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<h1 id="article-shares-prediction">Article Shares Prediction</h1>
<p>Shyam Gadhwala &amp; Kamlesh Pandey</p>
<h1 id="library">Library</h1>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(dplyr)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(readr)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidyr)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidyverse)</span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(caret)</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(glmnet)</span></code></pre></div>
<h1 id="introdcution">Introdcution</h1>
<p>We are living in a digital world where people are more concerned
about the digital footprint and people often consider the like and
shares they get on a post that they publish online as an important
metric. We have several social media websites and print media to share
our articles. Online print media platform like <a href="www.mashable.com">Mashable</a> publishes thousand of online media
everyday and it is important for them get a more user engagement from
the the article they post online. In this data set we are trying to
predict the shares using that data that would have several potential
influencing factors, in other words, predictors, such as text sentiment
polarity, rate of negative words, rate of positive words, to name
some.</p>
<p>Why this analysis is important ? From this predictive model, Mashable
can potentially predict the number of shares they can receive based on
the type of article they are publishing online.</p>
<h1 id="data">Data</h1>
<p>The data set summarizes a heterogeneous set of features about
articles published by in a period of two years.The data set has 39644
entries and 61 feature columns. The project is aimed to subset the
original data set based on type of data channel (one of the six type)
and then to predict the number of shares.</p>
<p>For this part of the project we are using <strong>LIFESTYLE</strong>
data channel for training and building a predictive modeling and
extending same models to other five data channels.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>newspopData <span class="ot">&lt;-</span> <span class="fu">read_csv</span>(<span class="st">&#39;OnlineNewsPopularity.csv&#39;</span>)</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="co"># select specified data channel from params and drop other data channel columns</span></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a>newspopData <span class="ot">&lt;-</span> newspopData <span class="sc">%&gt;%</span> <span class="fu">filter</span>(newspopData[params<span class="sc">$</span>data_channel] <span class="sc">==</span> <span class="dv">1</span>) <span class="sc">%&gt;%</span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">select</span>( <span class="sc">-</span><span class="fu">starts_with</span>(<span class="st">&#39;data_channel_is_&#39;</span>), <span class="sc">-</span>url)</span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a>newspopData</span></code></pre></div>
<pre><code>## # A tibble: 2,099 × 54
##    timedelta n_tokens…¹ n_tok…² n_uni…³ n_non…⁴
##        &lt;dbl&gt;      &lt;dbl&gt;   &lt;dbl&gt;   &lt;dbl&gt;   &lt;dbl&gt;
##  1       731          8     960   0.418    1.00
##  2       731         10     187   0.667    1.00
##  3       731         11     103   0.689    1.00
##  4       731         10     243   0.619    1.00
##  5       731          8     204   0.586    1.00
##  6       731         11     315   0.551    1.00
##  7       731         10    1190   0.409    1.00
##  8       731          6     374   0.641    1.00
##  9       730         12     499   0.513    1.00
## 10       729         11     223   0.662    1.00
## # … with 2,089 more rows, 49 more variables:
## #   n_non_stop_unique_tokens &lt;dbl&gt;,
## #   num_hrefs &lt;dbl&gt;, num_self_hrefs &lt;dbl&gt;,
## #   num_imgs &lt;dbl&gt;, num_videos &lt;dbl&gt;,
## #   average_token_length &lt;dbl&gt;,
## #   num_keywords &lt;dbl&gt;, kw_min_min &lt;dbl&gt;,
## #   kw_max_min &lt;dbl&gt;, kw_avg_min &lt;dbl&gt;, …</code></pre>
<h1 id="exploratory-data-analysis">Exploratory Data Analysis</h1>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(newspopData<span class="sc">$</span>shares)</span></code></pre></div>
<pre><code>##    Min. 1st Qu.  Median    Mean 3rd Qu. 
##      28    1100    1700    3682    3250 
##    Max. 
##  208300</code></pre>
<p>Dividing the popularity of the shares based on quantiles to classify
them as to how popular they are. The 1st quarter percentile would be
popularity index 4, next quarter be index 3, so on and so forth. Higher
the number of shares of that article, higher the popularity index.</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>pShares <span class="ot">&lt;-</span> newspopData<span class="sc">$</span>shares</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>pShares <span class="ot">&lt;-</span> <span class="fu">sort</span>(pShares)</span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a>quantileValues <span class="ot">&lt;-</span> <span class="fu">quantile</span>(pShares, <span class="fu">c</span>(.<span class="dv">25</span>, .<span class="dv">5</span>, .<span class="dv">75</span>)) </span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a>newspopData <span class="ot">&lt;-</span> newspopData <span class="sc">%&gt;%</span> <span class="fu">mutate</span>(<span class="at">article_popularity_index =</span> <span class="fu">if_else</span>(shares<span class="sc">&lt;</span>quantileValues[<span class="dv">1</span>], <span class="st">&quot;4&quot;</span>,</span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a>                                                                  <span class="fu">if_else</span>(shares<span class="sc">&lt;</span>quantileValues[<span class="dv">2</span>], <span class="st">&quot;3&quot;</span>,</span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a>                                                                  <span class="fu">if_else</span>(shares<span class="sc">&lt;</span>quantileValues[<span class="dv">3</span>],<span class="st">&quot;2&quot;</span>, <span class="st">&quot;1&quot;</span>))))</span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a>newspopData<span class="sc">$</span>article_popularity_index <span class="ot">&lt;-</span> <span class="fu">as_factor</span>(newspopData<span class="sc">$</span>article_popularity_index)</span></code></pre></div>
<p>Starting EDA with the visualization of the target variable shares as
a function of the most obvious factor, number of words in the
article:</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>newspopData<span class="sc">$</span>scaledShare <span class="ot">&lt;-</span> <span class="fu">scale</span>(newspopData<span class="sc">$</span>shares, <span class="at">center =</span> T, <span class="at">scale =</span> T)</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a><span class="co">#calculating correlation index</span></span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>corrIndex <span class="ot">&lt;-</span> <span class="fu">round</span>(<span class="fu">cor</span>(newspopData<span class="sc">$</span>scaledShare, newspopData<span class="sc">$</span>n_tokens_content),<span class="dv">2</span>)</span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a><span class="co"># plotting the shares as a function of words in an article</span></span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(newspopData, <span class="fu">aes</span>(<span class="at">x=</span> n_tokens_content, <span class="at">y =</span> scaledShare)) <span class="sc">+</span></span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>()<span class="sc">+</span></span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">subtitle =</span> <span class="st">&#39;Word Count v/s Number of Shares&#39;</span>,</span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a>      <span class="at">y =</span> <span class="st">&#39;Number of Share (Scaled)&#39;</span>,</span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a>      <span class="at">x =</span> <span class="st">&#39;Number of Words in article&#39;</span>, </span>
