HjE93Ycj0twBDE70WCWgVmHEaC1TpZ/d0y0lgbQPGm7CwMo0bN1NPRIh2agtaffabe7nS5CA1gYEB7AUL/boXBX9nZJnQ6coD/KYceyCE1YxPjbmOhMna/dUyGAsvgRChSGKRWeB+nnA/SbqlA3JmTIUHVfz2tygJmz4wRsctbBaPBpkMxjmmaIfzUvRCdBH2tanSPlEDNCtHY8oOGHwjgAQZ1uu9botNF1gYmFXeBi/XYDENTnUCGUnskyzSRslJs9FRG0dmp8Gj+6/FOk66jyiaYWHbkkFNWqM6o6NofHgkBY8rfJbeaUS/Zm6s+C8Rx06MCSoSnqPhbHWf6mLT/cCgGEJZU+IfF6FW2/rXdsdKfIbOh3qEAZWXs6jXa9Qd7T6AwQhQjq4r8hW6uBIvWHfYwSkgAie3amZ/HqWdhC9YEKAPQo+15MwR6rDi+9ZzEAoj2H+8np+LAYu+0SVjzXtzU08tl7ntQBQi3MiN3SCZEomiWzZwum4ViZIfH7jz+JX2Nl7besfPBlAaSjUUcpSzQboOEn8CmsBASaF2pho+FXlF5IhGnYJeQMO+1GuwNHNNokKolt2gp3TZV/udoKZXkA5fCDA4DRizUH4qqY1POCX6w60bq9ACvggppUTNOns5TH9RFJp+fWc6SFqcQSpFkY25aiWCNXXPQW2zw/LRrJw5oZQBha9sOXnyTNifHZLcnCtANCO0P1XqYlI3ScooDcICMQSD6fdUkaAlm52+g2kCz1250G8DOEkXjoxRkmV6G4xqQV79XWSMwBqBA/SGUiSbsQTkUh9bwPDYKGPtA+7DcnZiDyxrMTg+RqbMTiaYPReaiCHIlhKEbaXxuGui6sGcX5s8nDmsuVAVQoaY9OAIqWGuxvFy1dlC6jfUWYywOKOlIgjEFERtYA5oXejXa7oVS93en3u3XETweO6Pd1mJlOjSb4sJlx8TXOLANZvF24/ZwAipNCm1Eonb1NOk9gMDNIehSwwONxUzm0A/US4RtlIszicBU37AnPLcKS8KjQAlCsU17t2zrPL3xxAL362Z8SAKUfzqJB9fwz+W1Pg/mnIBtjGOuw2+7X65/3OcAMtrTrCBlkdljoDpX7EWpoLFElpu3IxHqMX0R6RdkNMwMo4e2a22cnyAKI8WP834mjKo7kXZKcQz0NTMPToJW8bEpcJl8X+82UT5VZmT3RaYpVfkpItBebJkWRvSVPgQrWnjyseQCEVteLAJANJPFlSXQGiclD1t3b3fbnWBaxj9p6tyuZhGSOpgTWCIWiWIef6fkyncFXCaB0T9mEt2tuH2fZfOYlaPxoF7wluvIqtKtCrNCyaRBzgJiESVOOGFde9TwfJSIXMUMHB4HObA4oJrqonicBKBW8lj5KP7EVAOgV/lGtFEA26Ym1Gs+SC5cl66N+jtoY0Jk+B9V3un0daUZSc39E/vw+ueijEUpNdusVY6Zky9LZtFXOY4lOASj9YIgKZdn8N6nxiH/9AQb+hv29XoZ90oZer9fsNZv2puax7zebvu8f+7SjCQN+HB/DttKDUqnkN+EwOA3P1J/hQzN7geQS+T3ZkVr8WBY/AUDs9bH+0OLVA0hv7UscNJmC+qRuYeX6sA98DAlNH+PLhsS+SLxByQhFaLQx9hMtLGnoLB0SVguglJswA6DETT+GAj3SFhYdwpFfRRKwY4sl56HJ68Gw6FhMzrS1iY7UHRcNjeLQMk7TjDM1NXphcqnsSF7bkhTouz/nh7MSNd6clGZhZutIjDzRiPOY0fYD1CUcdUDp6rTbbbQGgW5PYhCAiTehxAyameUcSSLs2bg9WiGAMtXt0gB6VWQrs+HzKGPjLViFrSqJVwO/tQIquRFLhQ6JcibZJ2gGmFWIkrNOPAw5KTqMLV9YnOVYkcFPHkHWa1sOQC+kcwZQ7uUNidawRZRkK2NHAhNBvUJFq90FFtZv11ED6wiKOJIDA13JDtQfYip9MrUVUs9u1rNpy1xYBkoB6JVlGyoCEIk/hQAyvrBEMdLRg2J6bgUc2aEbO4Wc+kVFFvxAOdLrSeLPKKAsEC0s1tNa7rXQiki0d+hhv7Zlhej8WAZAkdVNLjOF2BcjiocGULQ7oLI32o1PMaOn066rOtab6qKfgyITu31EEzpeOTDInid1gVUCKCMD2bw9FeNRAKB87S99iPGF8Rd+28J7JCJ+ECjT5ZKaFVJzFQ6P9pVuAa67epP1kEwBA4MY42TTxsMouby1CB6p17ZOAIrY614EIBF+qf4h1lFok6Vn2K5/2o3Qa9Goo2ejP0RLEVmlMWxahySyFSh1HYvGXZwMZPF2ze2zE8wLIPlu0rjYdzHQfZclPdVzyODsgOyDAPJcshsZlwbHIxKATP+WIEiulQo/Si2CR/q1rROAmD1ZXMYG0IgiWeEfeS46DZRtOo3PO30q9dLoDInJUYIYBy1S4aloZDXWiDUl006TVWdlvEoboYW3v/jQcPvsBGn82ACi3cb3bsdXmFdOQEBx6JylaiIrKPBQEDTFIXpe0xQsI0nI9RKLEcYRmaQfY3cuvulxLCy5ieS8qwCQ9oDZjSplColo7ZOzC/lXn9MI6yD5dBu/66Is3VaqjdGKoIohfLpdnIZbOUc6nSNloIxjE6K20oCyecv8pvGTBVAiM9sRXprrKCkiRZ0HdXiiLnCHgzJ72JVBxiBA1M4OeeVl3nP0tiphW3bH1MnvLvfErhpAbD1IGWkSAEVSVwGpTnfYF20M2Fa9XkcZqIFG6XrVryNpQu1+1OVSL1yqVdKjo2IAjUZrASDjv/g2jZ+gCEChFleU0r2/WxTNQY7RUNwU5OtAYbknXzFbDORpByveYR4rTtLibGgmY1IuRkZPZesuJPvyT+xqAaRJQZq/jAyAiP8AMjDomQoDcXZYW2EI0FdttPc0alVQ5UHtQs0d2RtZjYZ9I/8YX0Y6LmjFAJp1ZACU+L++TeEntLVs41vQnIbkIKrHEbTIPcHaudItmhWFA4U9acTrYZHEgEorSLmgEMNApHN4lgCFvsogyGJvBU/sqgGUUovsFFJEFtmZUfaBQdU0R1RuAR3znW4PkDQEYVo1GkCS6m02EHU64tUwSfIZ/4V1rSsHkOU//dbCT8YEEyW0h1xajCPW3gdcVkFRbg/sAqxQGRfs3Nxk2kIODvRtEAHyqAWm19LVNrUelrhW5wQQ3IlZ5lWwMGubDSAKbOY0VAREl2LKiDFFwzZafYadr4aodXXhi/IpDKiP5TfJqxqxyJ2zINrRZSukQAu1OpgEoHQYTgIgVtYlJIME6YEo8YAfj6IOaXgYPqZ6bFYUTsVGaASa6wTqfWU18NUWAr5gTweLmKVOYmHph3V1diA+K3njDCB2lrLHfUjfMNS501CNTr//OTK2/qjTbig0/HQp6xDDyTpDKp6oAWSh1GKYeImrBpAdwJEGUKwzL2gV+h2j8cfzdO944mUt9o0GFCvGHg2OUQT61CMJx+OCC4Ho8SrA1vLqhGLsE2NhkMjX2uw0xRJd+LCuGED6ZC7kEnGGKbGjBhkJqVo9UKUG8qvuZx0ukdjGrzo3DLMOsRQnBeAPsxObslU8rpiF5WrAP39+moqkkLa4vklh536WQSIPUY47KlQeBrIKvijnEFhWkzDnYqozRQpx/g/SIEfZTXcNH8sAKMgjaG0BZNWdi3RBIJ2YQa0xyFgopaTQmdGPsFdGhNFlIEHjz/awz3jqkiloiMXsLQMQf0jKC8W2DFSYdlh0G6uMiU4HkH3LsRyWwCGWvkD53OA9NLGrMdMnlH4ZQDuuGBA9nSqP0fVYpTXEskAoL1Fchw5p5DAQM5llRUxuupAErSuAJBBa4n5G4qrSlaWiIdoP0dKMnIuDEgFUX3WR3AD5qTcaqg6ydLePnGzYHUrwYbc/0iZuuQ4ZAoYjDVe9iEQZzIxZKdAiMdGZCFYGUGgBSAQhTFEW+7H1QsUVRuk5LBpjNoYnufBeGANijknBp+J3QKQAZB6Bh+Y9N0AU86RZV8bslB7rDSCWnrXhj+JYR9xiDiFE9elJ1mmTGt/5XRuzxAA9jbqq1xR6UKneprYeYqoqx6BxA5ZYslqHBlCWKrgcgFYSEy2lFDJvDUDSDC0vht7K+KHYZqo4TlkXAafuuMTMnGMq9uuS5Seg6lOBZPBwpfrQFJbS0CQo9caEefBp48fVszB+k9rup8seYiBrTBV9VR0DfABGvmoAXf8t6O8o8LThF5CgBhVsNZGJmCUmxYHRkM2dfiLJHhMSRIsQU8IyLGyOMTkvrPgc8cbHKQCxBwPVeI/9XGJZFCMiOjUeSrUpgge6yjimmi3Rsa5QFuq603pcEwBZlkPzIYqSqFPpLoeaPMaIdes+cKtOHyPnO8C1atWjX/lKEUUCTIGQ3emPMEKxS84OLmkfSQ/VYVcynzVQ5SIGQONWeXUAytiBkmCLZD9J2QPK9aKi0Zy7rLSw7Ckf96HlkIQnKRqkm63o6Fh2jZFAJQahVG78mJDWonG5ADrT2hAfrplMEsJMdaKlXRjQFGRUyMGQl3Xgs1+pfNSo18mbgdZDEKtBim74jS7ISWRpFEs2TU9O1qHmkoZNahY2dpVzAGiGZjTpCQoAlBxmmYaDIMpIuTJIz0dDIntTmX2h40tJAxYfoeViSFAgLtTYFKk6T10lIT+Zm87K0esJII45lE8j89b5G0rPVH8DmRh64fv9tu8rv1r5DGmRQo0MKA8mhHXrDb/WxvQeUMq6jBMp8YLejaF1xdGqnamzNKNJT5AHUHJUqKzMHaw4n7xI6zf+G3DZqVCqRyGAqNuKy8J36LGnA0Emte3JLB0MUpOlvlwPAFksLCJJx9SjM2CiItB9yiKkXqhRn0zQ3UatVvVV1f8dRo75qt2mmokdEILadZ+YGmaGUW3EkSQXxsa+bXjlaLV2oFma0aQnmAQgU++AAORr/IShtgIZA86AozViMieKxRBBg4XKfMrDQDy5rkROSxkYqpGYL9dQcNNry8LSLS9HmoVFUho65s6oqJX3+yMJm+/WUWWv1/1qtdGoqU87WJZDoS++g1gCGVv5aAWC7fW+DoEdWlFq6U+rBtDUZjTpCSZSICvinbzqGjRiT06OGKB3AoOeuR9PyEH1jufueO5D7ZbfAQ2fZSNieASgQHJW88YefdN5JX5NAaT1aPOViRHGpnYofwfVqg7bfBrofAdJB5HzKexF0xAG0ddVA5UxFIrQzggbsZ3GcCStC01ehhVbBv+vMKR1lmY06QlyALIPS708K8pdVK1EIxsE1IeQiieIhk60yPWcnWMWr7F0K8aXoR8WjUJ0yImu3Cr2SfZr2DddJHatKYDixEllviOiKL19yIp5mxStTkPVQIdHYajb/h0mhZErA/VYFIdQm6cQjwb5QKj6FIXZD8UtL0GzWhI6myA/F9/GeCF6hmY06QkmAig1jF7N0Ts6MJWoR4vTBbkBhsQbkjbvOs4xd2BBM6MbYEgHuVIJZRLOEeq4NK3IWzetr7CuMlD26ikAsTOVfw05nKOhyAikSMoBwbnT+QzV+mEfuZpP1RUaSKM6XYrowJNJdRe7kI4viwyKVgygGcd4AI09hZyi9jARrRLXg2Ql8JSu3MLhZgCbh5KPwYo9K+xSUiHgcI5QV8fLAsh4a68NgHKBHcYehDVcOgiedgfQUlNtCuEAwvO7aq0ONIl9812KMgM2VgdpmkJfo36XI6UpnXUkrIwYmwbrKtN6yBS9DAUae0rYzKQA2pUSW1QJSDyoUkaKm/O4znEiLnHpKDqZLc8nSpMeqbeYYmF5pU/GGgMoTmFI1KQIo8i6aHDuk8Gw7vtIddpYmaP9W+JmQHTqtcYILY0KmVijjroaq/Z9tmSjLofZzlT4bmj6q640K0NcGYur8eNfTQ5Axn4DUDmRWkCe+MsUtTRA77u781BrbElR11ia1akTgpztcy8IP8qPdQSQHalsI0g6MyH3ApWLnRj1Kgg7JPUAcj5VKA2BRI1yEShegKBGAwQgDHBttBFZXcQhhnmMCD9UrRNtitp6+XJ1FGjpKq3JA8m+uxwL035QdHQ95qhUVuWpimbA+HHe23ngif0w5E7O4vcin/1jdJ+J9GPbBWLDwgp1/AsG0LkZ0fms4wxG+tMZjxF/eNn7Kvzst7/73VfhV59/+ulHH3366eeff/bRrz//6vPPfvvbz3q/++i3v/3o2P3V7z779KNff/TR78Lw5eefweffwo9G7yWc/7IXvnz5Mnx5Bv+/PAt7n38Ov/A6cOjLKYvL3caE1GbMC3uxsBaWvJr8X3/OOaXx4zkABAaJqTXOTS0RQHd/odidT2ka2lfB/emCEzYLUSpH5rJR8j23ljWkQFZYtDbyod40ikbs2EAbEejldbQnopSM/zCEozP81AeBqFGr+X7tqOajgahca3exJB5SKmBz7S4bCLim1Ihs0UPqtyF2goKKtulhryt7i9ZYOKR1NgClLXumJj2V13wsvS+UbiSvuMIdgGvnYWCqwZDcHZhDw3hg6FESn5a63HUAUOJBTWtg2pvOBcZQasGSdRT9jIp8pVr3awCkz2qHR412teL7Db9abyu/XqmCNIS9nEGxr8GhbIdGNY5lKmr5PBRDJXx9GcdxPEkTMwssuEVrLA8g+9VkPV5p34LxnJO6jrJMEIiWxXZnzZo875gMiaKtWwM1+fM4cemn+q4YZ+pVsLD0ZBPHufViUmZERhBVmaeEDEx5R4t0F4Qa0rHK1SP4V2s0Pq1WgAQpv+LXqigV1av1o2qjjnp7t12vU0OWSDvadLF7IUd8nfNMOn5uzAigOUbC5r+1x1gmOoBhM9JBq3XSGtA4H5zglxP495g+0Rf4eAI7W63W4yZ8he+D1oDOarX0WfBTpqYZBzIfbWoNeoNZRI9ifn8lACoI5+KIeqQdGOTT7gAiqL4vwEWp6uFB7ajsq8+Aa6luo1o5OALK49cBQD6wszaFf3Q41VDSosmzT30Sku6GMXl0R1a8Yn7MyMLmGMUUKB77t42kIc3CjAOCJOeWCrUjnodwJhw9kn043ZCrSWuuFXJEoqY6bFaKJRD6msQDxWkWliEDUtAO48jaGGWIFh4f8IPO00rNPzzyDytfUYhiu3J4cFA9qqryEZAdv6LqHSrk0e1LOSqyQxIdGnGTVbEPwP8vKXBxNJ4EzWEHer0MC4vHv5owVS4jNJV+KFHHUwPRsyQBXjfjpfSxHkOJOrFgpKs2GcInYWE8rRU7kosHyox1AlDKw5kxI3LABfIejB7D6NSOqqOnolqrg3Dsk7jzq+6w0anX6keHZcBU+chHQbpWUx0qr9ClCGmKMEMGGCOORiyVD3XV1rNhf1ww65jbWH1uvOBn0qtJvJsBd4uXr2j0OdFkROrQU8yqOEqpQLnypMCCLmcfoJAklwszGrx9uUJL0BoByPaMp3dJFA+X/EUi0x9xUSDl+5UalgMCPaxarRzDh5oPWhj8p1S5BpIQ7PT9NklBWG2cqk6h9N3B/lCUPS+59pw49FJCscdK0vOFc/zk69cT22GlJ0jjZzqAKMrQM1VYxaTcEt+EuDDYDi2Cdi8mt6qra0NLPAfpXXQ5S3S2L6cnX29v/FjhlV8w99tBEbpDxVzgJ6pWPtmb+0CPaocfAWKOKnW/3QatvlKvVOp1pUAQwggz0NfQsdohM3S3gRlkGOeBUUcUJUu+MmBhUcZNn13LhFtMjx++/BCJ0EIUiB/I+HNoFURDmJxYuhgCSBpdSDeNgDzw5JiIJJ3HDcUGjbwr4NZiA92qma6Q+tUL7TTD9FgjAKUdF/Y6KAWDhWi0H2NOGIjEDXRW+PUu5sH3uyAtV3+tqtU6iM8Y4QrYqtRqR3XM76l3ukrBxobfBhEKuRhGMnbbFC5NABpKwwMd1WYi+bNjHm/8n3/9akpDvvQEkwGUjYmm6nQmL4PF5pAyUyVGVaoGEYKkFUKPgjyouLgOJgrFdxGecNuVJKI1Nj62np1lmBnrBKDkWK0I6Wh6pDzoCpXOgx3ugIG+iRrBqN3x67VK/dcKVC8fzUCqVvertUoVdLBqXTU6tSo8bgqi7gKOFJVPBBT1Ma5jpGuhxYLiKJU5ln8m425xsVEAoNwDiTNiCa0iFOYlQR06vHDAShVtVlwRGkFDcRwsRHtG/7LcGcEJEzMLQJRFj8iLtB/DWo3+tI4AEge5VutFqccgQyrgCxytDbIyer2AAqkGkKCaqh8d+eojEHca/lG5Vj0izlbz/aOjWtWH46qVGlAl7CwGmpnC7lBIiLh3L1+LZJ/zKCrUAcffxtUByPKghlJqE0lOCkCK3RJKrIk9sS2K18LkgWGQ4ols05cj/ClyeORu2lrMNQCQdLIAMaZLilOMbVYo/6KjgNqgKF2rVg6Pjiq/Atm5UysfHpWrlWobxB/ATfmoArqYqgLSqj4GlHXrigpwjjjlEKXxIatgQyyymdMA889k3C0uNvIAyj0QGjkWluEzmmedS7oOeVRJXmYkIbnyyaPhaVMQ2XtIIwNMtQRRyQXZnQb/NbNrXnMA2SyM3ix19AKSwR4NLGzXJYEYA8fqaOrxaweH5YOye1jzG9X9/cNqGQiSX1G+qh0elH0s96IaIFM3qCgwyENcdhN1M+KGHKYIoD0zpqgxq7w6ABWsIjSEhr+S0HwuWV0UvUrVoxQnhcEPX7nK23G8QIeMmdx4Tw00UzNXYREqxCSQ7AIun4WdfmM9msKRWgm/QKI92ipDnk+yIlNvZnzvKN0olHrKtcPS/kH5+LBcI8gcHRzVgCQ5R5WDSg1IEIW2olI2pHDpOhZ1ZcxgLnSjyxXJ4VJWnb0ry0wtfCCTVhEEltBMnQe5ObPrcfNCqhREVp9jjKSnwmS60lQoUdIBNWnJ9OLRHHIdLNGPHqWfziwr4WbvuqUgR5/GI+wBRhnwIBCD7ANyMwjL5YMDp3rkohO+UgYElQ8qlcMDp7R3UD0qV2rtdk0Bo6uB3tWp+41+o83teUfcEGGIdgHCqQaQsM3iZzLmFhcciwHIZmialXHpqBa5SwEyjsPtoLBWmesSgo4dLyQ8YQ+xQNe7Q2O1Igt2bEoG26PYEi1HXR4FejQFQ4UA0m2apTMcOq2wbibI0ApABKr7gd/wARpHh0Bz1K9Aca8BmI7K6FytHexvbB6Wy7VKBbuHgVBNzjN0qmKYNJUu49hodM9G6wKgCQ8kWYUIOfJVq07kam+JbRqN0GLk8RxJgz/GfB8kR67rShJ8KC3FVMsodBlZqFj80GLQpbKwiRAqWIl095YgIA5iJrMfogBgoPzDw8MjEGr8chnkoNqvQfQ5KIP6fnBYQQujs7e7dwjfqgq1M9TuQfRGczRWhaFwe3KPcak8u8jmVbKwSQ/ErCKJxNCbtCrPLS8V1xHSMfJcnQMoEJAeEospP15Owr3AyFqJ8TAMAiML4cZU9IjZfgUAQgiNxdCYEnc6FpreqSmMgPYcICO1w/J+pQNMrFYByFRcYGQHB4d+5QhYGFCdo4N95who0FG1ji4xinBFG1JDNbA0TIOaaWATKM66B3Qm9YHsX5lnMuYWFxwZACU7prGw0DYOi5cUVK2WFOmlfEIlVac81rp6VKcexW5HGQcaN24OBzyZ1sukahDhxLrp0LritFVegBZ2apGhLIbGAih5nRTUwe1RuyRIq+rhkV+tq3L1YA+Q8k92nRLq8EcHTrl8CDr8/j6I1uUKQAj9Y3UMXOwi+apjXaouh9ZjB7GYqVs2N76Ai60BgMwbtYmQRHME2PY7ZL1LyoyzasVo6tFGbqDKkatsBEI4DkgWDySZQ3vLxgNoyipxXIQaL2SIKVHxSrJ+eCl+EEkDeJSg0Q6IAYcdH/V1Vas5zkGpUv4ne9ugzlfLu6W9jd39CkAKvgJtqgCiUASiSBDgX36dsoI40ZmDy6Qt65kN2FxoZLwOAMJXmArnkHhoSQoEWYZYGGVmcDdCpEYkOasmxyrGXC/IU4Qf8XecENdi/4hGXZhmYWGBhH0FdiAhQEyJ8ivJvjOWR0YjrugD7x3DN0Dsrfu1as0HeuOravWw5OxVav9pqQRoOTws7e5tbpec8iEpZL5/eHB4WFGYl4H/MOO5KwWChuSTZwCJN94WoPMIumgAWTtmCyhjAIWSlozhHIEuH+XqXdTcwAFJ55gApLjalMQDsbgDspPHzemo+wFHFAVpAIVBkE1ah22qAAAgAElEQVQnuiJDooGQTYbGAEgKtFJnVC4XjpU2QINSwJXKNfSYdur7pb29crXi7pXK1epuqbK/52xtHRwBlg73D2vVSvmgWkPPhgL49KkfL1oSaUYunMhl8zicYyTmg6LVXCWALOEjJ9VS3g5ZdrwTzm0PObFZUgUV1uZwPZ/yU6myrxc6DqtrDCLvfR1LL46wwLC/9QMQjwwZGsPCkEiQxwpedcRlX7pY9wck4XIFFPhKDRSs8vbuPrCuf+o4IDcf7O6pilPaLZVBlj5APQ1E7GrtqAogQv/HEFkgztQl71qHyn2IpH5GIruUMdOrSQX4T7jFxcasALKlj/zDJGcFpWC0hK3p3AsOxUA9DFkY9lgR1R00MQ63J3mICo3HieAsNI0sizYLy44rdWVYelnRSvDFURA9t/emFApqlorZ76oBQnIF5J+KUpVyabcM45f7BwfwsVSqVA72t/f2DypHJYcE6jIISfsVVUMHCDphuxQjQloYwghD1IjOcVxtlIrpTxGhCwaQveM8TgkcGQDlrH3EnVALY7eFSERKatkpdmVgiQX2bijHdXYUlgmiAgsqGKggnauh+9KFhe9O1nTlvrAEQwW58UxxkNlQQfohhe50uyPOx6hW/XKlWjk6qvv7eyVQ3QFA+4fVgwdbh0754P7m/v4RIKe0vXcIINre3tgFhc1X9W4Dpe8uVlnEMDKMz6cOY6TIv4yF5kTrAKC0ypPyxmdtfTpbOQy5bVOgmxpwQydupOI1w9B1iBhhuLTjuC6aprnN00DMPwZDOgotbfjOYvqqAaR71DwylCijAxH7ojR2TKWIh1hEoY0lFBr1ShnhU62qxuGegwbD4yPU2/e2tnZLDzZ3dw/Kh4flvV1nr7RXKm08KB3WAHEN4HiVqsKSd+jbb3NoWQfzNUCQfilicwZBE25jpQBK7cgCyBpRUlWDhsgqtGHA1VeT1AxGBdEjLO/iuVKeFett7jgeN5cP2QmbwMcqActhROZKlr9+HQCEb4cw9K1QIlv8kHgOqjPfp4ZNI+BA9TaZA2uqUqkdYYHfStkplZVf+XV133F2dzc39+7c2bi/R17V/VJp7+CgtF9yDo/ghKpqq9pRBYShdrvb6DRq9Tr2g6JqwHCJM87RGJ8bdqkAKg5jx1VorctksSsp8IIl7ihzkNIwECmoa4lipR46WBqa+RlRJSwzJc17TFaGVt4Ty3QvKAbQOrCw5E19y5ToGymImOwULayPLAxkIORejUaX1HjgYlif9ehgb9+v1dRvy4fbu7t372zsPnhwZ2tv7wBtiKDKO/vo36hhoGJNYUFgKkOOUWk1deRjxCuwsRHGl/VQJ2PnrVlD7pmMu8XFhgWg9I4Jr6anq/Dqqi46OJWKbIbU1gBNPVhGyvV08SlQ44FrKV2/hUCIpmk6VRO8PGY5kDH5NvMq5wYQNSX+4cu52n4nADo3AtEQ/xSJqUlAGbxS7PKEtVj6WLFX+Y1Ov47udQwzBIhs7VV8kKh/Xd6+c3/r3btbW87Gxt727vZ+tQqqmLO3j3hR2ADBb1D1lxrAr9vt+OQyU20sS4Xm7dFXHbsveJyrk3ahAEqN8cwBXmGPaY9dSEOnN2OOexxSMehgx+GKmrAfu4ap4BjkHt0XNVY6/Zl53Dnr+0EBgorzwlbuC+MGI0lz4nhmFka/eCWnQIEIO9/gDvpEijzWRxxGkmCqsJRCt1HDqNWjWnX7QQn0d79S/tXB3fv33rl/d9fZ3Ny8v7HtHBwclXe3SvtAZrqdWtXH8A/gfUi1avX2sKEwg6PdwA4JiKH+sNfp6naY/DObnbE4gFJ/WboB+NgJQux+Mm6P8JREkNZSC8lAJP1QI0LnPUdxfCvKO8CpfG9nx5MAWKX7xwv6BqGu25q7ZOG7E2a2OgC9uvUX8FSS9uiYVTdzRCKaYPA3IWaIZOibb745pXBoxtOjbgc7hVG1um6DSnJ0FAY7V6oHpd1NUNkPK+V/ur9xd2Pj7r2N0vbd2/e3NpxSCeAD4vM+Vl+oVY7wl19XtUa75mNDOqwqBII0lgNGYI6GITZ3jg1hTOvzhbcxM4Dsvyyrmc8iAAp6ibwbx0l5DhoDTjUFvDggI4dcBRgjWYEa9Zz32A8f6nKtKtC2w4FYAtRVAej/+xMC5zsBkQAomnGQK5N5FnmlvsHwoW+oWS4Ffo36ACH43VbYJwzLQ9cxf7AGYtDR/uH+5va24wC9cTYfbG3e39q6/+7bt29v7W3df/Dg/uYGIGjv8NA53AelHyMU6xjdAZJPv60oWBGdq+Re7es0Z1M3cTSatGocswIo+cvSf2syFmBhoQaQlGeVWoi8+5zaXAYeGZ116d4YO/eowHffu7sDWnsQi3omhYDlcqGWh+yLxcXhHBfAwuI0gOJ4NjVedgNg5JNIHaLbYyUWYiVDRFcfdCbq0uP7PkjHFR/EaIUQAnZVKv0SVK6N+xt3Hmzevn3v/v29vQd3725tbjv3tpzNEpCjQ1D74Z8Pk3Qa2OYZY6qpVDDSNOw8dpaWnVcYzmE/GP5bi3NUOj1yryZ5dz27KaXgQAsvLW5zKdFASIdIraKgjWPvvXfQ+uOFoV2SlWbGyxkzUHLJTDxQzrKwJgAC9BS4Mk6BjQGEqJ4qkB8gUP1OoxNhk+96tUbRPujiqlX2Swdo8fnlXmnzwca9u+/euXP75w+2dzeA+Gzv7+9t3986ONiD/w9rR4cVoF1AyFD+obznDkY3Um+NzpBLhJhVFCjzKwGQkYFmpNK9Hv/k3+lt8H+zCXvwB35v+k344zpuRvip1/N/8YvSMe7wYXuzWbrzi4elh8fHTTi+iTP0mnyqzNxsRnRaT8+dumZuETOMSwEQEZ9UpXr9SWRqZmad7qNHHUxJBQg0QIk/LB9y+HwZ+Fdpf8/ZRmnowb1tIEB3fv4OcLLNrVKpVN7fdUpV39nePSofga4GsjfmrdYohx4jFEGtQ5EK05zPE+lHwiEzS10tgCZOkK1QZv3xR+YL+9uNAxTDOaTAJifleO85jqcFZWBhOzsuRpNZflE6iXPjxTKgO7BKfNk4FpZZZcFYhALZrH5GAAnvsvPCoshQgGg4+gYx9Pd9rJc5fNRtg8SrUCWv1yoYOna47+xug86+tbsFss7e7l5pa/Pe7dt3gRBtbO/tbe8fHh3uH1UO9/edcq1aqWCGarV2WFFVUOJroNZ3MekHGBpmZiQAkopoRc8kNS4PQNa7ixJQ6RLjMafhUJlfj1kY9yV0pJQCeuqPUbgmV6qlrQfcM+xchKnAGJfM1MXv7mJkoLnVeC36ZAAkg8KV4b+/Bwx90fji71Anw0wceOlYOwoAVNrYLO3ubWxv37t/7/7G7t6u42zdv3Pn7dt3Htx7sLm/u73r+IclJFL7B9VapVzGCvbA/sqVev2ohon0/QbwQUVdwocvI91XYTgsTI5fGEDpv6y5AJQ37hlnqg66kJAOUsepXzPn6sQh94zHHHqss3nsOpSm4Zmkevaa4pcWQSyMjVStPauXpYXJU/n+43kMiQY+WRZmEMSVM0AZ+nsgQ3/3zd93O6iPdYD8wKj65dL27vbm1t7uz99+9+f3NjcfAC3a3bj7zt133r4H4NnbA9kZZJ/d7cO9vaN6DSNgFYAPCFIZLZE+udYaWGoIvWL9l9ryg9pg5mlEhbexkBo/J4ByI1mFkYGFZJAvjNJ2uJGctOpRJE+7v0DbtO5jyDmr4mrFogx2ec1Qq3i2FpbRz1YOoPyYAiALPnZAmfkVSe0e7nHQ/7d/R3rZ34JK36gS/zqq1Q4PnK3Nrd37796+ffudexsb9zd3d+9v3b/97tt3N/f29g9ANto+3N87AC2/gqagGrZGUJUjEKh95Tew4JmqU5tDlKJ7ZDPAFZj2B2ZZzNom3OLkIX9ZVPx3dQCyXyp/HKCB0NN5OwiXnR1ugOm6Dx3FElFMrTTCUOm2GJhTT7H3QntSypgOKCvQ8K8UQI9S3+yMGmuY5LBo1OkP//7/+rdfAIa+eFQ7qtTKh9Va/ajkOLtb23feRcH5/uYD+LextbF9H/B0+wHws90He/t7eweHB+i39zE5Q1WPVANUuEMfo1yH6NfA3rwN7L/6Vbc7MlnVSePoeAUAGjcWBVAoqjxvSV7tOcnBHpfjQIh4XA8IWZfvuIGS4kHcL4ObzSE7G1BEfZBmXsnl4gIVfsoqLxpAafyMA5CEBVEaMlKHtt/9