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a>      <span class="at">title =</span> <span class="fu">toupper</span>(<span class="fu">str_replace_all</span>(params<span class="sc">$</span>data_channel, <span class="st">&quot;_&quot;</span>, <span class="st">&quot; &quot;</span>)),</span>
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a>      <span class="at">caption =</span> <span class="st">&#39;Source: News Popularity Dataset&#39;</span>) <span class="sc">+</span> </span>
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a>      <span class="fu">geom_text</span>(<span class="at">x =</span> <span class="fu">max</span>(newspopData<span class="sc">$</span>n_tokens_content)<span class="sc">/</span><span class="dv">2</span>, </span>
<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a>                <span class="at">y =</span> <span class="fu">max</span>(newspopData<span class="sc">$</span>scaledShare)<span class="sc">/</span><span class="dv">2</span>, <span class="at">size =</span> <span class="dv">4</span>, </span>
<span id="cb7-16"><a href="#cb7-16" aria-hidden="true" tabindex="-1"></a>                <span class="at">label =</span> <span class="fu">paste0</span>(<span class="st">&quot;Correlation coefficient = &quot;</span>, corrIndex), <span class="at">color =</span> <span class="st">&#39;red&#39;</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqAAAAHgCAMAAABNUi8GAAABd1BMVEUAAAAAADoAAGYAOjoAOmYAOpAAZpAAZrYzMzM6AAA6ADo6AGY6OgA6Ojo6OmY6OpA6ZmY6ZpA6ZrY6kJA6kNtNTU1NTW5NTY5NbqtNjshmAABmADpmAGZmOgBmOjpmOpBmZgBmZjpmZmZmkJBmkLZmtrZmtttmtv9uTU1uTW5uTY5ubo5ubqtuq+SOTU2OTW6OTY6Obk2ObquOyP+QOgCQOjqQOmaQZjqQkDqQkGaQtpCQtraQ27aQ2/+rbk2rbm6rbo6rjk2ryKur5OSr5P+2ZgC2Zjq2kGa2tma225C22/+2/7a2/9u2///Ijk3I///bkDrbkGbbtmbbtpDb25Db27bb29vb2//b/7bb/9vb///kq27k///rAwDrBAPrBATr6wPr6wTr6+v8AAD8AwD8BAP8BOv86+v/AAD/AAP/AwD/AwP/AwT/A+v/BAP/BOv/BP//tmb/yI7/25D/27b/29v/5Kv//wT//7b//8j//9v//+T///9k8U7tAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAgAElEQVR4nO2dj3/bxmHFIW+eImtdt5RKXNldtnatkix2s0nZ4ixKu87s1nS22f1q6x9ZQmezkzbzaKUaLeOP3/0E7vCLAHkHPJLvfT42SfDu4R3x1d0BBMAkpShgJUMHoKgmEVAKWgSUghYBpaBFQCloEVAKWgSUghYBpaDVFdBJovRHH5vXs+RIPswPE6NLd5zFVhf/+IdJ8ns/UAa6gKgxcg2E8ShfXnhhtJvXNrYnl+9b87+4n0W0ZdTbkzyXa+TUcrOPbW75JF+ZV5PqU0sCmuQbUm2zIqBjb1Oe7en3Xk3LgNqSk2TnNFteeNEI6MWJfveyJbQVoE4tN/v80P6BeSsjoIOpM6Bqo138Yk8TdLb3Df0ktf1ZWlys6H31l2n6b9+RVBcAzUpODGKWSeeFA2UFoLPksujOvz7J+uwCoHkNt3KhVpZ9prvXE1nUAdRbLdWjlgNUbsiRfvmzvZF5ywHUXZwP2Gd7DjAG0Kzk5NL7qphh0nvRCOjEdra7xTJNgBZq5dnVID9R3BJQAC0LqN6iYvvmmzZ/5i023ZHUf6TFHjQvObn0zycSGsOk92JBDzpKPbXsQb1abvZLd872dv3yBHQwLQtoOpZP5B5Otj+Ub2RvsdO3KQM7nVOE5CUnkgs1IxwVX5jyktiqnaSfJjt//He/rIjozkHVkO0YFWo5f0+z5A/MX1R5DurMW6h+tBqg8r+MP2eYdBc3ApqXnKi9mFHeaeYvFgCa/vvfip2wnR+UIjYC6tdyABWDvD2wQECH10qAmr1zb9RP08LiIqDuEO+UlMsvxLieAeq9KK3eX2N68a9/mo3ZrYb4Qi0X0Cwvh3gArTQHtR1LYSP7i5056C/+5GMfUKekWi7G9V8dVr4orD711+g9bw9oXouAomqVvXizVeeH/kYuLHYPu8uR2wHULamXT5Jv5Ux6L/zVa8n62WrG9q02gBZrEVBULX0cVDzaPeGxnprZjVxY7B4HHflDvFvSGJ/k3an/wl29lVrjOBH9cnrxL3udetBCLQKKqlW+SbIE6oPb2UYuLE7zb5LszpCUBNQtaZaLojmT5kX+RU/VpMJ+EZTtwGRlSoA6RoVa1YBmK3NrUr1qOUB3ZPdjjhZmk0yzkYuLpb6We8yl7+K9knb5xO00Jy0A1d+qq0RuxAWAFmoRUFTxbCYKWgSUghYBpaBFQCloEVAKWgSUghYBpaBFQCloEVAKWgSUghYBpaBFQClodQR0rC9wM9fmVlwlPvMuk2i8ROLrj/3XZ9+877wyp2zMak7POLuy6OoLe219FmRxFQpPHQFVvFycfFdf0jmqKZDa04Mm/g1GPJV4mXh280NVd2lA54dm1RN7dR8BXUd1BPRsT2z2+bUPr4ltPavqHy1QuqtNJ5fvl8sYqyIvYw/m+eH3ZI+6NKC2wMXJkclDQNdRHQG9OBHd3Ozyr+XDxNx3RgzFZ/vvq/vGJDu3NFBZ/5WmWZkrepg9u/LBXpIcyZOYR9ZRdnPz6+YqPF1TOIxHClC/4kiWkd3hLX33Eekur99TCfLVyVK7WWIlVUW6q7WMTBVT3101BaTOJyzLiyxG6URs/PFITUPlP3XqsRzy7b2NnN4qK2M5M/cXsUU056N0ZovsmduRHZ3t3/EAVRUTU1u8sM7Swjn52Vmd1Cwp3NhE/fFMzO0ZsvrOqikgdQV0Jvsc0YHtq+2sBmDJkNyyM+d+RpKtvIbfEcqyqkPUBMlH+W8ycmupPlgsKlW0tc2jcpcwW7a81WlN9NUmtsrv7qe5RVZ/n+fKQ6oroPNrp3Jb2v5NDrIWNjXfNBvawcMrU3xM9Rgsql68d6rumZDf7uFIrswb4k+dicK+BstcjDHKO0x3dXnsQ9tJyv9mar9eh7ZXdYx56zpIdT4OOh7J4d081AJq56ASsQWAmint/I37umLizGInuwsBtTeLaAbUrT8/3Dn1Q2tlq6aA1BnQye54lD2oHXnLkB1cdTGzF3/pjlemCtD5tQ9kZ+x2nfbh4r1bdYCaR3soIQfUXV3+hltFRpuZHtQ7FOHu2lEY6gzo2TfUFtcP3h6JPLRud5Kc46C2jL5Tw47TkVka1D1sx3ZCaIjSb8/UwQG/YrbHpJ3lDe52ctxLO0nq2mZ3L00yebZnqtj67qopIHUG1NyTw1yn6x5CSp3DTKmaT+rvckwZdSDn+9dyzrK7MMuj6GoKaiaHZj36+KW5BZRbUXeHt8ytvE9UlZwtL5LUxFyn7Kw42flQTKKvnOb13VVTQOJ38RS0CCgFLQJKQYuAUtAioBS0CCgFLQJKQYuAUtAioBS0OgI6bVDjm620ugNECDYjgAUBRXaACEFAIzhAhGAzAlgQUGQHiBAENIIDRAg2I4AFAUV2gAhBQCM4QIRgMwJYEFBkB4gQBDSCA0QINiOABQFFdoAIQUAjOECEYDMCWBBQZAeIEAQ0ggNECDYjgAUBRXaACEFAIzhAhGAzAlj0BmiSJO1DdWtDHAsEB4gQ2wGoundc61BdWxHDAsEBIgQBbefQTQjbhc0IYEFAkR0gQmwHoJyDrm2ILQG0U6iVHSBCsBkBLAgosgNECAIawQEiBJsRwIKAIjtAhFhLQCmqX7EHRXSACLGWPWikNMEcIEKwGQEsCCiyA0QIAhrBASIEmxHAgoAiO0CEIKARHCBCsBkBLAgosgNECAIawQEiBJsRwAIZ0C4nQEULMagDRAgCWuPQ6RTSWCGGdYAIQUBrHAgoRggCWuNAQDFCENA6B85BIUIQ0AgOECHYjAAWBBTZASIEAY3gABGCzQhgQUCRHSBCENAIDhAh2IwAFgQU2QEiBAGN4AARgs0IYEFAkR0gQhDQCA4QIdiMABYEFNkBIgQBjeAAEYLNCGBBQJEdIEIQ0AgOECHYjAAWBBTZASIEAY3gABGCzQhgQUCRHSBCENAIDhAh2IwAFgQU2QEiBDyg528eHByn6YubB1cfEtBeHSBCoAP64oe30/O3br/86Dh98G0C2qsDRAh0QJ9LKu8ev3j3Xnr+9j0C2qcDRAh0QE0vev7OQ9WZpukrQo2lKSq4GgF9+dGN9PlVC6hUpD+XYA4QIdiMABZtAH1x84bYVXqHgPbuABECHtDzN48lpZyD9u8AEQIdUM2nGua5F9+zA0QIdEAfHEgd8zjoAA4QIdABrVSkNMEcIEKwGQEsCCiyA0QIAhrBASIEmxHAgoAiO0CEIKARHCBCsBkBLAgosgNECAIawQEiBJsRwIKAIjtAhCCgERwgQrAZASwIKLIDRAgCGsEBIgSbEcCCgCI7QIQgoBEcIEKwGQEsCCiyA0QIAhrBASIEmxHAgoAiO0CEIKARHCBCsBkBLAgosgNECAIawQEiBJsRwIKAIjtAhCCgERwgQrAZASwIKLIDRAgCGsEBIgSbEcCCgCI7QIQgoBEcIEKwGQEsCCiyA0QIAhrBASIEmxHAgoAiO0CEIKARHCBCsBkBLJYElKL6FXtQRAeIEGvZg0ZKE8wBIgSbEcCiEtBJojQioAM7QIRAA3R+aMmcJDunBHRIB4gQYIDOr9/JOfReENDeHSBCgAHaTpHSBHOACMFmBLAgoMgOECHAABVTUKtLNeM7Ae3LASIEGKBSE4nm/PCIPejADhAh8AA1aM7Ygw7tABGCgEZwgAjBZgSwaBrieaB+aAeIEICApjO5j9QwBSWg/ThAhEAEdKEipQnmABGCzQhgQUCRHSBCIAI6EQP85PJ9AjqwA0QIQEDHl391eHRxsktAB3aACIEH6PzwSB5p4mGmwR0gQhDQCA4QIdiMABaVQ/xEDvE8Djq8A0QIQED1cdAGPgloPw4QIRABXahIaYI5QIRgMwJYEFBkB4gQYIDyfFAgB4gQYICyBwVygAhBQCM4QIRgMwJYVAJ6tschHsIBIgQeoBcno4uTI17yMbwDRAg8QCWa41E6azhbJEIa0WWv6BAgBJgDRAhMQCe7PX/VqSYVKzkECIHmABECD9B0rOhsOt8ufBoCihoCEFAxCU3Hzo2Zzt++l6YPDg4OXr9HQPt0gAgBCGhBzxWYd4+j9qCcg6KGgAf07ms/ET3oyx/djgtoUAeIEGxGAIvaId49oV4O8S9uiiFedaKvCDX0txQVQcWdpNQlVAJ6/tZtpxeN9OcSzAEiBJsRwKIK0NKdRdROklQ2D42UJpgDRAg2I4AFAUV2gAiBB2jp1jcS0OdXH6YvfxzvMFNYB4gQbEYAi0pAi5d82OOgr2U78pHSBHOACMFmBLCoBnShIqUJ5gARgs0IYEFAkR0gQsABOtk5VRd+8KrOwR0gQqABOhN8ymOgvC5+eAeIEGCAym+R0rO9I3n7hl7PBw3qABGCzQhgUQJUHQSVvShvfTO8A0QIREBV50lAB3eACAEG6MXJkfkafswhfmgHiBBggMreU01BZ003qY+UJpgDRAg2I4BFGdB0LI8wXZzU/tIxAe3NASIEHKBtFClNMAeIEGxGAAsCiuwAEQIMUP5ePJADRAgwQOW3nGbvaJLUzkMjpQnmABGCzQhgUTnEj/XtF/lV59AOECEAAV2sSGmCOUCEYDMCWBBQZAeIEAQ0ggNECDYjgAUBRXaACEFAIzhAhGAzAlgQUGQHiBCIgPLXjjEcIEIAAspfOwZxgAiBByh/TBbFASIEAY3gABGCzQhgUTnE89eOQRwgQgACyl87BnGACIEI6EJFShPMASIEmxHAogpQed0cAUVwgAiBB2jjb8xR1BAq7CQ1HKNXivTnEswBIgSbEcCiClD7k/E8zDS0A0QIPEBbKFKaYA4QIdiMABYEFNkBIgQgoPy9eBAHiBB4gPL34lEcIELgATrM78UHdYAIwWYEsKgDtPffiw/rABGCzQhgUQXoIL8XH9YBIgSbEcCiEtDi78VvFaCfPxV61uTwiXzbPv9v72WbDGIFz8S/3+TVqhyEcYXF46dPv3jiPX/0VOmrurBrvjV4mKmgzxQAn4sN3grQWjjrM3wqvD+tB8o3Llh8/sUTEbD8/HFGbcsQXURAIzgsbWE2tdj6sQCVVRqruca+heL60dMnxeePGuzWemtMeRy0IKdrSz8TI+cXEpUvnz79L/nfE7lEIKERE/rtJ/q/Z9Os7G/y4dYs8x6fPvlED8lPv/CqPZtm3spBGcsQtrgiUFFrIjrPs4404AcR1CH8cdCGy+U2G1Cna/s/sdnlpv9EI/SFAUH0raKQIuNziZvqDj/Lyz6Ri2V9+VoWs+85tadONVnEPNXvaofKHlR1mAZQ53lTB7rWW0NVrQC0xel2kdIEc1ge0Gwy96V8+kii8pVc/lXOhIDnP5+ows8MaY/8sqa7+1/lY99zaltA7Z+DdVDvfjV13qoE9LeF548bOtC13hqqamUPusWAZp3Rl3I2alFR/32uR1s1puu95wzQUllZQGew77m1Xa6npXcXAVroQZv3uNZ5a6iqFYA2HqLfbEDtxv706bMKQL/IePr0ad4HtgU0r10FqPOuC2iLOeijp7W78Mt/EEEdggJqTwbdzp0kC6GYBX6p+8knOXSPnBH5CzVu50N8saw7xD8zQ3xWu3KIz9+t7UGr9+I/rz/GtMIHEdKBh5nCWeTHQfOdJAvdZ/rA+DPDk+jcnjm7OH7ZqbdzZP49cZguVHPfndq9sFIzHvvHPvXzxinoem+NKQEt67H9Jsk5BmSg+0y/JV/IUv8jIHpcOl6UzWMrDzM9c3vQ0mGmZ7nDY1Wn6psk6fTb7Ll5EeGDCOcQGFD+XjyMA0QINED5e/E4DhAhwADl78UDOUCEAAOUvxcP5AARAhFQ/l48hgNECDBA+XvxQA4QIcAA5e/FAzlAhEADlL8Xj+MAEQIO0DaKlCaYA0QINiOABQFFdoAIQUAjOECEYDMCWLQC9Pzte2n64ubB1YcEtFcHiBD4gD4/eP1e+vKj4/TBtwlorw4QIcAANb9B4+juaz8RPeiLd+/pnpSA9ucAEQIeUD3En7/zMH3xw9vi1StCTRMCigov50B9+Yx6CejzqxZQqUh/LsEcIEKwGQEsyoBWXNXp96AEtDcHiBB4gJZ0zjnoMA4QIRABnfi/NCfBfPnRDe7F9+0AEQIQ0ImcfTpn1PM46EAOECHwADVzUJ4POrgDRAgCGsEBIgSbEcCi1RBPQAdygAgBCGhxJ4mADuQAEQIR0IWKlCaYA0QINiOABQFFdoAIQUAjOECEYDMCWBBQZAeIEAQ0ggNECDYjgEUVoFt8h2UwB4gQeIBu8T3qwzskSTJ8iIEdwh+ob7inCAHt5KBOrB06xNAO4XvQ7b0FeGgHArqiRWUPuliR0gRzgAhBQANYENDIDpyDrmZRDegkSY4aJ6KR0gRzgAjBZgSwqAR0fPlXh0eNP4gYKU0wB4gQbEYAiypAzZXHPB90cAeIEAQ0ggNECDYjgEXlED+RQzxPWB7eASIEIKDpjCcsQzhAhEAEdKEipQnmABGCzQhgQUCRHSBCIAKqhvimM0YipQnm0GjR7tg5fDPWxyH8TtJGX9XZ8ttH9GaskUOEw0yqG93Qw0wEtG8HAtrJgoD27RB8iJ/pIX5Tf8iLc9CeHYICak8G5fmgAA4QIcAApShE8TgoogNECMAe9GyPQzyEA0QIPEAbzwQloD06QITAA5SXHaM4QITAA5Q3bkBxgAiBB2jjIXoC2qMDRAhAQLmTBOIAEQIP0IuTpnOVCWh/DhAh8ADlThKKA0QIPEC5k4TiABECD9D0bJ87SRAOECHwAOXNw1AcIELgAdpCkdIEc4AIwWYEsCCgyA4QIfAA5RCP4gARAg9Qg+m1U/agAztAhEAFNJ013H8xUppgDhAh2IwAFk2Acogf2gEiBCygY/agQztAhMAD1Owk7XAOOrQDRAg8QFsoUpolHSquI0bYLgQ0gMUmAFp1JwaE7UJAA1iUAI10XXynH7sgoEghwADNNG66g23XNN1+LijtxjMBBXeIAej8sGkfKTagHX/+inNQbIcIgM6S5p/r7JomLqAtQ6yfA0QIREDHyYIr4zun6TYHJaBAIfAAvThpvLvyUoB2C7XiDwgGCjG8A0QIOEDP9hZedYx1mAk1BJsRwKIM6GTR8E5Ae3OACAEGaLz7g7YftrllkUKAAVqrBwcHB6/fWx7QDjs+3LJIIdYF0LvHq/WgBHRNQ6wJoC9/dJuA9u0AEWJNAH1xUwzxqhN9RWhhf1shwecy1SgqbQHo+Vu3nV400p9LMAeIEGxGAIvWgCpl89BIaYI5QIRgMwJY9AVozNPt4lggOECEWBNAn199mL788bKHmbqebreyELYLmxHAon0P+uDg4LVsR75rGgK6viHWBVBPXdO4gC5GlVsWKcRWADr1+FxEKLcsUojtADQXAV2zEAS07LDy6aAQ24WABrCIB2gtZIvpW/2EeojtQkADWEQD1Jyyt1Soupod/BC2CwENYBEb0KUIranYxQ9huxDQABaQgNbMQQnomjpAArrKGF9jT0DX1AET0GnHL+ArHXxxDrqeDrCALh1qZQeIEGxGAIseAO3ej3LLIoXYdECXmIlahxWOhiJsFwIawAIZ0FWO1yNsFwIawGJIQGvxI6BIITYd0FoO6/kjoEghNh5QRx5wCwHlHBQixBYB6iNZcyRfXp28fHsWh1gnB4gQWwtoNaEBzmRqDrFODhAhthfQShoJKFqILQK0NKkkoGsQYpsALanco3IOihZiGwBt2Sna3pNbFinEFgDadtgmoIghNhbQHEoCus4hNhXQnEp7NMm8boDVvMUtixRi4wFNXLX6bp5bFikEAZ0WKqywm1UMsYIQHCBCbCqgGVOrAaqXdT46irBdCGgAiyUB7SSHT/OyvljNwsr3qC1S3NPtnA604xx04cS1ZYjuQnCACLGWPWiHNEkNoA3ElQHlHHSdHbAALaJUA2hTn1ieg3Zv1zKV4BwgQmwYoCXwLJreY/MtbbllkUJsOqDO8fmMUL9c/jThgXq8EBsLqE+qO8rbBcUq9smC9rQZ9RG2CwENYBEc0MLhT2epA6iPmD89TRadbtdqjx5huxDQdhaNmzM8oN43SWVAq670KALajB8BXTeHZovm7dkzoFNnLloRkYAChthUQKvmoNmTQqTCfHQBfpHmoAVb/C27Ng6ggDoBpm2H8TZz0FbqblEMhb9l18YBcw7qrN75LigpA1qaCAyzZQloNAesvfgmQJOkDKj7oh2gcYZ4AhrNARNQb0wvnDJS6ECLk9NmAmPtJNXOi6tethEBDWARDVCXtiKgjceYil8ylfxjAdq4llYrDZ0BA6/tADSplimZlXeqOiYVZ58sbNcyH0bDWgjoQBbxAS1MPsunNxWKVx0zrfxyv7ldXT+IoghoOAdIQAtdaFJBXRnQ4otqQFu1q3ONogprXSIEAQ1gEQ9Qi1kjn5X78tM0ezUgoAgOECE2DdAMp6SNKqulxd38JdrVvQqgA0SIDQM0x64VoElFbf/k0CXbtXxVIAeIEAS03Ok6zxvWM22AOF0R8PXfskAOoIC2JrTM9HTh/pF+q1zAvk6X2u/2PpkV6oZygAix7YAmZUDT6TKAeguQAF0hBwJe2wdo8UhTsdOcLgVo4tUAAnSVIAh4bSyg9X1mBadTd3xPveq165l6nVMRUJg5KAHFBHQRn0mRQR9XZ0m7luiitjjCdiGgASwGBLQIZO2Clk3xCiNsF85BA1gEB3RaxVsLQBuWTAvw1a84L7TCR5Jkk4QVxb34ABbhAfVPFmkL6OIl2dKaod/Hefk5qDVZ9y0L5IAIaCc+WyFbV86qUHPpqR8BDe7QD6Avbh5cfdgC0KRqxI4nZ7X2NQEFc+gF0JcfHacPvr0YUIeOPhl1XxXeKuWrfF4qse5bNphD9afUV4jWgL549156/vY9REALPXbxiFNFvPLzoB9qMAeEEM2fUvQQrQE9f+dh+uKHt8WzV4Tqy6n2uHf97kH+6twbhif5Uzde+TlVJ+9TGu4DW7je51ctoFL1xPeDZJOqTz5xDwC4SUP91VdYbVAP6n5k/nuxQ7QGNO9BgQHNTxjJXppn2YdbeKsq/zIfapXZZgDqElpoZfUnWMEt3Bx0KNUHKALqVCjHzz/UqiL1zS5+tu2qNgkB0PwCnJaAlhf3sxd/o/1e/EAqrd/tQt0Hr0bNh5tO67uImmYXP9tWNRsFBmjhD7bm4ykvRjoOGha5TnJWPy0uyT7cUo26D7cboJs7B52m9eNI9RvlTw3pm6SoCNapdIqK/rOv/LjyGnX58w+1WLfjZ7t0zYAWQziUPjQkQL1vy2Mj6X2RZB/V07QQaIlPZoW6jsNqWk9AQ1qEB7TTd/Gm6FQ/dxe771acnlzLToLzPRABDWARC9CVxC2LFIKARnCACMFmBLAgoMgOECEIaAQHiBBsRgALAorsABGCgEZwgAjBZgSwIKDIDhAhCGgEB4gQbEYACwKK7AARgoBGcIAIwWYEsCCgyA4QIQhoBAeIEGxGAAsCiuwAEYKARnCACMFmBLBYEtAmNVyT3J8QQiBk2JgQBDS8EDJsTAgCGl4IGTYmBO+wQUGLgFLQIqAUtAgoBS0CSkErFKDe/Uf61fmbBwfHWQL/oT/JG/0OnOHlRwev3R46hNgar98LGCIQoP59mHuVvPXe+Vu3TQL/oUc9EH8kA2e4eyxvljlsCLk1HoQMEQhQ/x54veq5bPndY5PAf+gvxflf/tVxOmwGub40HTiEulvnu/fChQgEqH8X0d4lVm0S+A+9BXj5o38QvcSwGc7f+Xs5xA8bwvSg4UIEAtS/D3PfkreINAn8h94SPLghh7FhM5y/qf5Ehg1hppvhQmxCD/ri5o102I5DrO4lQA9asfbeQ7x1O33++j24HnTAOajqOQaeej04kLox8Bz0rxUGw4YwnSXcHNS/D3Ov0nzaBP5Dj5I96MAZ7h7rrnzIEKYHDRdi/Y+D6t7rmMdB5fqCHoJcSs8Pwh6M5TdJFLQIKAUtAkpBi4BS0CKgFLQIKAUtAkpBi4A6mh/uyofZpTuVb59dOV1gMEl2ZJHx5fvqhXS7ONktlyusodH464/d9xdn2DARUEfzw+QoXQHQ+eGRelQGFyfflZzOD0flgnVrWLxSArrNmh9+75v3VwDUFjjbE6DOr314Tbyc7VRUIqCtRUAdiR5wPFL4KA7Ef2dXPthLktGZ+O9IvL6VJLJXvDhJEoHY2f77iSZNLthNZald/VK6XP61fJiICvptU1500zu3ZG1ROtE9brYi/VK/NVLlpUYyjfUwT9sTvuYioI4EoGf7dzxA9wRfE0nlRCwUL+SUUk0rBXhne2Z6aRdm3ZukUqA+Ee+Lh+xtWV4O+fNDu4Y9hWS2Io2dmimo9RkixT9ZXy43T9UatkIE1JEkYDLyAT0yGGUvrpyqAVrCvGd6PLXA1jILLk4ETft3pGX2tiyvXkj69vM+0PGWL393v7BM9bCntqhdfa8fzWAioI7kVp9fO/WG+FPDjXyxr8mYJPnIqzST3ZlDkTSRhW2P7L6tuj65dGzmA2lhRcpQ2O/kyyyVuqhdfb+fzVAioI702Lq7EFAzvNYDKgZ2Obybh2pA1UEDjV0B0Pnhzqm3rADotozuSgTUkQL04r1bdYCaR7tjngMqF7hDvKBc7m2ZB+9tO97nKywBqoCe+T2oO8RXHRfYWBFQR5qXmdrVlvs2OwVAs50kQZAFSKq0k5SefUM91Q/e2/LLALmTpBg1FYqAyg50z/g7e0bGw65+gA9oABFQR6ZDG5uDQN+/VuxBbyXm2yE5RXR4dI4BWSc1DiuWCm/bw0x6nqlKF+egYnq686GYv6qX42S34jDTtvBJQClsEVAKWgSUghYBpaBFQCloEVAKWgSUghYBpaBFQCloEVAKWgSUghYB3QbND9tfJKJPw3bPp64o0nBCql9TvHIW6IpHNWUrPQjoFkif59ryNNKzPXWeVSOg6sTYa9Xnq5RquoDu+9CHqKwAAAI0SURBVBcDEFBKKgNKnyItX8qe7Y++oy/hc5fLwv+0q6uoperSlSun8iTVme2GVUH5hq43v/6+OrnL2O7rc8FENbGCn+3/XJT5M/Him9mJ2vKpKqGq67KpMVeLsjO5UwK6FTJn/akr+ARoliQxlkvKxBJzgZ+SeGd8pC9KUUsn4v9EXqs1v37HlFKcSWq1nzy3cKavstKAyr8FswK9YCbKjWxF+adiS2RlrbleJ3vQbdNMnUEqKTCXS9muzhKj3lOStLxx36Ajlor+7qe3di/eO83HdDuVNH5yzBbvO7bS87pL7Bv3f3qaWkBFWaeEfmbM7ToJ6PbJXFTlk6QGXrUPlZ0CLRdPRuqCVLV0fv3n18VAfV0N3LqQ5cf4KbjGRy6gYzlg5wsu3vvwjfup04M6JfQzY27WSUC3SzM1MI+PanvQ686+iqbuAz3qqnrfe/XivVt6BqAul8oAtT2oAM7jXl2msu8Amk6+O0qzimpWcOSXNeZmnQR0u6T2myVGZs4onpkr883V+3q5LqwnmHJX3iydJXoWqp57gGZz0F3fVpF5xftDuJJ3vRZJXcI8s+b5LNmIgG6D5Mi5c5pd6DxJkm+ZiV62F292wy198iYneqneh7+UjcWpA6jZi7/256pgbiue/f537Jh/cXLpzsXf6IrZcVBdQr6ln1lzvU653EQnoNSqqjsi6ujs1WXNCSi1qhYDOln+IlQCSkGLgFLQIqAUtAgoBS0CSkGLgFLQIqAUtP4fnppVeehoW08AAAAASUVORK5CYII=" /><!-- --></p>
<p>We can inspect trend of Number of shares as a function of Number of
words in the article. If the points show an upward trend, then the
article with high number of words are shared more. However, if we see a
negative trend then we can estimate that with increasing number of words
in the article, number of shares decreases. This trend can be
investigated further with the correlation coefficientm which in this
case is 0.07.</p>
<p>Now, creating a new variable here that help eliminates the dummy
variable for each day of the week. This new variable will take the value
of each day of the week that corresponds to the dummy variable’s
value:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>newspopData <span class="ot">&lt;-</span> newspopData <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="sc">-</span>scaledShare)</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>newspopData <span class="ot">&lt;-</span> newspopData <span class="sc">%&gt;%</span> <span class="fu">mutate</span>(<span class="at">day =</span> <span class="fu">if_else</span>(weekday_is_monday<span class="sc">==</span>   <span class="dv">1</span>, <span class="st">&quot;Monday&quot;</span>, </span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>                                            <span class="fu">if_else</span>(weekday_is_tuesday<span class="sc">==</span>  <span class="dv">1</span>, <span class="st">&quot;Tuesday&quot;</span>,</span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>                                            <span class="fu">if_else</span>(weekday_is_wednesday<span class="sc">==</span><span class="dv">1</span>, <span class="st">&quot;Wednesday&quot;</span>,</span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>                                            <span class="fu">if_else</span>(weekday_is_thursday<span class="sc">==</span> <span class="dv">1</span>, <span class="st">&quot;Thursday&quot;</span>,</span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a>                                            <span class="fu">if_else</span>(weekday_is_friday<span class="sc">==</span>   <span class="dv">1</span>, <span class="st">&quot;Friday&quot;</span>,</span>
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a>                                            <span class="fu">if_else</span>(weekday_is_saturday<span class="sc">==</span> <span class="dv">1</span>,<span class="st">&quot;Saturday&quot;</span>,</span>
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a>                                            <span class="fu">if_else</span>(weekday_is_sunday<span class="sc">==</span>   <span class="dv">1</span>, <span class="st">&quot;Sunday&quot;</span>, </span>
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a>                                                    <span class="st">&quot;-&quot;</span>))))))))</span>
<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a>newspopData<span class="sc">$</span>day <span class="ot">&lt;-</span> <span class="fu">as_factor</span>(newspopData<span class="sc">$</span>day)</span></code></pre></div>
<p>Some statistics based on the variables is as shown:</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>knitr<span class="sc">::</span><span class="fu">kable</span>(newspopData <span class="sc">%&gt;%</span> <span class="fu">group_by</span>(day) <span class="sc">%&gt;%</span> <span class="fu">summarize</span>(<span class="at">Count_of_Articles =</span> <span class="fu">n</span>()))</span></code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">day</th>
<th align="right">Count_of_Articles</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Monday</td>
<td align="right">322</td>
</tr>
<tr class="even">
<td align="left">Tuesday</td>
<td align="right">334</td>
</tr>
<tr class="odd">
<td align="left">Wednesday</td>
<td align="right">388</td>
</tr>
<tr class="even">
<td align="left">Thursday</td>
<td align="right">358</td>
</tr>
<tr class="odd">
<td align="left">Friday</td>
<td align="right">305</td>
</tr>
<tr class="even">
<td align="left">Saturday</td>
<td align="right">182</td>
</tr>
<tr class="odd">
<td align="left">Sunday</td>
<td align="right">210</td>
</tr>
</tbody>
</table>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>knitr<span class="sc">::</span><span class="fu">kable</span>(newspopData <span class="sc">%&gt;%</span> <span class="fu">group_by</span>(day, article_popularity_index) <span class="sc">%&gt;%</span> <span class="fu">summarize</span>(<span class="at">Count_of_Articles =</span> <span class="fu">n</span>()))</span></code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">day</th>
<th align="left">article_popularity_index</th>
<th align="right">Count_of_Articles</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Monday</td>
<td align="left">4</td>
<td align="right">84</td>
</tr>
<tr class="even">
<td align="left">Monday</td>
<td align="left">2</td>
<td align="right">73</td>
</tr>
<tr class="odd">
<td align="left">Monday</td>
<td align="left">1</td>
<td align="right">85</td>
</tr>
<tr class="even">
<td align="left">Monday</td>
<td align="left">3</td>
<td align="right">80</td>
</tr>
<tr class="odd">
<td align="left">Tuesday</td>
<td align="left">4</td>
<td align="right">87</td>
</tr>
<tr class="even">
<td align="left">Tuesday</td>
<td align="left">2</td>
<td align="right">71</td>
</tr>
<tr class="odd">
<td align="left">Tuesday</td>
<td align="left">1</td>
<td align="right">77</td>
</tr>
<tr class="even">
<td align="left">Tuesday</td>
<td align="left">3</td>
<td align="right">99</td>
</tr>
<tr class="odd">
<td align="left">Wednesday</td>
<td align="left">4</td>
<td align="right">109</td>
</tr>
<tr class="even">
<td align="left">Wednesday</td>
<td align="left">2</td>
<td align="right">103</td>
</tr>
<tr class="odd">
<td align="left">Wednesday</td>
<td align="left">1</td>
<td align="right">82</td>
</tr>
<tr class="even">
<td align="left">Wednesday</td>
<td align="left">3</td>
<td align="right">94</td>
</tr>
<tr class="odd">
<td align="left">Thursday</td>
<td align="left">4</td>
<td align="right">90</td>
</tr>
<tr class="even">
<td align="left">Thursday</td>
<td align="left">2</td>
<td align="right">81</td>
</tr>
<tr class="odd">
<td align="left">Thursday</td>
<td align="left">1</td>
<td align="right">90</td>
</tr>
<tr class="even">
<td align="left">Thursday</td>
<td align="left">3</td>
<td align="right">97</td>
</tr>
<tr class="odd">
<td align="left">Friday</td>
<td align="left">4</td>
<td align="right">79</td>
</tr>
<tr class="even">
<td align="left">Friday</td>
<td align="left">2</td>
<td align="right">74</td>
</tr>
<tr class="odd">
<td align="left">Friday</td>
<td align="left">1</td>
<td align="right">69</td>
</tr>
<tr class="even">
<td align="left">Friday</td>
<td align="left">3</td>
<td align="right">83</td>
</tr>
<tr class="odd">
<td align="left">Saturday</td>
<td align="left">4</td>
<td align="right">9</td>
</tr>
<tr class="even">
<td align="left">Saturday</td>
<td align="left">2</td>
<td align="right">64</td>
</tr>
<tr class="odd">
<td align="left">Saturday</td>
<td align="left">1</td>
<td align="right">57</td>
</tr>
<tr class="even">
<td align="left">Saturday</td>
<td align="left">3</td>
<td align="right">52</td>
</tr>
<tr class="odd">
<td align="left">Sunday</td>
<td align="left">4</td>
<td align="right">17</td>
</tr>
<tr class="even">
<td align="left">Sunday</td>
<td align="left">2</td>
<td align="right">70</td>
</tr>
<tr class="odd">
<td align="left">Sunday</td>
<td align="left">1</td>
<td align="right">65</td>
</tr>
<tr class="even">
<td align="left">Sunday</td>
<td align="left">3</td>
<td align="right">58</td>
</tr>
</tbody>
</table>
<p>This table shows the shares of articles on each day of the week. For
tech based articles, we can expect a rise in shares in mid week or
Fridays or after any tech has been launched. For entertainment and
lifestyle articles, post-weekend period would be the most active period
of sharing. While world, social media and business would not have a
definitive trend.</p>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(newspopData, <span class="fu">aes</span>(<span class="at">x =</span> day, <span class="at">y =</span> shares<span class="sc">/</span><span class="dv">1000000</span>)) <span class="sc">+</span></span>
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_bar</span>(<span class="at">stat =</span> <span class="st">&#39;identity&#39;</span>, <span class="at">width =</span> <span class="fl">0.5</span>, <span class="at">fill =</span> <span class="st">&#39;tomato3&#39;</span>)<span class="sc">+</span></span>
<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">subtitle =</span> <span class="st">&#39;Number of Shares (Million) Vs Day of Week&#39;</span>,</span>
<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a>       <span class="at">caption =</span> <span class="st">&#39;Source : News Popularity Dataset&#39;</span>,</span>
<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a>       <span class="at">y =</span> <span class="st">&#39;Total Share count in Million&#39;</span>,</span>
<span id="cb11-6"><a href="#cb11-6" aria-hidden="true" tabindex="-1"></a>       <span class="at">x =</span> <span class="st">&#39;Day of the Week&#39;</span>,</span>
<span id="cb11-7"><a href="#cb11-7" aria-hidden="true" tabindex="-1"></a>       <span class="at">title =</span> <span class="fu">toupper</span>(<span class="fu">str_replace_all</span>(params<span class="sc">$</span>data_channel, <span class="st">&quot;_&quot;</span>, <span class="st">&quot; &quot;</span>)),) <span class="sc">+</span></span>
<span id="cb11-8"><a href="#cb11-8" aria-hidden="true" tabindex="-1"></a>       <span class="fu">theme</span>(<span class="at">axis.text.x =</span> <span class="fu">element_text</span>(<span class="at">angle =</span> <span class="dv">65</span>, <span class="at">vjust =</span> <span class="fl">0.6</span>)) <span class="sc">+</span> </span>
<span id="cb11-9"><a href="#cb11-9" aria-hidden="true" tabindex="-1"></a>       <span class="fu">theme</span>(<span class="at">plot.caption =</span> <span class="fu">element_text</span>(<span class="at">size=</span><span class="dv">9</span>, <span class="at">color=</span><span class="st">&quot;red&quot;</span>, <span class="at">face=</span><span class="st">&quot;italic&quot;</span>, <span class="at">hjust =</span> <span class="dv">1</span>))</span></code></pre></div>
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" /><!-- -->
From this bar chart we can visualize the shares trend across the week.