278lSgR86KihaqXdcmlra/Md4GEPNu6+fX/j/jsPNu9vI0V6+8Hm1r17W0CHdjdK6K9HvatyhGljIBMd+pjk01FYChg7HSKCvup30WVLvVQpU8OuHJvchrX0qwJQaPqhWJZobc/hkHqWgUPMG+RyVN5xyE2aRVqmClVKxJ5znQyvw6xzFKgwOODKAPQogx+LhSVVd80mAA+G78RoCMK85Bb7N6ptdXCw7wAb2733YGPjwYN779y7d/ft23e37/8cAHTn3ju3b7/7wDncu3f3/sY+yD/VauXoEORp5xBIkmoAC2v75UPMOayqhuqOehJYxm1Z+6NcYEeUXfoVAkgFpsEO5e3wO5dah1xTCqERYGewGA3T2CqTMsSox5MUVeBaMGz45lwxLVLlADTnKi8SQDn4WCuhXAltxqPw9ogrKmCxVez13e63VeN//B8IQrVyqbR3WD7c2y7tlkD9urcBpOedO3fffedtUOXxx52tw/L922/f2S2VDg/24b/yoVMqA/vzG9QpCumRqlZBowc97Iwz8InYSXP5nDM1vfQrZGGhJkBcdlWqunCtQ/FSBByygZ3ikWX1JMoMc+WZVXmerlbWSvll46zVYIFVXhyACuCTAlC/b+KA+iSU4CvF6Hes8tvANk+qUvH9//6EMLS1V9oHRasE2te9O3fuA9V55+7tO0B63kUq9PbG5u42bHx3t7S/vbUHaj7I1fsgPWFER6XWBomofFRHkxAo8v2QQDOSRiwFVcqiLOe9MgDFScQXB5BJRNm5drZLpXqgNu85wMSQTkVSyUy5KtQtWSjcI0AtTIcW5USdqFD6mbrKCwNQEXzslaA7lU7BNOZuh0IRMTgaW6F2sFBZp1uvYJ9dv1wmCD3YcxzQ5e+/ewcY2IP7b9+5e+ft2z9/5913UJK+d3/rwb1793advd3Nra3dvdKBs39weFQF7ByVq/WGX/HrdQCkQi0s5NZh3Gm8qNBmDvtXCSAZIUk02JwHR0vQFAo+AEEOyM50WCTN4nU3zJDCPJARKiwwFVsEyKoUZIe0XqglOj8KAZR9BfKWMpZo+YhRHH1qUIAiSbfd7gBRGjb8erVSV37V2T88IAzt3n/w4N17CJ1NYGMP7oIsBPj5+e07998B0Wjz7gMQk0q7QI0cTJ/fL5fLVQxorKouBnfUKdKMAURFZKjgXUG96Ec56+JlAChvSEzFlZIlGUMQmRUFbIlmvYu7z6H3VLo9cxoh97sMpTUdZZSdBAnjCpOeK5mIxAt1puZHAYByf8IaLoW+MMoY7evsdWzzjcXFOm1VqVVBka+CBHTk7G7+l/8NYOi/un9/8923799/sPXzO5t3N+/fv3P73rvvPri3sb29sbe7Vdredba3tw8qh85BpXwIylgFAFSr1LHgPXnjO41OyC15uZXGaJhBy6NHUY4oXQKA8kJJz9j4YtHCFZWNwhc/oJzTQKJ7uFUYpb8DzvxAtwRTSreho0ILZEg02OCqdzaA4uxa8qssGBcBoDz7KgCQ3kH1WSkxg1wLoxgDObr9fr3eBvkFROfDErq6Shu7+w7KQ7XNO++8fXcT9DDAzYM779y7s7mxsbu5jdYhkH62t4AClfaPyvvlSqWCiYYgSh9W6xRhj13s2p2eZMtjBG3OmfEojq8SQNa764W2oYZULa7DyhXKsHxUrAuIs7pOtYJU0+NSZShRU/lETpInekURiayFSdk74261Q1qvmIUViT85FqY3E3ikRFCfFaNhu4OZOHUUXcrIlEoHlere1m7psHywi6zsX/x8c+POOyA93797787P725sbm/duf3u/bubpa3NPQDQRml/r+QAgI6OjirVyuFBhbIT643OsF1T3R7XvRsOqXRHGkC09itkYbZeHdqdu+g32XAQQOehFIqWNC+2QrOs7CsududRPgapZh5ZHSkrI2CVHt1mSpxscrkJy79UABVqX5mVJOIPm6DpE/ZWoXR2RA8lxvsN/6BUcvZLh7UD58G7W055f/sBSUP/4s49lJ3feffOxrt37zy4C2D6/9u7vh/Hres8cIsgox+kSFkERwrDMLQtKZxVim4fvFISI2qxrTIG85AHAZugDwthuh3RcYW67QKrQIEwlouilS3EL17tepb/ae85516SGlGaETk7khMe2DuSRqQuqW/u+f2dfFFjopR1TSnp1YrpQMu802w1W47d7TEUNVs9HLgxmCwCyo5rThhf+z4j0dey8SEFVKDh4OGroDCeiqNRnREJGQMQH4/gYtW9TwBq81kZWGTmw3gEb7U28UAAtAU+IbtcxICO8NuB2QNMhiOY9DQHgp+u04OeL9tpWXbpWFY0ZueUi6UcYQgQJEnH8nG+Ap6YrKrkgrGdqKiY9ZZt1yzHxjKPlsl8e6Peg14Pd/ic8wTR8IxwgcHaDySVMQsrEFc0HBJFwfwCghPURjfQ/kFr2XvQIAJOl9k9wBNE3j7EFV1eD8TLiLgWo7j0YQBo2+6DqFkDkM+z8RAVZpprjAMKYb5Ff9BqdZtOzzabDoNCOXdcyClsc1EkicHllEs+D1GgAkakdbPGlFmlWpYkSbXqrRbTesz8MQzDMqtyUWcnY3qx0xvNRlN0wMAI8oOygMjaD2QH4gnP6OsEIOaFQSdPmGZv0wRMoHPxGg+oDcxDNAU5LyR6ESXYyE1OnB0u14reIYx7Ot2GYtxpXorH0V9QLh5JXabQlArEYjCRpwORnKZVr9eMKqZNoZBewrjPcYghpsgARvlSBfYftgFBkZlWbXUNTTOcJtOBVctSy2XdAc7FTnc4nkCLM0QSEUC8ICm69j0CaMUGihl+wgsTL/nAb1EdRnWFWHfoGicNJAfC8A/O1/D5MBYAEO1guDPR/uUhkFx3EtPqs2mVUXnr5RzhLwFAVEm6+vqC70DIsQB8PtBYCMXMzVaHwYd55tUybDSKJpVkgR80gXIhivIlWdZksKMLkiqVddPRdcXsmUbVZFpQ1Q3bdoajbrPbn89o+soCIwdLmi+1Evs5DABN6Nt1Bc1hdAt65QMsZtShw4kQBW+CYYpaIBrljCVBNJ8XjO+ZqLH3xAQXzMt65zHdhptWGZX7AxAg5+XSX+vDIj+MsvFzJOWdLiAW5MIsHtsy9WpN11Wmo8plhp8ogBhsmO3z848QQwWwq4vMoc/n81JB1g1LLtumqTMVZphOzQQiPJiW4C5eLuacz4HPXGGqF3PzgWm/5RKTyU4qjH+RE9EXGJ2vzGvLXnEDBgo6ZqJhHuxmoPltu+SjocfPZyLQibCgrO2JjteVyM/55kzGwQDIRxV2rRM0WtkORfXgHI3Hg2EfKKJbLUszjFqtVlbKpUqZbURFOQoggFNeLpI+Y7/JKXopl2dWkaJVtTIznKsV7AWqW00TfDLm0A/nXxKhMOoxsn6W4dCO2Mu4VyNabEJLKsbgTJmi/IKUz+WMk4sTg12bSBaAh6PtPoBCRayI9humy6czQw8iEJTzEhB/xa+ji96Mn8MBEK1kNX1AewBZsshFN4a6QaypHw2BVcquGpaqlTVDliRInebRcg4lF9pETJGpZSkvF1SGG2YyGXVNN+pNUGOmZdlOx7IHY0hlAIvDlFN0nEb4HTZcxv0CiG8NS95Bwb/ysCQaaqJ5nQZ6XzPXBCQx/MjvnrTb70FaA/rjXfiXpkXR9B7Pu+S1rqKuKBKqPAgv7HYAWjOi+fcHgcQx9CKPgB0I+kiHHeZ8m8yJ0lRNVSolAkzheFWPkRQlTLmWVaWk1XTNNlRJr5u63mpahl6p1DSj4zhYXz+bjjD5hmOlwPkKunw2Xca+AIRPoQU1KOHh9FAXWErv8urCRtt8FwBknrz7rtl4DxrmT0wGqnfZv7QFUVyRtzbz+PNslYU6uOjDqki8zUrEBgDsQPMx54eGSQXjXt00DcOxmPulVKVjuRQDnCiEFFRlps50ly4piqxZ4MnblWJRldWq3ap3hv3x+DlMUx2DyT4XkcP1grJNl5hMdlZhGJgRoZ+oziFGzTPywfgkVWRZgATGu4WTk0YPQohtk0nbPHFp0IHHwUaVjJzMgwsH0zL68VtWuVYGsn559wYgEQUOmrSmc+6Szamoo2lbVQYh21Qq0I0qFYq5a4prRQpyhTtmXVVRi8e5EgQf66ZaKJQkTa81Hafb64+fA3cr7D+np6Ip41pt/ZZLTCY7BRJ5tFkU6FyLJcJz94wihFidijYQTDLALchsPMD2HtOEMnvMVmAUmtgQaVy4i9QLM1FwTXJLAK39eo8AAqyEh/I5GUyREVE90LR26pYFxanVSkljVpBSKgXmT5wWyxXzx8WSdvoP3dPTj7QcvKlYLOvMu5fkqqZbJqTnO8MvoVhkPIaW/GkA4QMCEN9m1iq8wmezM9cLaRdw9JNrMhsIpjwxAOGmhAb1jIpAXErcz6icg8cWQ9YYfH5LFXZQAIrwlCGAQGB3AFpDpEXoWk0IRVtqRVFNXVNVNW7jCfDD/K+CVCjXTlX5ZzzZkc9JlUopL5U1y2pallPvtLqT6XiKjWdQQssjCgekwnjFYGyNKVdi/qXHuX15VBC3GSiLZk/OMT3fYPa0x43uoEmj/ZBHlSgsRCfk5Hi3NaIPSYVRWbRP2QSKJS4pEzYadh232+0AtwtzvvVSiTljEIeW43YefC1fYPhhWkxVivLpaaH4EYSHfgHFiuUyO1yvOTZMZGm1+s9GQEU0Hi9xhkZMb+peA4m++CuPuZlks2BA0BNDMmjUHB9tAHDo0QAx5sLjuQQrPbaJPWyTFvTIKwtSI7NNDGXxq4zKHQDoVSDLV7vJy5fwH/v/5Zdffjn7En5OP332fDJ5/vHjBw9+8+gnjz9+9OjxT36gSZKiaUwRFcplRYkHEEYVc3JRUeHxKduLcj/7xenpzxW1Cj1k7//gxz/80fuPP/rx4+enp88+nTx/PmMfOWP/veQr2XIZbxVAK4WHEbNHeGGr8T4OIB8MY6SFBmvHdL1gK5mdewExmY/DnCPa7kzMPYQQgCda5BFEk6i9tb7KjbKnHWgZqI4lDnhacObUOdMuU2ZEQ4Pc0EV+KceuV/LFoqSrxUK+wNSYukWLSUoJau1zEBYqloK0699XTbtmQN8qe/LpFD4Di4+W2NVzDzbQ5j+iy8uLs8vwyWXwmGB8eXFxcRn+lj2+hBfgqIcPzy5eXTx8qJc/YI/4ixcXEziEPYD3vro8++AD9pA9hhNfouAP9o4zehs/9eRy5bNuLcv1P7B7ABCxg/EQNE2bo7DeFMic4cvtjxZA8+t2Ok6rDooLAjywzajSVmc+J0O6o4i7EMYWpbL+y1+env6jYeBz5sdPpgDTMRSTgb8nevS3XMbb3IEihcm+aNqKrCLK0RK0ssO8MIwvzqh9Gcle2h7l4ycYOBTEC6DKfJHs8C6DftRZyDxFJ59EIk7rq9ws+9mBFnM+3VKEoHmfxHQ8GLJXpyP4sZzDCEJmB1VVKDgsYyNqrlTGFvl49IA2k4tq6Vj4+/nTUH5lmL1+bzifIYknlQBgZfRyr3EgL8J5GfVxlvyFkONHNKlCbTNRh4tYMnhdbYz1NNrnoKvQrQfzp8375/EE7gciAhQGooXeWvqUft2wyo2yp0j0gs+g5FXRfEYGVNIPobFn0AOWO/as63Y7HVvPS5LMTGGAhKIr0kb8oBTlSL5MLqlqRVOq1q/PTk/POu541H8OBIxj4hQW+Fm7J5suMZlsNaIjVk4AIB7Z433I9Eo4II7tJDgklUwiHymjTbSlG23TAEwy2DSQLVpMToUzuO0fmg33uqXDP3PJ2842rXKT7AlAS+JE9Kk7C7OrmAkbAL/meOS2usMxU2Att9PqtWxNUaQieFk5uZCT46OIbG86Bj/sOFc8zgd4yuUVpaKpRlUzW9Y/sW1o8C+f/OtgOkKiIFHSer2Gft9eGH2pmAsLyFjE3AOihDoDGg6i16RqDYhDYxXZycl7TGW1adoK4It46/EcXgMAdH2PCQEUN6gndpVR2Y8KC9kwaOoSfY2gWkZjiEK3uj2XbUN1G+Z5dwxDLZRyUhFKx+Lc+NUN6LjA3Xq+BZXVcqWiVPRq3az9Gnqlz//93zAGNCVSovh7sukSk8lOcSBOGoYkm7x0fiamOvGinwvqZW5jVw81ZVB1q8cA1PARXTNiWIBODtEG5j1suJHOMF8oMrrolbj3jasUss84UEhxIIo5ppDNWMLEU3cwcutms1bvNDvNspw7LhZUiENvAZCATKEYgZMMtWZaSZbLulU3LLMJ/faf/PHzP8BHTacxjc1vH0CRLynmq6HWC+z0C9x6EfPxONP8JXUZuh7vlufeOBZCv+fx5FhAekcG0AyPc0VdmicSaysXHZfIOGwA0bx4rE3GPglwrpmJwmygfr1p16x6s+NY5TwzexQVeuG3hKJztPMwLRd5U54dwQxvqaBYlt2xrXp3+BtijvkjtmVsuiebLjGZrJwg+iVtApCPvcbBEa6gQOSx5zOfWr08ymPwE4Ll7HnnYvYlR5vLG6ChE+PhTNjOnicYP1Yu+rsFIB5+QQ9+OoVs/GI+gglfI5wXD30VdafZNCoVtZiX1DwGeHIbIVTC3xQDL78ITr0EsGI2eFnVgWyh1en2n7n9Tz75wx+BnzqeKXq/ABKu/CQwp/2ZSEYgxTz0uFO0mXpSXSpvnXnItcmOQ+oyYpbi7YPg5YOVdCaKWcWvQqsnqB6JWdGBAoh/b7jxQPEGzlaG1gygpD922BMAAA9TSURBVBv065Ztdx2LwUdTa7qmSnKeWUGbo4i5PAHoOFpvViSPrVAqSBWr40CH6vDZoOeOx3/4/PPPafbUvXth21XY6iq428UtF1Q5THk9xHm6WLbqUU4CfXATJl32GJCA45e3vhPEGi7myS486vJxZxCInkVHHkxmG9CzfZX7A9Ay7CjE4g2s0AFqFyR4GQ26dUieNw1NLcpaleGozGyg3JYo9FbJ5+Vy1e71Wu5g8JvhcDDG6usFcJz/6auvvtqrGx8jYS6MF0EHOY4Z1ih+4IoRPbzwGbYcrGN12z3qE+OD4zFvga+DEXSGeMJphm1XkEXTJ06CD7n1KlH2BSAxosLn9e2jqQ91pjDiFKZ1j0ctu+k4pmVV1aJaMaqVqpyXFTl/M1ZWcCNCRrm8VKpaHRcGPz2DCRpjHJHITCAc+rI6Bm7vAMJvkgcSowji/7jtszZ5VzjiCfakxkkDw4DAE03YcoXJBAZQmxtLoPpcStoz25pcOO59TYKg0m1XSbI/AAnzGcsRsRAI+3mgsxkGDfYc06w360ZN02t6pVKSpHyuUNpmRG+SXC6nQBe0Ydm9QafT/Rj4xkekMSGAuTbe/qAAxD0lHnHmqdAz0U3YRn8dR6PSVEuv/R6DEfEBzWZ8Wgs3h9z2QyosQ8+fDOvAJJvM+HbHV3DzKknuE0BiXpgflLEuFkFSdUExoDE0N/eBo75pWxYEgmxD00uKjOGdQmHHLQhy9MWyqqgVpVypODAPynp/APPDBiPk86QF0MwXMeF+7wCKqLAIbCJx6jOX97U3yF4+OaHZB6Dfzslu9qnjlDoPeQdi+wOOKB6a5N5/kPyPBMJXEHQgAAo7U4P0JYWgqaQeWlKJdgWGDrq9uuVYZr3nNE25XCbgYMnPriKXFBioqmmK1qwDXdX7HRwo3meO3yJA8J8iE+73DyC8R+JBxJ3nX693wWdfEIlCu0EWDTHenQcMvsRSRoWtABgwokU2ZCZq08JAYuSjDh9AC5E+XYqmjAX0SoBBxOxpGHTRbdmG02o5XaeqKvIx9612B1ChoJQMq1bVdGDqbFmm+aOW2+sB9eZ86Ud7HIPp5F9dG2y6TwDFmLUzThQlzGpoL+TN8aCdJiFE0DXjVGaooS65VuMj6jiMQgBFPuOWq9yTCluGzOJLXpe4nA9H7NscD2HQV7/jdmHqjtOxuy3DkOUCxX+2xKE3S75UgZl0NcM0batumI0ONL0Ox+P15YYT7jddYjK5BYDWkCJsoGvuNZq6Z174IpaWeUS6CcXPYTG+6CcMJ85dBkVpbjBWNaLCbl7luuwrF8Y9MGJqxpfGzANj/w56veF0OOx2esAwZjE72q5pqpQrKrD/JEKQBM6bqmvMpatZRvNxH8auwODUmPUChL66ZlTfB4Cuu9C8yl0YwtF8PUPERfiCR944NcDDTrQMQAcpe3eFk/6VOAcvDZmFlvNycxjoAAEUZFORHJFS4nOKAA177mAEw+L6HZgUZpu2YxrFolxEGqnkktcMo1qr1ZzO4xGM38W2Qj+gio0IU2G4DcVeYjLZGUDs2SR4nbNvcLJwSLuvAAhafHiRvUs0vzPuvmG00BdDCr3IAPgo8T3Sd2BB2XctkEjO1xRTYFCNiAPnhqPB0O30+gxAjmXYll6zzapSKBS2VyJuEwSerDL82Lbd6j4bDMRninKO60TjqMpiLzGZ7KzCAgAFCQxP0M27ODQlPAK5WCE7z7EWeG8Y8sFqIY9nYWevovl3yot4PFp0Hk2MrazkEAG05FNOYOAS8V2SIT2HptHhoNfqtPr9rmnAEEtVq6r6cRL/K9x92P9FvVa16vV6y/3Y7Q9xwBSQlMEE53UAoSqLvcRksrsRHaFN5f2DwbwCpKrzA3+cup0bxEbPfidKYTkRmRfmYJEfKFBdoj6EF+Sfu15cGBHfe08AWmdcXpOwoIw70GRNQwwaewznOJVy6Paa3V63A23NZUWRy8wTB+Mn8RYE4xCkqmZatbrjuI+6zAQaQtBpsRiPF6uumLgn8ZeYVHbtC/N5Np6sXIrXeEElBnyjQS4d7WEoRfR4gSsmtfiIJ5yz4s1Ebz0OnCNIhQAixeWdb9qA7g1AgIqb3hupSOQqzKdwEM4sZCpl2odvlukwt9tpNmFEqiyXpFJBg02kIN8IlVhRKyr8UylVLNt2Wo/73cEIhjjjcIXFPktao3Pjw7QUoWYSmD+eaMYJ3veKVNSM4skzGv3ELZ8JZ73DfDu2fwUcVd4FKSw6oSgJopNGiMZXl3hvKmwHAF2fzwWFiZCaYj9hpCAoskHf7TSZCW3piqnKFRnGqxSk4sZ6+nUJTe5SCZJokq5UdL3e6j7uwQbk9kfT5Zzm3F0rK7s3AAHRT/g4GsWbAeOTyISJWsHwDdyW8aigA83lRoNnviYzalPFGnvKiwlCFwhABhWO0ZhzxOSKk4NTYZEjlpSXx0w8WLVIrQAcQcM+s6IdaGy2tFJFqkg5OS+VbuWIrZtLJTknFWWzWq6Zze7j7nAK/a/TMd98gg7ZyD2Jv8SkshOAeNZispLG4MYPf+cFH/LEtRCwk0EyDEHVA95fs83rfdquF0HQRdDazHO0QUj6IEg2b2dEr86YDAwiYHyCrQi7/Ub90dh1oP7LqVsVvaLomnxcyOeK+YSuvFaWlTLbgphV5TyCzQda8Je+v5qR23QZ96vCuKMUkivwLzlCDX1B+dGZx5uWkeKlTequ56JFLYalcnpNam++8IQ5xPWfOPw6gA4zEo0riRCBUTngYsn5EcGxno+n4/lizFywbstxmCndq5VVSa5U5TKY0DtosBXJqeViQWcOXbne6jzouO6Yx4FoHftSYZvoXSiytwogERDEb/uSzziALYZeJepnaCnsYW5sxiM8oh4Eo9HQzREwcrorNNTeOX8QXcK2VQrZH4ACYjnqy8CI0GIOafLF2IUpGQ5M0K0bFcjDl+R0YcQi2E9yRa8aVucjhyEI5tMHxST3W9J67YasSZBbWCGJ5hFpyqufeT7OUQEW+jbGn6leA8s5GtD3jn1AHGMEOtBwl9E2s5CEGnTaJGpnvW0Avflsl7Hf11YSbkBCf9DEE+xUXQx6gxEzortOCyYVOF3HKAO1eFIHLNiCigVZVpgZZJn1R91Or+8OsaZ+HpfPSA6gyI3ZdI/Wb8iaiOzmbKVTiywiGqqCWXUcQdcGMjLgSoSmMOgtbD8gTnEokW7zsnvajWYeEo0HEFnNkKwAyJ+50ZjQnQNoZTx6uproJR9aQQPgmBfWd8eLxXjQ7bRaLbvb6ThVsySXjoulxFEgoHiRVFWHSWKaVW8+Gg56IxyNiK2FdwmgyI3ZdI+23JDrq7i2SxCAUHddCMsYQdM4aaDTjh5Xu+eBBe3zCQii84Lijq+im8zKPhNkTuhppCV2+yoTAejqty/4UPQjJim6MnyuwrDBmKYejEbDKVaXDfq9bs/tu/1es2lo1apZ01VVE27YWm9GPl/SsX5VkkvXWp+Z6WzbdafXqjG12HL6n0KgYE4zpq6bP/GXcVsAhTdm8z266YZEVyFIwUmEBTRDb8ptCzyxrYYnVHH8AYaU0THjo8QEYpBkc9Xbiyiq1Yt+uwCCGwM3iN+cZSpBlg4+OH4BoWG0TbBAcTgaTefD0cBlOoftRTD+tOcAkBSgn4cQdVUtK2x/KspWE0jJ7Vql5nSbpgblGwaUbrAX9FoHWKeBO7jrTkfQdL8QY6aWoqpku9wWQOGNuat7NDmfTCbBk+DR8pwJezqBH+fn7DfwO/77CbzCfvTOV17mb4qeJfLwuuApbivJAQSSbgcSRwaGdWRLoBQDRqkxUQ+UhovJaDzqudP5iIGi3x8PYYRTH5jGgBkGZq2OlnOmBucDd77EI7FOTaTe4NHLDWvYfBmpALT1BDdXJMbGh1+J5rGYdvbN45eDYStbPi5W3t4O5Pt3BKA7PMVbOMM+AbTrYUmPywD0Fs+QAWj7ccmNaN/PABSRWCN66wn+MgF0R278xvWkO8UeAXTHbvxm+a4D6OpJikDidvluA4jfmC8+3HyPbr2WP2cArUgGoJslA9AWyQB0s2QA2iIZgG6WDEBbJAPQzZIBaItkALpZMgBtkQxAN0sGoC2SAehmyQC0RTIA3SwZgLZIBqCbJQPQFvl9IEdHv08r6U/xVs6w2x3Zdo/e+nUkPC7dx6UCUOTAxEfe4SkO4Qx3IUlXkfC4u/y4DEBpz3AXkgFoT6c4hDPchfwlAiiTTEAyAGWSSjIAZZJKMgBlkkoyAGWSSnYF0Oujo3deBM3gKz3htxcsQE9xim9/enT0vW/SnIEdc/Rh2su4Swlr8m8viZed5MPwrr/zYu3VHQH07d+88F+zVfMq8pVi8tvLF1hLnPwUr+mAFGf44nvfwKWku4y7lC8SQCHxspN8mH/15Kn/9fqBCVTY1W9f8D6W1XaWW8vrv+Z9VElPAXXsfpoz8CaudJdxl4K3ZEdJvOwkH3a9+S2QBAD6mv310sk2nPMGefOf/8OOS3GKN/8RbedLcgZ+31Ndxl0K3ZIdJemyE30YKMyn/mtmOFyTnQH07U/feZHuzn/94bfpAHT12789SreI19/776Ojp4cDILolO0rSZSf6MB9NrnX8JNmBmA2U5s5f/fM3KQEE1svV79Is4jWzoF+/8+JQAMRvyY6ScNnJPgxsoA/vzgZKc+e/oL/8lF9eukW8Rh/u6SEA6Oujo+/zW7KjJFx2sg+7SxsonRF99QQ4dI6epjRg0y0C3s8AdCBGtLglux6WaNkJP+yuAAQu/Ld/901K/xcvO/kp7mARzI9LH424S0kC4MTLTvTX8uazO1FhbMeFk/Bm8JWe8NsLXkCKU6RfBAQSn6a9jLuURLtw0mXvMZCYSSarkgEok1SSASiTVJIBKJNUkgEok1RymACCYAU6GMGDZBnkP3u5ehKTXbhXOUgAvfnsr/4Pb03kwd4d7YOUDECxcvXk+6sPwo0okxXJABQrV084WsSDq9/972cZgGKEAei/kuQl7k4OEkBQOEt/WcGDNxmA4uTqyTsv3nwWEyC+NzlMADGb+ejo+9EHGYBiBVXY631uQYcKID/4u6IHGYBihQPow/2t4GAB5H8t/q7wQQagWMl2oFh5zbQWIiZ4kAEoXph7+nS/t+YgAQT1GlQ6EDzIABQrmReWyXdcMgBlkkoyAGWSSjIAZZJKMgBlkkoyAGWSSjIAZZJKMgBlkkoyAGWSSjIAZZJK/h87rJEnuoSBewAAAABJRU5ErkJggg==" alt="plot of chunk perfectmodel" /><p class="caption">plot of chunk perfectmodel</p>
</div>
</div>
<div class="section slide level1" id="empirical-tests">
<h1>Empirical Tests</h1>
<ul class="incremental">
<li>We can do two tests, Breusch-Pagan and the Goldfeld-Quandt test to test for non-standard error variance</li>
<li>Again, in R these are simple to use</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">bptest</span>(ss_mod)</code></pre>
<pre><code>##
## studentized Breusch-Pagan test
##
## data: ss_mod
## BP = 7.499, df = 1, p-value = 0.006172</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">gqtest</span>(ss_mod)</code></pre>
<pre><code>##
## Goldfeld-Quandt test
##
## data: ss_mod
## GQ = 0.8302, df1 = 263, df2 = 263, p-value = 0.9341</code></pre>
</div>
<div class="section slide level1" id="correcting-for-heteroskedacticity">
<h1>Correcting for Heteroskedacticity</h1>
<ul class="incremental">
<li>After all it only messes up the standard errors, not the estimates themselves</li>
</ul>
</div>
<div class="section slide level1" id="accuracy-of-predictions">
<h1>Accuracy of Predictions</h1>
<ul class="incremental">
<li>Even if the regression models fit the assumptions above, a somewhat heroic assumption, they still might not be accurate!</li>
<li>What are some good ways to address accuracy and outlier sensitivity?</li>
<li>R model diagnostics can be easily run on any <code>lm</code> object</li>
</ul>
</div>
<div class="section slide level1" id="convenience-functions">
<h1>Convenience Functions</h1>
<ul class="incremental">
<li>Using <code>ggplot2</code> we can run something called <code>fortify</code> on our linear model to get a data frame that tells us a lot of diagnostics about each observation</li>
<li>Example:</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">damodel <- <span class="kw">fortify</span>(ss_mod)
<span class="kw">summary</span>(damodel)</code></pre>
<pre><code>## ss2 ss1 .hat .sigma
## Min. :416 Min. :392 Min. :0.00189 Min. :10.9
## 1st Qu.:478 1st Qu.:457 1st Qu.:0.00207 1st Qu.:11.2
## Median :495 Median :471 Median :0.00275 Median :11.2
## Mean :494 Mean :468 Mean :0.00377 Mean :11.2
## 3rd Qu.:510 3rd Qu.:483 3rd Qu.:0.00416 3rd Qu.:11.2
## Max. :560 Max. :511 Max. :0.02920 Max. :11.2
## .cooksd .fitted .resid .stdresid
## Min. :0.00000 Min. :412 Min. :-46.36 Min. :-4.148
## 1st Qu.:0.00015 1st Qu.:481 1st Qu.: -7.60 1st Qu.:-0.680
## Median :0.00062 Median :496 Median : -0.42 Median :-0.038
## Mean :0.00225 Mean :494 Mean : 0.00 Mean : 0.000
## 3rd Qu.:0.00179 3rd Qu.:509 3rd Qu.: 6.49 3rd Qu.: 0.581
## Max. :0.06596 Max. :539 Max. : 58.36 Max. : 5.218</code></pre>
</div>