The users engagement with the type of data Chanel (tech, entertainment,
politics) will be different across the week. Users may be more inclined
toward sharing lifestyle and entertainment news during weekend and
prefer less to share technology/science related news during same
time.</p>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(newspopData, <span class="fu">aes</span>(<span class="at">x =</span> global_rate_positive_words, <span class="at">y =</span> global_sentiment_polarity)) <span class="sc">+</span></span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>       <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">col =</span> day, <span class="at">shape =</span> article_popularity_index)) <span class="sc">+</span> </span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a>       <span class="fu">geom_smooth</span>(<span class="fu">aes</span>(<span class="at">col =</span> day), <span class="at">method =</span> <span class="st">&#39;lm&#39;</span>, <span class="at">se =</span> F) <span class="sc">+</span> </span>
<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a>       <span class="fu">scale_shape_discrete</span>(<span class="at">name=</span><span class="st">&quot;Article Popularity Index&quot;</span>, <span class="at">labels =</span> <span class="fu">c</span>(<span class="st">&quot;4&quot;</span>, <span class="st">&quot;3&quot;</span>, <span class="st">&quot;2&quot;</span>, <span class="st">&quot;1&quot;</span>))<span class="sc">+</span></span>
<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>       <span class="fu">labs</span>(<span class="at">subtitle =</span> <span class="st">&#39;Positive Rate VS Sentiment Polarity Plot&#39;</span>,</span>
<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a>       <span class="at">x =</span> <span class="st">&#39;Global Positive Word Rate&#39;</span>,</span>
<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a>       <span class="at">y =</span> <span class="st">&#39;Global Sentiment Polarity&#39;</span>,</span>
<span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a>       <span class="at">title =</span> <span class="fu">toupper</span>(<span class="fu">str_replace_all</span>(params<span class="sc">$</span>data_channel, <span class="st">&quot;_&quot;</span>, <span class="st">&quot; &quot;</span>)),</span>
<span id="cb12-9"><a href="#cb12-9" aria-hidden="true" tabindex="-1"></a>       <span class="at">caption =</span> <span class="st">&quot;Source : News Popularity Dataset&quot;</span>,</span>
<span id="cb12-10"><a href="#cb12-10" aria-hidden="true" tabindex="-1"></a>       <span class="at">color =</span> <span class="st">&#39;Days&#39;</span>,</span>
<span id="cb12-11"><a href="#cb12-11" aria-hidden="true" tabindex="-1"></a>       <span class="at">size =</span> <span class="st">&#39;Shares per Million&#39;</span>) <span class="sc">+</span> </span>
<span id="cb12-12"><a href="#cb12-12" aria-hidden="true" tabindex="-1"></a>       <span class="fu">theme</span>(<span class="at">plot.caption =</span> <span class="fu">element_text</span>(<span class="at">size=</span><span class="dv">9</span>, <span class="at">color=</span><span class="st">&quot;red&quot;</span>, <span class="at">face=</span><span class="st">&quot;italic&quot;</span>, <span class="at">hjust =</span> <span class="dv">1</span>))</span></code></pre></div>
<p><img 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" /><!-- --></p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(newspopData, <span class="fu">aes</span>(<span class="at">x =</span> global_rate_negative_words, <span class="at">y =</span> global_sentiment_polarity)) <span class="sc">+</span> </span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>      <span class="fu">geom_point</span>(<span class="fu">aes</span> (<span class="at">col =</span> day, <span class="at">shape =</span> article_popularity_index)) <span class="sc">+</span> </span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a>      <span class="fu">geom_smooth</span>(<span class="fu">aes</span>(<span class="at">col =</span> day), <span class="at">method =</span> <span class="st">&#39;lm&#39;</span>, <span class="at">se =</span> F) <span class="sc">+</span> </span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a>      <span class="fu">scale_shape_discrete</span>(<span class="at">name=</span><span class="st">&quot;Article Popularity Index&quot;</span>, <span class="at">labels =</span> <span class="fu">c</span>(<span class="st">&quot;4&quot;</span>, <span class="st">&quot;3&quot;</span>, <span class="st">&quot;2&quot;</span>, <span class="st">&quot;1&quot;</span>))<span class="sc">+</span></span>
<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a>      <span class="fu">labs</span>(<span class="at">subtitle =</span> <span class="st">&#39;Positive Rate VS Sentiment Polarity Plot&#39;</span>,</span>
<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a>       <span class="at">x =</span> <span class="st">&#39;Global Negative Word Rate&#39;</span>,</span>
<span id="cb13-7"><a href="#cb13-7" aria-hidden="true" tabindex="-1"></a>       <span class="at">y =</span> <span class="st">&#39;Global Sentiment Polarity&#39;</span>,</span>
<span id="cb13-8"><a href="#cb13-8" aria-hidden="true" tabindex="-1"></a>       <span class="at">title =</span> <span class="fu">toupper</span>(<span class="fu">str_replace_all</span>(params<span class="sc">$</span>data_channel, <span class="st">&quot;_&quot;</span>, <span class="st">&quot; &quot;</span>)),</span>
<span id="cb13-9"><a href="#cb13-9" aria-hidden="true" tabindex="-1"></a>       <span class="at">caption =</span> <span class="st">&quot;Source : News Popularity Dataset&quot;</span>,</span>
<span id="cb13-10"><a href="#cb13-10" aria-hidden="true" tabindex="-1"></a>       <span class="at">color =</span> <span class="st">&#39;Days&#39;</span>,</span>
<span id="cb13-11"><a href="#cb13-11" aria-hidden="true" tabindex="-1"></a>       <span class="at">size =</span> <span class="st">&#39;Shares per Million&#39;</span>) <span class="sc">+</span> </span>
<span id="cb13-12"><a href="#cb13-12" aria-hidden="true" tabindex="-1"></a>       <span class="fu">theme</span>(<span class="at">plot.caption =</span> <span class="fu">element_text</span>(<span class="at">size=</span><span class="dv">9</span>, <span class="at">color=</span><span class="st">&quot;red&quot;</span>, <span class="at">face=</span><span class="st">&quot;italic&quot;</span>, <span class="at">hjust =</span> <span class="dv">1</span>))  </span></code></pre></div>
<p><img 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" /><!-- --></p>
<p>The above plots estimate the general sentiments of users based on
positive and negative words in the content. Ideal expectations would be:
an article with more positive words has a positive sentiment index and
more shares, and vice versa. Exceptions may be found in peculiar
cases.</p>
<p>Plotting the number of shares based on the number of images and
videos that an article has, based on what day of the week it is:</p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(newspopData, <span class="fu">aes</span>(<span class="at">x=</span>day, <span class="at">y =</span>   shares<span class="sc">/</span><span class="dv">1000000</span>)) <span class="sc">+</span> </span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_bar</span>(<span class="fu">aes</span>(<span class="at">fill =</span> <span class="fu">as_factor</span>(num_imgs)), <span class="at">stat=</span><span class="st">&quot;identity&quot;</span>, <span class="at">position=</span><span class="st">&quot;dodge&quot;</span>) <span class="sc">+</span> </span>
<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_fill_discrete</span>(<span class="at">name =</span> <span class="st">&#39;Number of Images </span><span class="sc">\n</span><span class="st"> in Article&#39;</span>) <span class="sc">+</span></span>
<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">subtitle =</span> <span class="st">&#39;Number of Images in article v/s number of shares&#39;</span>,</span>
<span id="cb14-5"><a href="#cb14-5" aria-hidden="true" tabindex="-1"></a>       <span class="at">x =</span> <span class="st">&#39;Number of Images&#39;</span>,</span>
<span id="cb14-6"><a href="#cb14-6" aria-hidden="true" tabindex="-1"></a>       <span class="at">y =</span> <span class="st">&#39;Number of shares (in millions)&#39;</span>,</span>
<span id="cb14-7"><a href="#cb14-7" aria-hidden="true" tabindex="-1"></a>       <span class="at">title =</span> <span class="fu">toupper</span>(<span class="fu">str_replace_all</span>(params<span class="sc">$</span>data_channel, <span class="st">&quot;_&quot;</span>, <span class="st">&quot; &quot;</span>)),</span>
<span id="cb14-8"><a href="#cb14-8" aria-hidden="true" tabindex="-1"></a>       <span class="at">caption =</span> <span class="st">&quot;Source : News Popularity Dataset&quot;</span>) <span class="sc">+</span> </span>
<span id="cb14-9"><a href="#cb14-9" aria-hidden="true" tabindex="-1"></a>       <span class="fu">theme</span>(<span class="at">plot.caption =</span> <span class="fu">element_text</span>(<span class="at">size=</span><span class="dv">9</span>, <span class="at">color=</span><span class="st">&quot;red&quot;</span>, <span class="at">face=</span><span class="st">&quot;italic&quot;</span>, <span class="at">hjust =</span> <span class="dv">1</span>))</span></code></pre></div>
<p><img 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" /><!-- --></p>
<p>This plot shows the number of shares (in millions) based on number of
images included in each articles for each day of the week. The general
trend might see a increase in sharing of articles over Fridays and
weekends when there is more leisure time. Moreover, tech based articles
can also see a rise in share if any new technology is released in middle
of the week. Entertainment and Lifestyles articles can see a rise in
share if any events happened over the weekend which is the case most of
the times. World and social media Articles should not have a trend, as
events from all over the world keep on happening throughout the week and
updates are posted on social media non stop. Business articles would be
more trending during working days.</p>
<p>in addition to that, not all articles would be oriented towards
images. For example, tech and business based articles readers would not
care about the number of images included, but only the content itself,
while for entertainment, world, lifestyle articles, images are one of
the major factors in capturing user’s attention, and thus, shares.</p>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(newspopData, <span class="fu">aes</span>(<span class="at">x =</span>  num_keywords, <span class="at">y =</span>  shares<span class="sc">/</span><span class="dv">1000000</span>)) <span class="sc">+</span> </span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_bar</span>(<span class="fu">aes</span>(<span class="at">fill =</span> day), <span class="at">stat=</span><span class="st">&quot;identity&quot;</span>) <span class="sc">+</span> </span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_x_discrete</span>(<span class="at">limits=</span><span class="fu">c</span>(<span class="dv">2</span><span class="sc">:</span><span class="dv">10</span>)) <span class="sc">+</span></span>
<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">subtitle =</span> <span class="st">&#39;Shares based on number of keywords&#39;</span>,</span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a>       <span class="at">x =</span> <span class="st">&#39;Number of Keywords&#39;</span>,</span>
<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a>       <span class="at">y =</span> <span class="st">&#39;Shares (in millions)&#39;</span>,</span>
<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a>       <span class="at">title =</span> <span class="fu">toupper</span>(<span class="fu">str_replace_all</span>(params<span class="sc">$</span>data_channel, <span class="st">&quot;_&quot;</span>, <span class="st">&quot; &quot;</span>)),</span>
<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a>       <span class="at">caption =</span> <span class="st">&quot;Source : News Popularity Dataset&quot;</span>,</span>
<span id="cb15-9"><a href="#cb15-9" aria-hidden="true" tabindex="-1"></a>       <span class="at">fill =</span> <span class="st">&#39;Days&#39;</span>) <span class="sc">+</span> </span>
<span id="cb15-10"><a href="#cb15-10" aria-hidden="true" tabindex="-1"></a>       <span class="fu">theme</span>(<span class="at">plot.caption =</span> <span class="fu">element_text</span>(<span class="at">size=</span><span class="dv">9</span>, <span class="at">color=</span><span class="st">&quot;red&quot;</span>, <span class="at">face=</span><span class="st">&quot;italic&quot;</span>, <span class="at">hjust =</span> <span class="dv">1</span>))</span></code></pre></div>
<p><img 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" /><!-- --></p>
<p>This graph represents the shares trend of any article based on the
number of keywords. A general speculated trend would be: the higher the
number of keywords, the higher it is descriptive about its content, and
hence the number of shares would also be higher. However. this might not
hold true for business based articles where short and crisp key words
can also do the trick. Otherwise, the trend of shares should be positive
with respect to number of keywords.</p>
<p>Now, the title sentiment polarity is one of the first things that
users read while making a decision about reading an article let alone
sharing it. Hence it is important to see how is the title sentiment
polarity, is it negative or positive. Here, we are dividing the
polarities into 4 sections; Highly positive (Sentiment Polarity between
0.5 and 1), positive (Sentiment Polarity between 0 and 0.5), negative
((Sentiment Polarity between -0.5 and 0)) and highly negative (Sentiment
Polarity between -1 and -0.5).</p>
<p>Creating the new variable to classify the sentiments into above
category:</p>
<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>pols <span class="ot">=</span> <span class="fu">c</span>(<span class="st">&quot;Extremely Positive&quot;</span>, <span class="st">&quot;Positive&quot;</span>, <span class="st">&quot;Negative&quot;</span>, <span class="st">&quot;Extremely Negative&quot;</span>)</span>
<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a>newspopData <span class="ot">&lt;-</span> newspopData <span class="sc">%&gt;%</span> <span class="fu">mutate</span>(<span class="at">title_Sentiment_Class =</span> </span>
<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a>                                        <span class="fu">if_else</span>(title_sentiment_polarity <span class="sc">&gt;</span> <span class="fl">0.5</span>, pols[<span class="dv">1</span>],</span>
<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a>                                        <span class="fu">if_else</span>(title_sentiment_polarity <span class="sc">&gt;</span> <span class="dv">0</span>, pols[<span class="dv">2</span>],</span>
<span id="cb16-6"><a href="#cb16-6" aria-hidden="true" tabindex="-1"></a>                                        <span class="fu">if_else</span>(title_sentiment_polarity <span class="sc">&gt;</span> <span class="sc">-</span><span class="fl">0.5</span>, pols[<span class="dv">3</span>], pols[<span class="dv">4</span>]))))</span>
<span id="cb16-7"><a href="#cb16-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb16-8"><a href="#cb16-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb16-9"><a href="#cb16-9" aria-hidden="true" tabindex="-1"></a>newspopData<span class="sc">$</span>title_Sentiment_Class <span class="ot">&lt;-</span> <span class="fu">as_factor</span>(newspopData<span class="sc">$</span>title_Sentiment_Class)</span></code></pre></div>
<p>Statistics about the articles that are in each of these
categories:</p>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>knitr<span class="sc">::</span><span class="fu">kable</span>(newspopData <span class="sc">%&gt;%</span> <span class="fu">group_by</span>(title_Sentiment_Class) <span class="sc">%&gt;%</span> <span class="fu">summarize</span>(<span class="at">Count_of_articles =</span> <span class="fu">n</span>()))</span></code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">title_Sentiment_Class</th>
<th align="right">Count_of_articles</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Negative</td>
<td align="right">1259</td>
</tr>
<tr class="even">
<td align="left">Extremely Negative</td>
<td align="right">58</td>
</tr>
<tr class="odd">
<td align="left">Positive</td>
<td align="right">639</td>
</tr>
<tr class="even">
<td align="left">Extremely Positive</td>
<td align="right">143</td>
</tr>
</tbody>
</table>
<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>knitr<span class="sc">::</span><span class="fu">kable</span>(newspopData <span class="sc">%&gt;%</span> <span class="fu">group_by</span>(title_Sentiment_Class, article_popularity_index) <span class="sc">%&gt;%</span> <span class="fu">summarize</span>(<span class="at">Count_of_articles =</span> <span class="fu">n</span>()))</span></code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">title_Sentiment_Class</th>
<th align="left">article_popularity_index</th>
<th align="right">Count_of_articles</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Negative</td>
<td align="left">4</td>
<td align="right">292</td>
</tr>
<tr class="even">
<td align="left">Negative</td>
<td align="left">2</td>
<td align="right">320</td>
</tr>
<tr class="odd">
<td align="left">Negative</td>
<td align="left">1</td>
<td align="right">320</td>
</tr>
<tr class="even">
<td align="left">Negative</td>
<td align="left">3</td>
<td align="right">327</td>
</tr>
<tr class="odd">
<td align="left">Extremely Negative</td>
<td align="left">4</td>
<td align="right">12</td>
</tr>
<tr class="even">
<td align="left">Extremely Negative</td>
<td align="left">2</td>
<td align="right">7</td>
</tr>
<tr class="odd">
<td align="left">Extremely Negative</td>
<td align="left">1</td>
<td align="right">20</td>
</tr>
<tr class="even">
<td align="left">Extremely Negative</td>
<td align="left">3</td>
<td align="right">19</td>
</tr>
<tr class="odd">
<td align="left">Positive</td>
<td align="left">4</td>
<td align="right">138</td>
</tr>
<tr class="even">
<td align="left">Positive</td>
<td align="left">2</td>
<td align="right">169</td>
</tr>
<tr class="odd">
<td align="left">Positive</td>
<td align="left">1</td>
<td align="right">152</td>
</tr>
<tr class="even">
<td align="left">Positive</td>
<td align="left">3</td>
<td align="right">180</td>
</tr>
<tr class="odd">
<td align="left">Extremely Positive</td>
<td align="left">4</td>
<td align="right">33</td>
</tr>
<tr class="even">
<td align="left">Extremely Positive</td>
<td align="left">2</td>
<td align="right">40</td>
</tr>
<tr class="odd">
<td align="left">Extremely Positive</td>
<td align="left">1</td>
<td align="right">33</td>
</tr>
<tr class="even">
<td align="left">Extremely Positive</td>
<td align="left">3</td>
<td align="right">37</td>
</tr>
</tbody>
</table>
<p>The tables above represents the number of articles classified into
each title sentiment category, and based on their popularity index.</p>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>knitr<span class="sc">::</span><span class="fu">kable</span>(newspopData <span class="sc">%&gt;%</span> <span class="fu">group_by</span>(title_Sentiment_Class, day) <span class="sc">%&gt;%</span> <span class="fu">summarize</span>(<span class="at">Count_of_articles =</span> <span class="fu">n</span>()))</span></code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">title_Sentiment_Class</th>