<div class="section slide level1" id="what-do-we-get">
<h1>What do we get?</h1>
<ul class="incremental">
<li><code>dv</code> <code>iv</code> <code>.hat</code> <code>.sigma</code> <code>.cooksd</code> <code>.fitted</code> <code>.resid</code> and <code>.stdresid</code></li>
<li>Some are obvious: <code>.fitted</code> is the prediction from our model</li>
<li><code>.resid</code> = <code>dv</code> - <code>.fitted</code></li>
<li><code>.stdresid</code> = normalized <code>.resid</code></li>
<li><code>.sigma</code> = estimate of residual standard deviation when observation is dropped from the model</li>
<li><code>.hat</code> is more obscure, but is a measure of the influence an individual observation has on overall model fit</li>
</ul>
</div>
<div class="section slide level1" id="so-how-do-we-use-this">
<h1>So, how do we use this?</h1>
<ul class="incremental">
<li>Visual inspection is the best in this case</li>
<li>It's easy to implement, easy to interpret, and easy to explain to others</li>
<li>Watch: let's look at an ideal linear regression model</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">a <- <span class="kw">rnorm</span>(<span class="dv">500</span>)
b <- <span class="kw">runif</span>(<span class="dv">500</span>)
c <- a + b
goodsim <- <span class="kw">lm</span>(c ~ a)
goodsim_a <- <span class="kw">fortify</span>(goodsim)
<span class="kw">qplot</span>(c, .hat, <span class="dt">data =</span> goodsim_a) + <span class="kw">theme_dpi</span>() + <span class="kw">geom_smooth</span>(<span class="dt">se =</span> <span class="ot">FALSE</span>)</code></pre>
<div class="figure">
<img src="data:image/png;base64,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" alt="plot of chunk simulatedgoodmodel" /><p class="caption">plot of chunk simulatedgoodmodel</p>
</div>
</div>
<div class="section slide level1" id="lets-look-at-our-model">
<h1>Let's look at our model</h1>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">qplot</span>(ss2, .hat, <span class="dt">data =</span> damodel) + <span class="kw">theme_dpi</span>() + <span class="kw">geom_smooth</span>(<span class="dt">se =</span> <span class="ot">FALSE</span>)</code></pre>
<div class="figure">
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAkAAAAGwCAMAAAB2PiqAAAAAdVBMVEUAAAAAADoAAGYAOjoAOpAAZrYzZv86AAA6ADo6AGY6OgA6OpA6ZmY6kNtmAABmADpmAGZmOpBmtrZmtv9/f3+QOgCQOjqQOmaQ2/+2ZgC2kDq225C2///bkDrbtrbb///l5eX19fX/tmb/25D//7b//9v///8YrBpQAAAACXBIWXMAAAsSAAALEgHS3X78AAAX3klEQVR4nO2dD3ubOprF6Z1WvXdnk85up7PJbrO1E5fv/xHH/JeEJARC4rz4nKdPg2PgcKSf9QqwnaqmqARVRx8AJVsEiEoSAaKSRICoJBEgKkkEiEoSAaKSRICoJBEgKkkEiEoSAaKSRICoJBEgKknbAfon9ZjaDaDlVa6bd97pkri9cH/M+ARIjD9m/HiAfv+o/vhpLL5X1acXz45cEt6BR/tjxo8H6PVL809b/PjzpX4fmCJA2f0x40cDdPv2Un/89dOx6NyRS8I78Gh/zPjRADXE9Lhoi2+ffzVb3UWAcvtjxk8C6ONrNwdqAbpQj6jEEYhzoHL+mPETAeIcqJw/ZnxOosX4Y8ZPOI1vytfH33+5d+SS8A482h8zfjxAt+f26uHr07j4Vo2XFglQfn/M+LyVIcYfMz4BEuOPGR8GoGrZGrMFi/ljxkcBqLkWubQ9ZgsW88eMT4DiRYAcQgGIJQzdHh2gCGG2YDF/zPgESIw/ZnwCJMYfMz4BEuOPGZ8AifHHjE+AxPhjxidAYvwx4xMgMf6Y8QmQGH/M+ARIjD9mfAIkxh8zPgES448ZnwCJ8ceMT4DE+GPGJ0Bi/DHjEyAx/pjxCZAYf8z4BEiMP2Z8AiTGHzM+ARLjjxmfAInxx4xPgMT4Y8YnQGL8MeMTIDH+mPEJkBh/zPgESIw/ZnwCJMYfMz4BEuOPGZ8AifHHjE+AxPhjxidAYvwx4xMgMf6Y8QmQGH/M+ARIjD9mfAIkxh8zPgES448ZnwCJ8ceMT4DE+GPGJ0Bi/DHjEyAx/pjxCZAYf8z4BEiMP2Z8AiTGHzM+ARLjjxmfAInxx4xPgMT4Y8YnQGL8MeMTIDH+mPEJkBh/zPgESIw/Zvz9ALpm1yW/BbI/ZnyOQGL8MeMTIDH+mPEJkBh/zPgESIw/ZnwCJMYfMz4BEuOPGZ8AifHHjE+AxPhjxidAYvwx4xMgMf6Y8QmQGH/M+ARIjD9mfAIkxh8zPgES448ZnwCJ8ceMT4DE+GPGJ0Bi/DHjEyAx/pjxCZAYf8z4BEiMP2Z8AiTGHzM+ARLjjxmfAInxx4xPgMT4Y8YnQGL8MeMTIDH+mPEJkBh/zPgESIw/ZnwCJMYfMz4BEuOPGZ8AifHHjE+AxPhjxidAYvwx4yMAVEW6YrZgMX/M+AAAVVUkQZgtWMwfMz4BihcBcggAIJYwEfbAAMUKswWL+WPGJ0Bi/DHjEyAx/pjxCZAYf8z4BEiMP2Z8AiTGHzM+ARLjjxmfAInxx4xPgMT4Y8YnQGL8MeMTIDH+mPEJkBh/zPgESIw/ZnwCJMYfMz4BEuOPGZ8AifHHjE+AxPhjxidAYvwx4xMgMf6Y8QmQGH/M+ARIjD9m/HiAfv+o/vhpLH58rarvnh25JLwDj/bHjB8P0OuX5p+2eHv+Xr9/enHvyCXhHXi0P2b8aIBu317qj79+aovvn3/dx6JmCGo+GkiAcvtjxo8GqIGnIcdcbEahHqAL9YhKBOjtPgo5SXRJ+AhwtD9m/DSA3oZpNQHK748ZPwmgt3EKTYDy+2PGT5hE6+NPNoD0L17AbMFi/pjxE07jP/580Z7OA5Dx1S+YLVjMHzN+PEC35/bq4evTsPja9O54JZEA5fbHjI9+K4MlDMVeKEC6MFuwmD9mfAIkxh8zPgES448ZnwCJ8ceMT4DE+GPGJ0Bi/DHjEyAx/pjxCZAYf8z4BEiMP2Z8AiTGHzM+ARLjjxmfAInxx4xPgMT4Y8YnQGL8MeM/EkCxf1Yqlz8BCgkfoOg/bJfJnwAFRYAWRYBCwgeIJSyH/yMBJNwfMz4BEuOPGZ8AifHHjE+AxPhjxidAYvwx4xMgMf6Y8QmQGH/M+NgAmVduMFuwmD9mfGiArGvHmC1YzB8zPgGKFwFyKDdASltmCZNsf9QIpKZF4R14tD9m/PwlTI1L+TswfLuUAGXwLzAHUsNC9g5ceMMGAcrgXwKgoVcJkGT74wCqBoJYwiTbHwjQnaB2QXgHHu2PGb/EdaA7Qe1P4R14tD9m/EIXElXzn/AOPNofM74foNvz0/3/1/GPYSxo4Uq0qsV34NH+mPF9ADV/TK6V/m30IS3dylDiO/Bof8z43hHorQfoS+TuCVBuf8z4SyUsWos3U9VCguUP3WC2YDF/zPgF78arYIKIj/0ltmDqx8KO7kFxAL3vOgeqzTvzM2UHKPmDqUf3oDSAbs97A3RVoWdzlzAClLj9hjnQ+6eX99iJUDJAy2IJO9J+NUC/fzw1g9CeI1C4iC0KswWL+WPGD8yBPv58uZ/L7zkCLUyDloTZgsX8MeOXfk+02myA2oLF/DHjEyAx/pjxS57GtwlU3O5cwmzBYv6Y8XOfxuunPl0CFbc/hzBbsJg/ZvzMtzKMiy99ArVmt7ouiSfiBCiDf6CEvcbeR3XtaNifA6DNBKVeCiRAGfw9APX1K0cJqzcTRICOtD8IIF1TAhW3T0ssYUfaZz+Nv66RWrV2r8uWjXbUwf6Y8Y/6cgW1wQLzJVjMHzP+AkC/f2QpYfUmgjBbsJg/ZvzDANpAEGYLFvPHjH/c9wOp1RaYLVjMHzP+gV8wpdZaYLZgMX/M+Ed+Q5laaYHZgsX8MeMf+hV3ap0FZgsW88eMf+x3JKpVFpgtWMwfM/7BX7Kp1lhgtmAxf8z4RwCk35FQKywwW7CYP2b8AwAy74mqeAvMFizmjxn/cIAMgsJ3SzFbsJg/ZvyjS1itE7Twfg3MFizmjxkf4Zvq1ehOgHDtgQHSCQptj9mCxfwx40MAFDmTxmzBYv6Y8TEAiiMIswWL+WPGBwEoiiDMFizmjxkfBaAYgta14Hw+RYAy+MMAFEHQqhZ0nNERoAz+OAAtExRsQRsXArSz/ckBmvPCEravPT5AiwStA2i9/5IIkENIAC0RtKqEbVtlu3+ECFBIu/zRXRV81pnAoCKISPK3bBIgh7AAChPkSmBQEUaEAOXwBwMoSFAiQCxhOfzRAAoRlFjCOInO4S8eoBUiQBn84QAKEITZgsX8MePjAeQnCLMFi/ljxgcEyEsQZgsW88eMjwiQjyDMFizmjxkfEiAPQZgtWMwfMz4mQG6CMFuwmD9mfFCAnARhtmAxf8z4qAC5CMJswWL+mPFhAXIQhNmCxfwx4+MCNCeoTZBwQ4sAZfAHBmhGUJMg5ZY6AcrgjwyQTdAI0EaGCFAGf2iALIKGErZ1FCJAGfyxATIJGhIQoCPsZQJkEDQmYAk7wF4oQDpBmC1YzB8zPjxAGkGYLVjMHzM+PkATQZgtWMwfM74AgEaCMFuwmD9mfAkADQRhtmAxf8z4IgDqCcJswWL+mPFlANQRhNmCxfwx4wsBqCVoxxbcdCWJADkkBaCGoIQWbIG5ag+3EESAHBID0J2gTX/2u92mA4YAZfCXA1CttnR7t40NEEvYbv6CAGoJWrtND51VwraJADkkCaCL2lrCdvJP3L4EQIGX2NEA/f5RDX8CfFz8+Gv8o+AlANryx+Z39U9TAYBCVf5ogF6/NP+MxdvzH2UBSiNIIkAaD8IBun17GQacYfGt+s/CI1AaQQIB0oEQXsIaYhpytMX//9UT1cQsBFAKQY8A0L72hvYHaJwDtQBdCkmVMoJQVR19BAvaBSAHiS7t9BJQW7cXOAIB2eccgRw7cmmvBGrj9gQog3/KJPoogLYSRIAy+Cedxh8F0EaCCFAG/3iAbs/t1cPXp3HxOIC2EUSAMviLupWhLasN2xOgDP6ZATKua+2aQK3fngBl8M8LkHllfd8ESq3d/gEACr1dgQDZCdTK7c8PUPAdUxIByljCGql12xOgDP5SJ9Gd1Krtzw/Q6UqYqQwJ1JrtHwCgjPbnBGgVQQ8AEEegkJwJVPz25weIc6Cg3AlU9PYEKIO/AIDGNvG0oIrd0fkBYglzaHpV+VpQRe7pAQDKaH9igGIJIkAZ/PEBWixhdUfQ8ocOzwbQyo9ZPixAowIdqGI+7n4ygNZ+0psAhTow5oPzBGhX/05nAagh6FD/CMGUsG3fs31ygCJm0oP/1j/XggZQvMzvltj4Tf8yAApFW2hBFem/+Q/+iAXI+nabMwMUzLbUgirO/+EBOnMJSwJoiaAHLWHD38d6jEl0QgmrLYJmMJ5tEh2nsRkS/tZjwB8NoJAiWlBNi1VlE/TYAKX8rceA/8kA0gjaBlDaCBjWcSWs+0GAYlaaPqyxpYSlzcEWdPC9MJawyBZUvqY6NUBHXUc9IUDeb3OVW8LaowraO8l3VfDt49DjAFR5bmuIHYG6o1oNkPW7q2+9SD0OQHeCtvoTIL8eCCDP557PXMKcB84SZmpVB6qD/R3iOxJDggBIf3mpA/zDKgbQ9nMIv9QjAGQWeFXcf0GlAPLMcxLsVTMlkAOQr0yvBGhG0DW08wg9JkBK9RNKMQB5TxTWlbB6NpW+hnYeISkA7VfCRnj8/ucCaCZl++MCtHhcpflV1utPDEDbS5hDyvYfdq6ZxCKVtQeXyS4IkFI2PV5/RIB82tSCyu2v9Vf0oLRrD9qeMAC52An4nx4gjaC8AK27mzk3hShhPnj8/ucHaCLINwLsUsJWfi5tw1wscwV1lq1l/xMB5O0SNbwlL6e/MaS5VwmWsDX225IEmr9hZ3GfZwdo9gbE6ZmWoOR35MWWMK/RXqfxG5OY9toulIra5QMDVKkCABkH4nwCCaBxH33ditjj2QHyl7CGoDp3CTPs3L/f7ULiDiWsA2hh1uPz1yUWoJWN2LTUo9wLs9U3lWm/OGeO9JcK0PphXD0AQM42GZpqsl/NTsD/cQCq1bVrYfeGmycB8doHoMCBuhvFAmgTPJq/JakAbZkHqP6zYqFWjvbfoF0ACh2o5zmthG2mpz4dQBt0VScHKPyquqbQUxOgxl+p9BK2/WQuVwmLOqJEemoC1I/hqf4Jl5MW84f3PI8f/6H3fCehJwdo/rkWleifC6CqWtr1xSasX39hs/F8nQDFAzS96Ue/QdX5q7hNvf55Sph/dqbZWyt0D0NbGefrBCgaoLFNp8Ztlobz2KhN4/2jiVoCaGF2drFeD8NFCe89ZMc7elP0iACZdzgH/9B0cj1A8TVtqYQFj6iqLlYct715iyvaPkIPBJDzTGUCKDgILZYw157jjmpbfq1QTUbeN4+0T7jPuNABumbXJWHbFqBJakd/Y8d7SdtpuzjMkaZful3bN4ZlOJ6rL/45RyCHxkl0p/1uBsVrRf75sHYvYfovPeNe6I1h6CPQ8ioZAYqqItbt6NX7yQKQb+I8v2tnTaLtM7K6WnhrDwHyduDSCbDDv50pOHe0wT9S19F62dFxgnUxgppPVk3pWriueBKAEt7W5evAxSsow2rmJo5BKBmg8M0oh4fHsZ8zzwYZ7WqR8VxTuqbLimcGKP6cZa4gQMZj31r2AzVfKfBwGaBwOhdAESVMv6alEzQ+rdo3NS/e2EgDqL2M4NAZAHJf4befqCyC2h8qaDivIQuKAShuDJ5K2DTiTCOM9ovZtNm7+ySAvMnOUMIszeYJ5kvYXFnF7SnWP6KELWw6GyYtgPQ1q6lyRRzQSQBKUOwk1rpeqw/583ZQod2sLWFh+fNPRzYfJiudf10xn6fQNzpHCUvRmg7Upg9jI16dLyTl3dZeNR0gT2dPM5v5FHg28HSKfHuPB6BNZeChAHLNd1wAdbMI57YZAPLVgREgxynU9JvLNHPrD3le9Ry7nuwd+1yjRwXIfAk659vKue28K+P9nfICNJawyklQv9BfSJzGHi/pHnttlwRoScY8qD8lvs6eHVrSHITMc7dpaX2rm1t4S9i0bqiEXfozdvup9QCxhK1QNemq/25Y6n+l/FvPF9d4aw99+UfCjSOanhsB0s/Y/Zv4dI4LiSnaNgcJAjTJnFa41twyAMUANB3g3Ef7dXfKblyTWCcCtHkS6y1hxiNVO/pFfxzhP9taf+S5DmYBZA16Q41V9UVfjQBt0EaAxpYOjADtgutrTvRf+P3tOZVbvivx9gCkLzXqJz4X40LW+vGQAG0vYUF/rU/nBDkB8p5qOwHSAbYmydPEeV7CJnwM+8hzdocIUMIcSPefzTW0dp/fGnCUsMAw5eTHug5VmU9V2v/2Ybdv0rDtrb2be3KtU4/2SXpUgKa+Me+Ge5q7m6ra2xv+8y3Dw4I+AhqgGN1ugNWvaByMK36/sT2IOUWAtk6iXQD5m7uybm9PXeMtYSFrew42G4LmBzJNfaYn7/8vAsQStqCks7DaKGGBl6s+7egf92tf7BUjjPWVBoD14ukDaKRnIuRirDJOoBxGbhGgzQDN/a0Gnw0KGkJTeTD9Y/rMBZDjRN3+wI7qzwf1AWi0n/hfeSJGgHYEqLb4MTvQRGgqEsam4Q6cVpoeXbV9Gd7GzrWxxzi/07/ehQBt0l4Aza6kGL0x9o2JkNaVEVdi9JFjfHSdpiz6agYNWuWyWdMAMudWocNwxN8qAjTOgbS+0U9ipjXH3pw2mAMUkhug+bCiE9R9jca4xuxcUSthkTIPlQBlAKjS+ku7zzTWHjVsoCHm7MH5ib0+gnT7vpq/1Dhp4TG620GQ+yzMfwh62dXiLxy4XwTIUcL0Dh6608ClHYQsghyanpt+zsata20j2D1tzHr0PZpFzBFf32R+eNZvPJ9rjCaIALn8K6Mz9YoydH+DkAGQjcqw8XxhGNT6Xdn+7c7NMy5rDKqTALJGFwKUCSB9yKimGer0/kDVf+iz42FeW8ata2sPBkvTM72Ufq0nRJAZ3+jwYAmLiM8StkZhgGq958fnxum0MU7oWw5gmAOXTpCDkcoNj2Ztz2CivqV1dfw1IkCRX25gAjSuNM5zJy7GlfS65/3NKGPoqc2Vq7FuaTjp8f0AbRuB4kWAovynk7HZxKY/03acLs0h0ZmYFqftDbzG3Vinhdrz9eJpvJ+sNfEDIkAx/nqf9T06jkSXuuNLaX+oxBw15tVqgGZAZw6auRttZ8YgthyfAC0qH0DmuYxLzSoXgxIVqcAOp1nWxIkx6BkALZUolrAlZQNIf/HOunnSxZoe+9AwpkGzKdFstWnV+SEZ/GydPS/FjxQBCgJkdNT0Cy9AtX+0ckJlwWIzpR3KdD5Yj6zWBKgGBmjeuxFwrOEnYm/WgeiPx+Vc8eNEgEL+Vm/mIyWOn9mJYOb4MSJAQX+z77yP1oKxgp6ZbfebMvEjRICW/aeLQMYl6W5m0nyyb3jUs1FPNW86359RoD20ntYuOmlGJlSjCBA+QND+mPEJkBh/zPgESIw/ZnwCJMYfMz4BEuOPGZ8AifHHjE+AxPhjxidAYvwx4xMgMf6Y8QmQGH/M+ARIjD9mfAIkxh8zPgES448ZnwCJ8ceMT4DE+GPG3w+g7Kqq/B7A/qjx9wIov1LfEyzcX0Z8AgTrLyM+AYL1lxEfGSBKgAgQlSQCRCWJAFFJIkBUkiAB+vjr5/jj94/qj59H+H98rT69HOB/960+/2p/fD8ifu9/N66eIvwhAXrtjrn98fql+Vfe//b8vX67/yzu/966Nfbvd4DLx+/869fPvz7+jPBHBOj9b+0I1P64fXsZBqSy/h+deXn/16f2GNpB4PsB8Tv/xrj/EfYHBOj3//xfW7vaH30/lve/917Ti8X9f/9rNLuPQuXj9/7aLCLsDwjQ21N79N2PAwDq/e/Vv5mKlPa/ffuPdu7VHMgB/A7+75//t5mDSQTo9l9ds3U/DmjB3v/5qZkDFfdvJh63fzQv/2YGVj5+7/9+n0Hf52ASAXrtuO9/lG9B0/iAEbCfgLw149Ah9o1jPwcTCNDtuf0mnf/ufpSfRfb+3w+bRNcdQG/tmegh9sMLJ2oSDwdQI/060BGn8V3rPR1yGv/eFK6/t6fQjcpfRej8m5Ox95j48ADdR4RDLyQW93+rGsPXbhw8IH7n315I/B4RHxIgSo4IEJUkAkQliQBRSSJAVJII0Ea9tidJFAHaprc7Pa+fSl8iBhQB2q7mftHDiwDFq7m29vlX93/z+I01jACt0R2Y8V/dXKQtfokcUAQoXm/Vl/H/uplGcwAiQGvUFK/qe/d/AxJnQDUBWqn3dvhp/n+vSr9HAFMEKF73mvXx9an7//bMc/hWBChe+lnYW/t2CxYxAkSliQBRSSJAVJIIEJUkAkQliQBRSSJAVJIIEJUkAkQliQBRSfo3xZxYPLgMQosAAAAASUVORK5CYII=" alt="plot of chunk nonsim" /><p class="caption">plot of chunk nonsim</p>
</div>
<ul class="incremental">
<li>The deviation here is quite stark</li>
</ul>
</div>
<div class="section slide level1" id="compare-and-contrast">
<h1>Compare and contrast</h1>
<pre class="sourceCode r"><code class="sourceCode r">a <- <span class="kw">qplot</span>(c, .hat, <span class="dt">data =</span> goodsim_a) + <span class="kw">theme_dpi</span>() + <span class="kw">geom_smooth</span>(<span class="dt">se =</span> <span class="ot">FALSE</span>)
b <- <span class="kw">qplot</span>(ss2, .hat, <span class="dt">data =</span> damodel) + <span class="kw">theme_dpi</span>() + <span class="kw">geom_smooth</span>(<span class="dt">se =</span> <span class="ot">FALSE</span>)
<span class="kw">grid.arrange</span>(a, b, <span class="dt">ncol =</span> <span class="dv">2</span>)</code></pre>
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAkAAAAGwCAMAAAB2PiqAAAAAdVBMVEUAAAAAADoAAGYAOjoAOpAAZrYzZv86AAA6ADo6AGY6OgA6OpA6ZmY6kNtmAABmADpmAGZmOpBmtrZmtv9/f3+QOgCQOjqQOmaQ2/+2ZgC2kDq225C2///bkDrbtrbb///l5eX19fX/tmb/25D//7b//9v///8YrBpQAAAACXBIWXMAAAsSAAALEgHS3X78AAAdJ0lEQVR4nO2dCXekyHKFmXF3zIyfpbHd08+SPXJra/7/T3zFlhm5RS5AkQn3nj4tVNQlguAjF6BKXQ9BK9QdnQDUtgAQtEoACFolAAStEgCCVgkAQasEgKBVAkDQKgEgaJUAELRKAAhaJQAErRIAglapHKC/zqqNKnv0buwmczdXAPQaXvcWXhV2FZm2d20GUHJEIc/72gSXtgGgiAsAybZ0gH5+737921h877pfntSGrg5QrD7JEc8K0PPX4R9b/Pj9qX9fagaAYvVJjnhSgD7/fOo//vjbs3hz3XR1gKT6eLZzPYCGiszlYIsvX370C0DnVCpA0fokH5wLAfTxG8ZAi6T6XOgEy22BMAZaFK1PcsQLtUBGHw+A5PokRzwpQNFB4sUBwiB6VM40fmieP/7xY9nQxQGK1ic54lkB+nwcr449P6jFl05dOgNA0fpskWfTAEV0eYAiAkARASBZACgiACRLAKgzqw6AcjIBQONlRr7q8gBRTiYACADNGwJAotCFRaQA6ignEwDk6OIAdR05GwFAACgqDZDbBAEgABSV7sIAUMJ2AJAtNo2njEwAkCMARBmZACBHAIgyMgFAjgAQZWQCgBwBIMrIBAA5AkCUkQkAcgSAHIIAEACKCgDJAkARASBZACgiACQLAEUEgGQBoIgAkCwAFJHxSCslZwKAHAEgABTfDgCyBYBkAaCIAJAsABQRAJIFgCIyPxdGqZkAIEcAqAdA0e0AIFsASBYAiggAyQJAEQEgWQAoIuvLFSgxEwDkCAANosRMAJAjADSIEjMBQI4A0CBKzKROgNj3ZQAg2QaAPC7+jT0ASLYBII8LAMVc+wNkENQaQOjCYi4AlOwCQLINAEVcAEi2AaCICwDJNgAUcQEg2QaAIi4AJNsAUMQFgGTbft9UT0mZACBHAGgSJWUCgBwBoEmUlAkAcgSAJlFSJgDIEQCaREmZACBHAGgSJWUCgBwBoFmUkgkAcgSAZlFKJgDIEQCaRSmZACBHAGgWpWQCgBwBoFmUkgkAcnRZgN5skfOKK9e1l6nQtRlAO+d5lG3HFkg3QWiB0AJFBYBkAaCIAJAsABSRByBFEAACQFEBIFkAKCIAJAsARQSAZAGgiACQLAAUEQCSBYAi8gG0EASAAFBUAEgWAIoIAMkCQBEBIFkAKCIAJAsARQSAZAGgiACQLAAUkRegmSAABICiAkCyAFBEAEgWAIoIAMkCQBEBIFkAKCIAJAsAReQHaCIIAAGgqACQLAAUEQCSBYAiAkCyAFBEAYBGggAQAIrqXACRWgJAsg0AeV2klgCQbANAXhepJQAk23YHaDgWAAgARXUqgEgvAiDZBoB8LtKLAEi2ASCfi/Ti7gB1ds0BkCkCQJ7tqIj8L0RPAkCmCAB5tgOAbAUBuh0NAIQuLCoAJAuD6IgAkCwAFNGZACK2DIBkGwDyuIgtAyDZBoA8LmLLAEi2ASCPi9gyAJJtdwCoJwAEgKICQLIAUEQnAoj4LwBItgEg10X8FwAk2wCQ6yL+CwCSbQDIdRH/BQDJtnsAZB6RQCKOAJBHACiYiKPDACJjFQCSbQDIcZGxCgDJtvsB5Dz3YibiCAB5dFGA3sj35J2ZiGsKbw8A3cUGgMpcZKwCQLLtbgA104WRuQoAybb7ARRJxDWFtweA7mKrCKDwPAwAOTorQD+/d7/+bSx+/NZ139SGrg5QrD7hiJbOCtDz1+EfW/x8/Na///K0bOjqAMXqE45o6aQAff751H/88TdbfP/y43auLafY1QGS6jPMQC8P0FCcoTLm4nCWzQU6CUBkrUoFKF6fc2olQC+3syypQHSf3VkvO9F1AE318YCIFmhcfFmGjbEuLNgEnbsF4vXZIs+zAfSihogAKFqfLfJsGSB3kMjPLwAUrU8wItN4tf6kALnT1I/fn9jqqwMUrU8wotZ0v/CsAH0+jlfHnh+Wxedhf7u0afwFAIrVJyHPcwMUUQSgEEG1AUT2qrveyjh1FxYRAJJ1+UF0TABIFgCKCADJAkARiQDd+naKJOKawtsDQHex1QPQMLugSCKOAJBHFwYo0ARVBhA5qwCQbANAhoucVQBItgEgw0XOKgAk2+42iPYC1HUAyBEACmRCzuuBz4pxk1e7AUTuKgAk2wAQd5G7CgDJtkMBqq4LI3cVAJJtxwJU2yCa3FUASLbdESAvQQDIEQAKZUJSIiGTT3sBRJ5VVQEkDBkBUMDk01UBEicdAMhv8gkAZdlOA5DvAAEgR+jCgpmQkEjQ5NFlAbr4IBoAORF9AkDBTEhIJGjyaCeAyLcKAMk2AKRd5FsFgGQbANIu8q0CQLLtrgB5DhEAcgSAwplQOJGwyRUAuosNAGW6yLfqngBNl3kAUDgTCicSNrk6KUDzhWYAFM6EwomETa72AYi8qwCQbLsvQO5BuiBApCLaQhcWzYSCiQgmR2cFaBIAEjKhYCKCyVHbAI2BkvM0758CoGAigsnRhQCynuC4PEDOUbokQB0ActU8QORftT1AHd2YQBdmCwDJYgDdCMIg2hEAksW20xFmYa4SAbKP0xUBGkJdAKDPx4fb/8/qjz1E1DpAFFgVBCi3PvwXOj9Awx9LG8W/bV3SxQDKrw//5QIA9S9zgb4KW+G6GED59TF+o/MDNDfRyUoFyDpSzQKUXR/jNwMg68M6ZwEoU40DRKFVO92NZ/HsjwsKebb1ubD3XcZA5wEosz7mryxeOkBtfTL18xEA9WIXthFA6V1YawA9vP/y9J7a0V8QoLz6WBGDAU/Thf38/jCcZGiBAsqtjxUxGPA8g+iP359uc9XNWyDzWLULUG59rIjBgOcBKE9tA0TBVXs9Ex2OCIAimZA3kYjJ0BkACrd5pwFop2n8aQBaNY2/AEB7TeNNgtoFqHQaP82kLgHQPrcyzgNQ0a2M+VqOcPNEmqu3BJD6I9ZpuhxAufWZf0YB2uHr+w8AaG6fr9KFUXiVH6CC+iwLSxcWigqA4pmQJ5GoialpgCYJz0CepgvL01+vb8mi8f+uu/2X4dIqMkkuCq/abBqfHLZs746yHXAdaD71pqa60RYoX74vV/CHPcssbNTP73t0YWPlTgFQRn3MX9/CcQFQPBMaY3V9JQBJD5gCINl2SBfGClcDQF05QOkCQBG1C9D4SdGgAJBsOwYgXblrA5T592cAkBI5iSSYlDbuwqg7qgsDQFotAyS5AJBsA0CHApT35f0ASImcRBJMSucAaLyMQe47AVBCJuQkkmBS2hYgEl27ATTfNCXnnQAoJROyE0kxLTodQMb9UwCUkgnZiaSYFp0CoIUasp/gAEApmZCdSIpp0WqAxuO1HDQ6CKBehQdAfVsAjQdMHTU6FqCJILYKACVlQlYiSaY+ZioAiGTXXQAyBICSMiErkSRTHzMVdGEkuwCQbLsmQHYihwKU/qVtAIiJrESSTH3MdFaAlkESANIiM5E0Ux8xnRQgNeAHQFpkJpJm6iOmJgESvvFm5gYAeURmImmmPmKKu+wPzVDEdShAChx0YR6RkUiiqZdNUZfzsT2KuO4BUPD7JpxsARATGYkkmnrZdDKA7Payqa+4y1QjAFXZhQU+7W3ccJleaOlLNjO1AiB/Ve4ziKaY6ziAzBsu6pWQrgfQWLXXYFkuBZDv6wJcgNCFmaIeAJl5jAp3YRhEm6IeXZiZxyjcykjNhHop/7sARFEXAJJtRwI0VA0AmZn0ACgjEwJAdiY9AMrIhACQnUkPgDIyoaMBorjrXgClfNIJANkiAOTkAoAyMgFAnmQAUHomAMiTDABKz+RIgLpO9xpVABR/yhcAOaLDABpuoFCC6wiAwre8AJAVDgBx0fj/q3DTHQCZ0aQvl7teF8YBCtQFAJnRWCOQbOq3G0Sr4HUB1IcJAkBWOABkiIb/XoUnxwCQLSoxbQSQii09p3UIQMGMAJAtKjFtDJD4pOgxAIUEgJxEqMRUFsp+YQldD0CRR6QAkCcRKjGVhbJfUKGr6cIAUHYmBwLEItcyiI48oACAPIlQiakslPU7iwyAMl0VARQcRl8TIPH2IADyJUIlprJQhnhcAJTpAkDmELoigKT7y5MtMOQHQDmmslBM+hr4MIlvA6CJ9NBFh8sCFCJo252+Ff3V+LVagHr/Debpj4wDIE8iVGLKDDVU3QRIH6bKurBbZp6j0CmA0IXZidAc2oq9K0C9eRe3FYAwiPYmQmPkbb6MK7ELs9q9mgCy2FavdhHbNgDxgwCAJBclupIB+vm9W/4EuFr8+EP9UfB0gMLXVvcHyDgKGwMUK9CKo0pjaB67uLVOdVGqKxmg56/DP2Px8/HXEoA2f0QhYBsrfj+AYgUqOarzwITc7wIUZ0Y1AvT559NyPi2LL91/FLVAdwJoguVuXVi0QEUDk/nvndj9V4MADQUZCsMW///HXLBhd3IAChO0O0CJwQoAihZoS4Aa7MI89VFd/FSfDFHOm4t1a//Xaw1A5QWyd4E22ZccJR+iLQDygJgyr/Co4Wl8tEBrmgVyXt+5C7MC7twCebYDgPYFSHzKtEqAPGNEAMQVLdBmAA3otAeQb5ZaDtC293eqAChaoFVHlVgK3URQY11Y//k4Xhx7flCLAMhQrEArAVItztL47AkQpbvufysjNCxMsvlVBUARrQSI9Vmr/jRW/QAlnh7kXQeAQomQM+g5KUDzmZLVq2vhZmooEfcZhp0AGuJQhutaAO15LyyiUoDYH99ON5WFGv4bK+QEq7AL8xMEgGypjCnD1DRA0YhHAtReF3ZvgPT3SiWW6jiAfARhEO0kEiRov0H0GCm1sb4YQM21QK/6lnyOqSzUrDESAPLZ2hsDvS5/mO+eADl/ya1OgDabWZwboH7+w47U64M6/NwNIPfpo3oAMh/xImc9ujB/IvPcaDmyKz7B0jZAY2bCBU8MokOJTJf39gVoocZ5AhsAZbuqA6ifPg61ZxcWvmBQD0BWF+ZeoN8NIN/TM20B5Hzp+F4AUZbr0EG0e4twL4C8z1+1BtA4jM4zZYUKN0D1AmR/zhkABRNxvnR8r0E0eVZVC5D9VR1378JCD4ZWCFDGR21yQulTq0mA3KJED6lHJbUUv0umToCSP6+eEarTJXj1P8oRiXUfgPhhkgGKH1KPCmq5PFkMgDRA/jvxkVh3Acg4TjUB1FYXtgdAvAvrnIF6QqyjAXKKcp8uLPLh8gsBxFzBBuhwgIQuTN369dm4NgWo64ItnWWrCqDUr94tncbXCxCXvXfEOuL7AiTQUD9A23+wMNyDNQuQ0HCVRlNbbhwgMf01AHk3WzVAM0EemzR0Ko7Gti5ssTqA7MvEmwPUdcPz+7TMTpMTrAEgne6+AKXfeKsOIOtG1fSIWcyUE2oKQMvja+mlqgAgdj9j4y7MvPevy7L0l+GDUCtA7HHTbQfRC0C99/JYowCtbYEGvw+geeFN6AZqA4g9rNPv8zzQWCqyoiUkWAFA7It/AVAwkUU0ptFtPo03AEp21QFQ8M9Lb9uF6c2114VpUYkpHkq4CCTHqgIglfm9rgPFXFUCZD3vBYBGmVW5A0ChKV/AVg9AxkRsnzEQZbsOB8ianu4PEBv3hF1UO0CRW3mFoajEdSeAQqNhG6CEUYlH2wJEVG0LpK/VXAwgPt/xdWELQSnzIo+27MKIDFs9AGmCul2uAzUK0CJy3mcpFSBrA7m1JMtWEUDqat98FSLRlBRqvOJBJQke3IVp0WhTN2IckBIBshHMq+XU/PS1AjQ1QrTmyQXXNZc7eCc+EuvoWZgSLTb/3Zg4QJNhDUAKn1oBmp9CoWkWVjRedELNBRtvpJYkWA1AI0GpAHlu1SyO8i6MfLaKAOo6BdCyFDdFQ+m6UZjIpgBK6MLs2r15XotE6+2RE2t++ioBUvzMD11sBNBcuJGfBgFiOYceZvLY5kbKjOY3v4Yf/OEjJ7La71oBmhZpwy5MVVNogOoFiJ1F0ykQ3gebO/5mMVpwq2/LpjzfwlwhQD3romkyWTf3fKZgKG1Z5navni3FE2wTINO6BqCpS3DqViNA7LyhfroXvDy8kz9z4JaZyVfr5bQEK+rCxEZUuiIYiSZ2YZ09+rGi1QSQHvkMxL/p6UYxQNpHy7nWCEDeNOmOd+PVpVwfPhUDNLVCc5+rx9VlXZjyjpcGXsMD8+oACiRKewPEOsz5ZhJFbDUBxC51mQDZJ2RqKAbgbRLxGp7YtQOQ3TObtpAiYyD1iw47A+RvfvpaAZpSmIZt3ZtaduqZD9AwenjtQ/zUB1BoXELmIXZsAUnRzNEin7e8CX9/vF6A5jZn6e6919+TQunGa2qACu/h13MhcdDOAJncvpFgWxbqBGgcL/KuK78LY4OnbroPdgaA3kjowooulL4GatwLf72+rxmgZT/U1WjPhfscgNR1pZMAFLYFR3hOx+6J5k4wSBqx1wxQP+0iA8i5dZjRhS3tWarLUS0ATQUQhiWpAFlv02ME4/Vh9NwsQPNBZxeB8gAyajINqCZX2hlqqgaAllNomBiRtYLZkrowq5a6lzf5ieTYBED6vMgYL77x++9qQDX+EE7RugEyTyMyV3hs7l4GHihTpbXO0Xny3ixAUwXedCeWdy9MF2MZAU2vNA2QeZuHr3Bsnt30P9KqsGGNPI/QKkDzHk4AeS+pRbsw1jD3ejjVchc2/dAzAmOFaYsAxN0MoF5VjGSXFa0+gJb9f1P3M5wDHw3FzyfeFxYkuBlAb6l6Da0YduH2g2K28V0Rje+Zy8IcAz95SW4IUFLgYCJs15bdoXlR7WfY5NnGXJi5IvYmklVDC7RIvD0lzv7dLbGZBm+z+L2LRlsg1YWpx5hYFx00WaE6JvOKUm6CRz8P5LGRd20KQOxGRaf7RdZgE99mqwDNmXT6q7nyAeqz+KkWICfpaYhHvrUyQHxMuHj1RGMZCpFRpqYBmnaEpkX7OkUGQL0CqLYLiUGe+XzcAmgpBanVPpt6q462EKJvW6hGZyZoWCazzCcBSO97DkBq2pvSAB0BUDghE6De6nj4REk10KaNWa1oVgPUMfW6rVau4M6w76WqFaDlnGBVy+rCfABV1YWlAMQ6HtYFWReDFlZEgJz2rnNFnQq5uALiG68WoOmSIHV6X1NMav91Vebq1wZQShc2yTrO42tkrXdtZhdmruAXD5ezk4g7pku5oX2pHyC9k9SblRNMk9GsD3XslaIEK5jG253NIGJrfV1YKJreiNrq+LIx/Zq32W4XxnbSO4SRAVqsGqDplcoG0UF58jQai/EV4itCNua3NtTpX/jmeDx+Y1pIsm6A+t77KdXwyFudV/NshePXLkCqyWDDalpWJACky2cUUzXO0+e+fF2YVXhPklUDtFwLSgRoeNebn76uvml8UAGApmOqBtO0rDCmYn6x8lkt0LQpMorGc2wUINbrq1tZcZMJ0AzfKQDS9WD3imleoVd7tuWhS6EyYzmiGAKo0S6sN84UcnZN6MLeekYQ6Uo13YUNUvXQdbFWeY7d8qr5oK/Cbtwc9Yoly93yhUTWcLgf7E97nMP5LHnbAClw1E5Rz0kINEAmQEtN9Xacq4dpOTYE0HQzol/GjpJpCbXUiMzBU+MA9boLm37TTXP4OtC898s3nRhlHdto3xwlIcfqATIufMwXg/S5Fxh5q1DTIi2biYSSE6wJIKsvWgByemhnTKR+6zqrsP7RTzTH+gGaL/b7ARK6e/U4B5vnRkM1AdC4JwZAfIw32fj1HV4rRtrSPE8E2s/iG5VtHSDfaLjvTSi0NEAzdKxmsVAtAaSvCPXq70AtXRhvkViTw//v2HvG8fOr2rwensdzbAIgdrbQUgFxxjGF0vxYBJ0CIHP/NUEdA4i3I9NLb6oFN/hhQycF19kAGheNS8oBfgwXfzTq1ABNEIyv6C7McvUWQLNhHj/bAKXl2ARAvVmoLICo65k5FqoJgOZBtLn//DKgepPhmTt2ByA+/ZoX7LqeCKCe3VeXAFJXosnzrtYBmm3qoPcTCD0HyN5rDpAe5HTGXeZgSZsHaCnS9I/YONB+rzFJ7dU9DPOEPAlAfF7VmQRZxdHD57dOv5+dYINeWUvkCRZNsmqABundI7VsfwycnVnjgrqCaBTmJADpWbhDkM2P2cjoV/jlw1fbNlkjObYDEKtLeBhkFsqqaEKolgCyajAWxjuHMt/JpPGZZmHekXcn59gMQEZlTIL4ew2C9MTEfNsJATKf+9YosAtmLj+dMRZ45Rbj4pHxfHkwyVYAGn/xEtQZvHTzh+M8mJ0DIL5zaifJ3FkGFyNtGjxT5wVI09g7AFl1NJOsHKCejYQ7azLfL6+aBJE540gJ1RRAo4wRMZ+TO6cTq4PuvSIAWWOgpgEapatCRk3c4eH4R0FMwhJCNQeQ08DwM6v3dl7mxTR9hX4ZA/EuzM6x4S5slC4XHwc5Y2e7kGcHyJh6kbHnXrlvGaN5KhXPsSmA2A7biDg18s5no6GaA4iPdpMK48PHA1CgBZKSbAqgYCW8AJ24BVrU8eaXps8GJuMzlYhP462inQUgpyQhguwqJYdqFSBjb187cwTIuBLOOSPaWQFKI8iskmfgdy6AAo0NOQqys1SK6ZxdWO8hyC1L+CpjPFSDAE07GYMjiEysVrEcWwNIXbYIIRTpvSKhGgWokCDbHA8mJdkIQJ5KLa2zr53ODNUgQIWNz1gc9sN3iSclx/YAsmYciiFPZ5YfqkWAigkyWvPSqrQI0KiUAuWHahKg4gEQW5CjnRGgWNUKD0yTALFGmf8f4IWdXsZ5djWAIqZrAbSzDQBt4QJAsg0ARVwASLYBoIgLAMk2ABRxASDZBoAiLgAk2wBQxAWAZBsAirgAkGwDQBEXAJJtACjiAkCyDQBFXABItgGgiAsAyTYAFHEBINkGgCIuACTbAFDEBYBk22YAdd1fBSpy3THUX9Ijn1naOc/jbBYGxQUqq3SR646hCl1rVBixEhsA2sS1RpWQUGgDQJu41qgSEgptdy8XdC4BIGiVABC0SgAIWiUABK3SGoA+/vg73/Nb133Ls/z83v16l0CTr2CnCjWHGn9k7OT4/tvu/fKUYRvK8eXHUpVc2+393YPftgag5/zj+vn4rX8f9jwnzNfh3x0CTdEKYC3UHGr8kbGTw/uH3Xu5/Uy2vY/vWqqSaeufv/z4+N1vWwHQ+7/ln6zvI85ZLcPnn08FzUJBoMlXsFOFmkONPzJ2cnz/x+RJtz0/jN6pKrm24f194EiUA/Tzf/6vrNbDaZChuVb7BxpUvFP5mkNNP9J3cnr/cG7caEi2/fynetOtKrk21tc6tnKAXh4Khwsvt9MgQ+UAZQYaLaU7la851PQjfSdn2204MgxpUm2ff/57N3foLxnczbb3L/87DJ22Bejzv36U1folc5BRDFBuoH7FTuVrDjX/SD+ks+3xYdi/ZNswgvn8z2HPhqrk2t5vI+jb0Gk7gF667uvzt9yRyeC6/Z87si0FKDvQTfk7Vaw51PwjeSfN92fVZnzjWJVc2zx02rQF+nwcv3Qme5CR3yyUDaJL2p/inSrQHOq/54ipO7lkmD2I7qdCTlXJtX1Mo66NB9FFl0yGNjFXRdP4kkCT8ZjrQBk7OR3Oh6xp/PvQcf3jx1KVTNswGXsPRLszQM8Fp/jtrMtvTUoCjToIoIyd5BcSk2238cNAwFyVTNt4IfGbPxpuZUCrBICgVQJA0CoBIGiVABC0SgDoJHq+0wUsWwDoHHq50fNc8vjKWgGg82i4ZXV3NQDQ8FRc9pXoK2i4vPflx/T/8PvLEX1Y/QB9Pn495tyqXjdg1L9+KNT9HqbUqh+g90PGhi3oZWyYX5bm+RmDaK8OaZib0NB5dd+m/4c6HdJK1w8QWiBB72PzM/z/ftA4sX6APh+//MAYyKdbn/Xx28P0/+fjEXP4vgWAMAsLic/CXsYHNTCNh1oTAIJWCQBBqwSAoFUCQNAqASBolQAQtEoACFolAAStEgCCVulfBdCD59a1jPoAAAAASUVORK5CYII=" title="plot of chunk comparisonplot" alt="plot of chunk comparisonplot" width="800px" height="570px" />