<th align="left">day</th>
<th align="right">Count_of_articles</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Negative</td>
<td align="left">Monday</td>
<td align="right">189</td>
</tr>
<tr class="even">
<td align="left">Negative</td>
<td align="left">Tuesday</td>
<td align="right">201</td>
</tr>
<tr class="odd">
<td align="left">Negative</td>
<td align="left">Wednesday</td>
<td align="right">247</td>
</tr>
<tr class="even">
<td align="left">Negative</td>
<td align="left">Thursday</td>
<td align="right">216</td>
</tr>
<tr class="odd">
<td align="left">Negative</td>
<td align="left">Friday</td>
<td align="right">199</td>
</tr>
<tr class="even">
<td align="left">Negative</td>
<td align="left">Saturday</td>
<td align="right">91</td>
</tr>
<tr class="odd">
<td align="left">Negative</td>
<td align="left">Sunday</td>
<td align="right">116</td>
</tr>
<tr class="even">
<td align="left">Extremely Negative</td>
<td align="left">Monday</td>
<td align="right">11</td>
</tr>
<tr class="odd">
<td align="left">Extremely Negative</td>
<td align="left">Tuesday</td>
<td align="right">10</td>
</tr>
<tr class="even">
<td align="left">Extremely Negative</td>
<td align="left">Wednesday</td>
<td align="right">12</td>
</tr>
<tr class="odd">
<td align="left">Extremely Negative</td>
<td align="left">Thursday</td>
<td align="right">12</td>
</tr>
<tr class="even">
<td align="left">Extremely Negative</td>
<td align="left">Friday</td>
<td align="right">6</td>
</tr>
<tr class="odd">
<td align="left">Extremely Negative</td>
<td align="left">Saturday</td>
<td align="right">2</td>
</tr>
<tr class="even">
<td align="left">Extremely Negative</td>
<td align="left">Sunday</td>
<td align="right">5</td>
</tr>
<tr class="odd">
<td align="left">Positive</td>
<td align="left">Monday</td>
<td align="right">105</td>
</tr>
<tr class="even">
<td align="left">Positive</td>
<td align="left">Tuesday</td>
<td align="right">100</td>
</tr>
<tr class="odd">
<td align="left">Positive</td>
<td align="left">Wednesday</td>
<td align="right">109</td>
</tr>
<tr class="even">
<td align="left">Positive</td>
<td align="left">Thursday</td>
<td align="right">105</td>
</tr>
<tr class="odd">
<td align="left">Positive</td>
<td align="left">Friday</td>
<td align="right">80</td>
</tr>
<tr class="even">
<td align="left">Positive</td>
<td align="left">Saturday</td>
<td align="right">67</td>
</tr>
<tr class="odd">
<td align="left">Positive</td>
<td align="left">Sunday</td>
<td align="right">73</td>
</tr>
<tr class="even">
<td align="left">Extremely Positive</td>
<td align="left">Monday</td>
<td align="right">17</td>
</tr>
<tr class="odd">
<td align="left">Extremely Positive</td>
<td align="left">Tuesday</td>
<td align="right">23</td>
</tr>
<tr class="even">
<td align="left">Extremely Positive</td>
<td align="left">Wednesday</td>
<td align="right">20</td>
</tr>
<tr class="odd">
<td align="left">Extremely Positive</td>
<td align="left">Thursday</td>
<td align="right">25</td>
</tr>
<tr class="even">
<td align="left">Extremely Positive</td>
<td align="left">Friday</td>
<td align="right">20</td>
</tr>
<tr class="odd">
<td align="left">Extremely Positive</td>
<td align="left">Saturday</td>
<td align="right">22</td>
</tr>
<tr class="even">
<td align="left">Extremely Positive</td>
<td align="left">Sunday</td>
<td align="right">16</td>
</tr>
</tbody>
</table>
<p>This table further shows the shares of different title sentimental
types of articles for each day of the week.</p>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>newspopData <span class="ot">&lt;-</span> newspopData <span class="sc">%&gt;%</span> <span class="fu">mutate</span>(<span class="at">content_Sentiment_Class =</span> </span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a>                                        <span class="fu">if_else</span>( global_sentiment_polarity <span class="sc">&gt;</span> <span class="fl">0.5</span>, pols[<span class="dv">1</span>],</span>
<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a>                                        <span class="fu">if_else</span>( global_sentiment_polarity <span class="sc">&gt;</span> <span class="dv">0</span>, pols[<span class="dv">2</span>],</span>
<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a>                                        <span class="fu">if_else</span>( global_sentiment_polarity <span class="sc">&gt;</span> <span class="sc">-</span><span class="fl">0.5</span>, pols[<span class="dv">3</span>], pols[<span class="dv">4</span>]))))</span>
<span id="cb20-5"><a href="#cb20-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb20-6"><a href="#cb20-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb20-7"><a href="#cb20-7" aria-hidden="true" tabindex="-1"></a>newspopData<span class="sc">$</span>content_Sentiment_Class <span class="ot">&lt;-</span> <span class="fu">as_factor</span>(newspopData<span class="sc">$</span>content_Sentiment_Class)</span>
<span id="cb20-8"><a href="#cb20-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb20-9"><a href="#cb20-9" aria-hidden="true" tabindex="-1"></a><span class="co"># average article length </span></span>
<span id="cb20-10"><a href="#cb20-10" aria-hidden="true" tabindex="-1"></a>knitr<span class="sc">::</span><span class="fu">kable</span>(newspopData <span class="sc">%&gt;%</span></span>
<span id="cb20-11"><a href="#cb20-11" aria-hidden="true" tabindex="-1"></a>  <span class="fu">group_by</span>(content_Sentiment_Class, day)<span class="sc">%&gt;%</span></span>
<span id="cb20-12"><a href="#cb20-12" aria-hidden="true" tabindex="-1"></a>    <span class="fu">select</span>(day, content_Sentiment_Class, n_tokens_content) <span class="sc">%&gt;%</span></span>
<span id="cb20-13"><a href="#cb20-13" aria-hidden="true" tabindex="-1"></a>    <span class="fu">summarise</span>(<span class="at">Average_Content_Length =</span> <span class="fu">round</span>(<span class="fu">sum</span>(n_tokens_content)<span class="sc">/</span><span class="fu">n</span>())))</span></code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">content_Sentiment_Class</th>
<th align="left">day</th>
<th align="right">Average_Content_Length</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Positive</td>
<td align="left">Monday</td>
<td align="right">591</td>
</tr>
<tr class="even">
<td align="left">Positive</td>
<td align="left">Tuesday</td>
<td align="right">603</td>
</tr>
<tr class="odd">
<td align="left">Positive</td>
<td align="left">Wednesday</td>
<td align="right">668</td>
</tr>
<tr class="even">
<td align="left">Positive</td>
<td align="left">Thursday</td>
<td align="right">634</td>
</tr>
<tr class="odd">
<td align="left">Positive</td>
<td align="left">Friday</td>
<td align="right">655</td>
</tr>
<tr class="even">
<td align="left">Positive</td>
<td align="left">Saturday</td>
<td align="right">683</td>
</tr>
<tr class="odd">
<td align="left">Positive</td>
<td align="left">Sunday</td>
<td align="right">657</td>
</tr>
<tr class="even">
<td align="left">Negative</td>
<td align="left">Monday</td>
<td align="right">354</td>
</tr>
<tr class="odd">
<td align="left">Negative</td>
<td align="left">Tuesday</td>
<td align="right">324</td>
</tr>
<tr class="even">
<td align="left">Negative</td>
<td align="left">Wednesday</td>
<td align="right">344</td>
</tr>
<tr class="odd">
<td align="left">Negative</td>
<td align="left">Thursday</td>
<td align="right">221</td>
</tr>
<tr class="even">
<td align="left">Negative</td>
<td align="left">Friday</td>
<td align="right">292</td>
</tr>
<tr class="odd">
<td align="left">Negative</td>
<td align="left">Saturday</td>
<td align="right">259</td>
</tr>
<tr class="even">
<td align="left">Negative</td>
<td align="left">Sunday</td>
<td align="right">197</td>
</tr>
<tr class="odd">
<td align="left">Extremely Positive</td>
<td align="left">Wednesday</td>
<td align="right">399</td>
</tr>
<tr class="even">
<td align="left">Extremely Positive</td>
<td align="left">Thursday</td>
<td align="right">161</td>
</tr>
</tbody>
</table>
<p>We further want to extend our analysis based on the average number of
tokens on an article published during the weekdays and weekend.</p>
<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(newspopData, <span class="fu">aes</span>(<span class="at">x=</span>title_Sentiment_Class, <span class="at">y=</span>shares<span class="sc">/</span><span class="dv">1000000</span>)) <span class="sc">+</span></span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_bar</span>(<span class="fu">aes</span>(<span class="at">fill =</span> day), <span class="at">stat=</span><span class="st">&quot;identity&quot;</span>, <span class="at">position=</span><span class="st">&quot;dodge&quot;</span>) <span class="sc">+</span></span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">subtitle =</span> <span class="st">&#39;Shares based on title sentiment and day of the week&#39;</span>,</span>
<span id="cb21-4"><a href="#cb21-4" aria-hidden="true" tabindex="-1"></a>       <span class="at">x =</span> <span class="st">&#39;Title Sentiment Category&#39;</span>,</span>
<span id="cb21-5"><a href="#cb21-5" aria-hidden="true" tabindex="-1"></a>       <span class="at">y =</span> <span class="st">&#39;Shares (in millions)&#39;</span>,</span>
<span id="cb21-6"><a href="#cb21-6" aria-hidden="true" tabindex="-1"></a>       <span class="at">title =</span> <span class="fu">toupper</span>(<span class="fu">str_replace_all</span>(params<span class="sc">$</span>data_channel, <span class="st">&quot;_&quot;</span>, <span class="st">&quot; &quot;</span>)),</span>