<ul class="incremental">
<li>These are different, but what do they tell us?</li>
<li>Points with a high <code>hat</code> value are what we call "high leverage" observations, and on their own are not bad--in fact our good model has lots of them</li>
<li>They help keep the model robust to outliers</li>
<li>What do you notice about our replication model's outliers?</li>
</ul>
</div>
<div class="section slide level1" id="one-step-further">
<h1>One step further</h1>
<ul class="incremental">
<li>A rule of thumb is that observations greater than hat of 3x the mean hat value are troubling</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">qplot</span>(ss2, .hat, <span class="dt">data =</span> damodel) + <span class="kw">theme_dpi</span>() + <span class="kw">geom_smooth</span>(<span class="dt">se =</span> <span class="ot">FALSE</span>) + <span class="kw">geom_hline</span>(<span class="dt">yintercept =</span> <span class="dv">3</span> *
<span class="kw">mean</span>(damodel$.hat), <span class="dt">color =</span> <span class="kw">I</span>(<span class="st">"red"</span>), <span class="dt">size =</span> <span class="kw">I</span>(<span class="fl">1.1</span>))</code></pre>
<div class="figure">
<img src="data:image/png;base64,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" alt="plot of chunk diagnosticplot" /><p class="caption">plot of chunk diagnosticplot</p>
</div>
<ul class="incremental">
<li>Yikes!</li>
</ul>
</div>
<div class="section slide level1" id="checking-this-systematically">
<h1>Checking this systematically</h1>
<ul class="incremental">
<li>First, a nasty chunk of R code</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r">infobs <- <span class="kw">which</span>(<span class="kw">apply</span>(<span class="kw">influence.measures</span>(ss_mod)$is.inf, <span class="dv">1</span>, any))
ssdata <- <span class="kw">cbind</span>(<span class="kw">fortify</span>(ss_mod), midsch_sub)
ssdata$id3 <- <span class="kw">paste</span>(ssdata$district_id, ssdata$school_id, <span class="dt">sep =</span> <span class="st">"."</span>)
noinf <- <span class="kw">lm</span>(ss2 ~ ss1, <span class="dt">data =</span> midsch_sub[-infobs, ])
noinff <- <span class="kw">fortify</span>(noinf)</code></pre>
</div>
<div class="section slide level1" id="then-a-plot">
<h1>Then a plot</h1>
<pre class="sourceCode r"><code class="sourceCode r">
<span class="kw">qplot</span>(ss1, ss2, <span class="dt">data =</span> ssdata, <span class="dt">alpha =</span> <span class="kw">I</span>(<span class="fl">0.5</span>)) + <span class="kw">geom_line</span>(<span class="kw">aes</span>(ss1, .fitted,
<span class="dt">group =</span> <span class="dv">1</span>), <span class="dt">data =</span> ssdata, <span class="dt">size =</span> <span class="kw">I</span>(<span class="fl">1.02</span>)) + <span class="kw">geom_line</span>(<span class="kw">aes</span>(<span class="dt">x =</span> ss1, <span class="dt">y =</span> .fitted,
<span class="dt">group =</span> <span class="dv">1</span>), <span class="dt">data =</span> noinff, <span class="dt">linetype =</span> <span class="dv">6</span>, <span class="dt">size =</span> <span class="fl">1.1</span>, <span class="dt">color =</span> <span class="st">"blue"</span>) + <span class="kw">theme_dpi</span>() +
<span class="kw">xlab</span>(<span class="st">"SS1"</span>) + <span class="kw">ylab</span>(<span class="st">"Y"</span>)</code></pre>
<div class="figure">
<img src="data:image/png;base64,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" alt="plot of chunk infobsplot" /><p class="caption">plot of chunk infobsplot</p>
</div>
</div>
<div class="section slide level1" id="what-have-we-learned">
<h1>What have we learned?</h1>
<ul class="incremental">
<li>Regression in R is easy</li>
<li>Regression is easy to get wrong</li>
</ul>
</div>
<div class="section slide level1" id="what-might-we-do-different-to-address-these-concerns">
<h1>What might we do different to address these concerns?</h1>
<ul class="incremental">
<li>Well, there is nesting in our data that is being ignored</li>
<li>Also, by fitting fifty separate models we are not efficiently using our data</li>
<li>Let's look at some quick easy strategies to address that concern</li>
<li>Let's start with the megamodel</li>
</ul>
</div>
<div class="section slide level1" id="megamodel-i">
<h1>Megamodel I</h1>
<pre class="sourceCode r"><code class="sourceCode r">my_megamod <- <span class="kw">lm</span>(ss2 ~ ss1 + grade + test_year + subject, <span class="dt">data =</span> midsch)
<span class="kw">summary</span>(my_megamod)</code></pre>
<pre><code>##
## Call:
## lm(formula = ss2 ~ ss1 + grade + test_year + subject, data = midsch)
##
## Residuals:
## Min 1Q Median 3Q Max
## -83.58 -6.38 0.69 6.93 62.80
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 415.92105 108.01823 3.85 0.00012 ***
## ss1 0.89548 0.00321 278.85 < 2e-16 ***
## grade -0.72909 0.08014 -9.10 < 2e-16 ***
## test_year -0.16754 0.05380 -3.11 0.00185 **
## subjectread -11.53144 0.15245 -75.64 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.7 on 19980 degrees of freedom
## Multiple R-squared: 0.9, Adjusted R-squared: 0.9
## F-statistic: 4.5e+04 on 4 and 19980 DF, p-value: <2e-16</code></pre>
<ul class="incremental">
<li>What's wrong with this?</li>
</ul>
</div>
<div class="section slide level1" id="megamodel-ii">
<h1>Megamodel II</h1>
<pre class="sourceCode r"><code class="sourceCode r">my_megamod2 <- <span class="kw">lm</span>(ss2 ~ ss1 + <span class="kw">as.factor</span>(grade) + <span class="kw">as.factor</span>(test_year) + subject,
<span class="dt">data =</span> midsch)
<span class="kw">summary</span>(my_megamod2)</code></pre>
<pre><code>##
## Call:
## lm(formula = ss2 ~ ss1 + as.factor(grade) + as.factor(test_year) +
## subject, data = midsch)
##
## Residuals:
## Min 1Q Median 3Q Max
## -77.43 -5.78 0.36 6.18 60.16
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 72.93813 1.35590 53.79 < 2e-16 ***
## ss1 0.91197 0.00306 298.17 < 2e-16 ***
## as.factor(grade)5 -8.39756 0.20701 -40.57 < 2e-16 ***
## as.factor(grade)6 -0.69535 0.27917 -2.49 0.013 *
## as.factor(grade)7 -2.92812 0.29120 -10.06 < 2e-16 ***
## as.factor(grade)8 -7.64546 0.32318 -23.66 < 2e-16 ***
## as.factor(test_year)2008 -3.08623 0.22493 -13.72 < 2e-16 ***
## as.factor(test_year)2009 -0.46178 0.22667 -2.04 0.042 *
## as.factor(test_year)2010 -1.86967 0.22716 -8.23 < 2e-16 ***
## as.factor(test_year)2011 -1.49652 0.22769 -6.57 5.1e-11 ***
## subjectread -11.59171 0.14416 -80.41 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.2 on 19974 degrees of freedom
## Multiple R-squared: 0.911, Adjusted R-squared: 0.911
## F-statistic: 2.04e+04 on 10 and 19974 DF, p-value: <2e-16</code></pre>
</div>