<span id="cb21-7"><a href="#cb21-7" aria-hidden="true" tabindex="-1"></a>       <span class="at">caption =</span> <span class="st">&quot;Source : News Popularity Dataset&quot;</span>,</span>
<span id="cb21-8"><a href="#cb21-8" aria-hidden="true" tabindex="-1"></a>       <span class="at">fill =</span> <span class="st">&#39;Days&#39;</span>) <span class="sc">+</span></span>
<span id="cb21-9"><a href="#cb21-9" aria-hidden="true" tabindex="-1"></a>      <span class="fu">theme</span>(<span class="at">plot.caption =</span> <span class="fu">element_text</span>(<span class="at">size=</span><span class="dv">9</span>, <span class="at">color=</span><span class="st">&quot;red&quot;</span>, <span class="at">face=</span><span class="st">&quot;italic&quot;</span>, <span class="at">hjust =</span> <span class="dv">1</span>)) <span class="sc">+</span> </span>
<span id="cb21-10"><a href="#cb21-10" aria-hidden="true" tabindex="-1"></a>       <span class="fu">geom_text</span>(<span class="at">x =</span> <span class="dv">3</span>, <span class="at">y =</span> <span class="fl">0.6</span>, <span class="at">size =</span> <span class="dv">3</span>, </span>
<span id="cb21-11"><a href="#cb21-11" aria-hidden="true" tabindex="-1"></a>                <span class="at">label =</span> <span class="fu">paste</span>(<span class="st">&quot;Title Sentiment Score range&quot;</span>, <span class="st">&quot;Extremely Positive = 0.5 &lt;--&gt; 1&quot;</span>, </span>
<span id="cb21-12"><a href="#cb21-12" aria-hidden="true" tabindex="-1"></a>                              <span class="st">&#39;Positive = 0 &lt;--&gt; 0.5 &#39;</span>, </span>
<span id="cb21-13"><a href="#cb21-13" aria-hidden="true" tabindex="-1"></a>                              <span class="st">&#39;Negative = -0.5 &lt;--&gt; 0&#39;</span>, </span>
<span id="cb21-14"><a href="#cb21-14" aria-hidden="true" tabindex="-1"></a>                              <span class="st">&#39;Extremely Negative = -1 &lt;--&gt; -0.5&#39;</span>, </span>
<span id="cb21-15"><a href="#cb21-15" aria-hidden="true" tabindex="-1"></a>                              <span class="at">sep =</span> <span class="st">&#39;</span><span class="sc">\n</span><span class="st">&#39;</span> ), <span class="at">color =</span> <span class="st">&#39;black&#39;</span>)</span></code></pre></div>
<p><img 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" /><!-- --></p>
<p>The above graph represents the shares of articles (in millions) based
on title sentiment category for each day of the week. Some of the trends
that can be thought of here is that entertainment and lifestyle articles
can have a shares of both extremes ends of classifications, mostly in
the starting of the week after any events that might have happened, or
any other controversy that their target celebrity would be involved
in.</p>
<p>For tech, a high number of positive ends shares can be expected,
while social media, business, world can have a mix of all the types of
sentimental categorical shares, depending on the latest news.</p>
<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(newspopData, <span class="fu">aes</span>(<span class="at">x=</span> title_sentiment_polarity)) <span class="sc">+</span></span>
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_density</span>(<span class="fu">aes</span>(<span class="at">fill=</span>title_Sentiment_Class), <span class="at">alpha =</span> <span class="fl">0.7</span>) <span class="sc">+</span></span>
<span id="cb22-3"><a href="#cb22-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">facet_grid</span>(. <span class="sc">~</span>day)<span class="sc">+</span></span>
<span id="cb22-4"><a href="#cb22-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">scale_fill_discrete</span>(<span class="at">name =</span> <span class="st">&quot;Title Sentiment&quot;</span>) <span class="sc">+</span></span>
<span id="cb22-5"><a href="#cb22-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">subtitle =</span> <span class="st">&#39;Distribution of articles on title sentiment and day of the week&#39;</span>,</span>
<span id="cb22-6"><a href="#cb22-6" aria-hidden="true" tabindex="-1"></a>       <span class="at">x =</span> <span class="st">&#39;Title Sentiment Polarity&#39;</span>,</span>
<span id="cb22-7"><a href="#cb22-7" aria-hidden="true" tabindex="-1"></a>       <span class="at">y =</span> <span class="st">&#39;Density&#39;</span>,</span>
<span id="cb22-8"><a href="#cb22-8" aria-hidden="true" tabindex="-1"></a>       <span class="at">title =</span> <span class="fu">toupper</span>(<span class="fu">str_replace_all</span>(params<span class="sc">$</span>data_channel, <span class="st">&quot;_&quot;</span>, <span class="st">&quot; &quot;</span>)),</span>
<span id="cb22-9"><a href="#cb22-9" aria-hidden="true" tabindex="-1"></a>       <span class="at">caption =</span> <span class="st">&quot;Source : News Popularity Dataset&quot;</span>) <span class="sc">+</span> </span>
<span id="cb22-10"><a href="#cb22-10" aria-hidden="true" tabindex="-1"></a>       <span class="fu">theme</span>(<span class="at">plot.caption =</span> <span class="fu">element_text</span>(<span class="at">size=</span><span class="dv">9</span>, <span class="at">color=</span><span class="st">&quot;red&quot;</span>, <span class="at">face=</span><span class="st">&quot;italic&quot;</span>, <span class="at">hjust =</span> <span class="dv">1</span>))</span></code></pre></div>
<p><img 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D77aHQTe7iJh+m1HQuDKEIA//f/xf/6n7QdrPbYx37WF/F8pDpj9+xv/Ff/wP2ZDF+ZBwD+uTc1m/Fbuo3Zb2q3jX7yXU++q3wN/OTbnmtztgEDh/fSaA2AQ3Xa20BX6o6Aw81yLY+Zn/mJ97f5hu0O1Wdfjf6J9ys2ce+9tmNhEEUI4I/+/n/5tmc0R8DVO/3VLfWlPK7lK/MAwD9/uGTjcz/8af+p3Tb6cz9SvgB+5qd+vz7QrW4YHQEHCu+l0ToAPxem094GutIQwCFmuZafzM0l/h/p8imPgL332cNhfxtbeQTsudd2LAyiGAH8uebI6CP9t8u6Nwur38oXl/ULTNfylflw1caTP9Slrt49Ob6D4jG120Z//u//5Kefe/Y3/vZHn2tz9gO+NVh4L40ev9HwZH1w9FyoTnsb6EpDAIeY5Vp+MteXA3eHDvURYa/dofrs6SroMmkvbLBe27EwiGIEcPdisbkKum3ks++rr6Z78k31P8/+5twnd4TkK3OzeyqT/Qc/X6f+we7s1XP+U7tt9LPvqz/kXf2nzdkE7JocKLyXRvcB3Da72SOH6bS3ga40AnCAWa7lKXP1Tkq1GTf5nn3fD3201+5Affb0OeA2dhs2WK/tWBhE0QHYTM/8lIcikWX2kjq2Rh/lMHx8md13Op7MXma5VjyZO3nrcyShPfXajoVBlCaAn/xBj9fSeahkJh+pI2v0US7DR5fZQ6ejyexnlmtFk7mTvz7HEdpXr+1YGERpAtiPMs6cZejQq+FVZM5DOQ90CgLAemWcOcvQoVfDq8ich3Ie6BQEgPXKOHOWoUOvhleROQ/lPNApCADrlXHmLEOHXg2vInMeynmgU9BKAO+O6v88kkfLZalYM7t8EqeNjmMVU2h0fMFmrAQ37hwzb7ZyHugUBID1VqyZAbCwJdTo+ILNWAlu3DlmBsA2lh0LgwgA661YMwNgYUuo0fEFm7ES3LhzzAyAbSw7FgYRANZbsWYGwMKWUKPjCzZjJbhx55gZANtYdiwMIgCst2LNDICFLaFGxxdsxkpw484xMwC2sexYGEQAWG/FmhkAC1tCjY4v2IyV4MadY2YAbGPZsTCIALDeijUzABa2hBodX7AZK8GNO8fMANjGsmNhEAFgvRVrZgAsbAk1Or5gM1aCG3eOmQGwjWXHwiACwHor1swAWNgSanR8wWasBDfuHDMDYBvLjoVBBID1VqyZAbCwJdTo+ILNWAlu3DlmBsA2lh0LgwgA661YMwNgYUuo0fEFm7ES3LhzzAyAbSw7FgYRANZbsWYGwMKWUKPjCzZjJbhx55gZANtYdiwMIgCst2LNDICFLaFGxxdsxkpw484xMwC2sexYGEQAWG/FmhkAC1tCjY4v2IyV4MadY2YAbGPZsTCIALDeijUzABa2hBodX7AZK8GNO8fMANjGsmNhEAFgvRVrZgAsbAk1Or5gM1aCG3eOmQGwjWXHwiACwHor1swAWNgSanR8wWasBDfuHDMDYBvLjoVBBID1VqyZAbCwJdTo+ILNWAlu3DlmBsA2lh0LgwgA661YMwNgYUuo0fEFm7ES3LhzzAyAbSw7FgYRANZbsWYGwMKWUKPjCzZjJbhx55gZANtYdiwMIgCst2LNDICFLaFGxxdsxkpw484xMwC2sexYGEQAWG/FmhkAC1tCjY4v2IyV4MadY2YAbGPZsTCIALDeijUzABa2hBodX7AZK8GNO8fMANjGsmNhEAFgvRVrZgAsbAk1Or5gM1aCG3eOmQGwjWXHwiACwHor1swAWNgSanR8wWasBDfuHDMDYBvLjoVBBID1VqyZAbCwJdTo+ILNWAlu3DlmBsA2lh0LgwgA661YMwNgYUuo0fEFm7ES3LhzzAyAbSw7FgYRANZbsWYGwMKWUKPjCzZjJbhx55gZANtYdiwMIgCst2LNDICFLaFGxxdsxkpw484xMwC2sexYGEQAWG/FmhkAC1tCjY4v2IwVdOMuCpul0s4MgP1ZdiwMIgCst2LNDICFLaFGxxdsxgq6cQNgb1bOA52CALDeijUzABa2hBodX7AZK+jGDYC9WTkPdAoCwHor1swAWNgSanR8wWasoBs3APZm5TzQKQgA661YMwNgYUuo0fEFm7GCbtwA2JuV80CnoJUARgihjSrY7SBUiSNgvRVrZo6AhS2hRscXbMYKunFzBOzNynmgUxAA1luxZgbAwpZQo+MLNmMF3bgBsDcr54FOQQBYb8WaGQALW0KNji/YjBV04wbA3qycBzoFAWC9FWtmACxsCTU6vmAzVtCNGwB7s3Ie6BQEgPVWrJkBsLAl1Oj4gs1YQTduAOzNynmgUxAA1luxZgbAwpZQo+MLNmMF3bgBsDcr54FOQQBYb8WaGQALW0KNji/YjBV04wbA3qycBzoFAWC9FWtmACxsCTU6vmAzVtCNGwB7s3Ie6BQEgPVWrJkBsLAl1Oj4gs1YQTduAOzNynmgUxAA1luxZgbAwpZQo+MLNmMF3bgBsDcr54FOQQBYb8WaGQALW0KNji/YjBV04wbA3qycBzoFAWC9FWtmACxsCTU6vmAzVtCNGwB7s3Ie6BQEgPVWrJkBsLAl1Oj4gs1YQTduAOzNynmgUxAA1luxZgbAwpZQo+MLNmMF3bgBsDcr54FOQUkAuADATi0ALNLo+ILNWGEHGgD7snIe6BSUBoD183ph91EA2J8l1Oj4gs1YsQ40AJa1ch7oFASA9VbQzADYnyXU6PiCzVixDjQAlrVyHugUBID1VtDMANifJdTo+ILNWLEONACWtXIe6BQEgPVW0MwA2J8l1Oj4gs1YsQ40AJa1ch7oFASA9VbQzADYnyXU6PiCzVixDjQAlrVyHugUBID1VtDMANifJdTo+ILNWLEONACWtXIe6BQEgPVW0MwA2J8l1Oj4gs1YsQ40AJa1ch7oFASA9VbQzADYnyXU6PiCzVixDjQAlrVyHugUBID1VtDMANifJdTo+ILNWLEONACWtXIe6BQEgPVW0MwA2J8l1Oj4gs1YsQ40AJa1ch7oFASA9VbQzADYnyXU6PiCzVixDjQAlrVyHugUBID1VtDMANifJdTo+ILNWLEONACWtXIe6BQEgPVW0MwA2J8l1Oj4gs1YsQ40AJa1ch7oFASA9VbQzADYnyXU6PiCzVixDjQAlrVyHugUBID1VtDMANifJdTo+ILNWLEONACWtXIe6BQEgPVW0MwA2J8l1Oj4gs1YsQ40AJa1ch7oFASA9VbQzADYnyXU6PiCzVixDjQAlrVyHugUBID1VtDMANifJdTo+ILNWLEONACWtXIe6BQEgPVW0MwA2J8l1Oj4gs1YsQ40AJa1ch7oFASA9VbQzADYnyXU6PiCzVixDjQAlrVyHugUBID1VtDMANifJdTo+ILNWLEONACWtXIe6BQEgPVW0MwA2J8l1Oj4gs1YsQ40AJa1ch7oFASA9VbQzADYnyXU6PiCzVixDjQAlrVyHugUBID1VtDMANifJdTo+ILNWGEH+gWbiU47MwD2Z9mxMIgAsN4KmhkA+7OEGh1fsBkr7EADYF9WzgOdggCw3gqaGQD7s4QaHV+wGSvsQANgX1bOA52CALDeCpoZAPuzhBodX7AZK+xAA2BfVs4DnYIAsN4KmhkA+7OEGh1fsBkr7EADYF9WzgOdggCw3gqaGQD7s4QaHV+wGSvsQANgX1bOA52CALDeCpoZAPuzhBodX7AZK+xAA2BfVs4DnYIAsN4KmhkA+7OEGh1fsBkr7EADYF9WzgOdggCw3gqaGQD7s4QaHV+wGSvsQANgX1bOA52CALDeCpoZAPuzhBodX7AZK+xAA2BfVs4DnYIAsN4KmhkA+7OEGh1fsBkr7EADYF9WzgOdglIAcPE8AHZqAWCRRscXbMYKunEDYG9WzgOdggCw3gqZGQB7tIQaHV+wGSvoxg2AvVk5D3QKAsB6K2RmAOzREmp0fMFmrKAbNwD2ZuU80CkoDQDr5/XC7qMAsD9LqNHxBZuxgm7cANiblfNApyAArLdCZgbAHi2hRscXbMYKunEDYG9WzgOdggCw3gqZGQB7tIQaHV+wGSvoxg2AvVk5D3QKAsB6K2RmAOzREmp0fMFmrKAbNwD2ZuU80CkIAOutkJkBsEdLqNHxBZuxgm7cANiblfNApyAArLdCZgbAHi2hRscXbMYKunEDYG9WzgOdggCw3gqZGQB7tIQaHV+wGSvoxg2AvVk5D3QKAsB6K2RmAOzREmp0fMFmrKAbNwD2ZuU80CkIAOutkJkBsEdLqNHxBZuxgm7cANiblfNApyAArLdCZgbAHi2hRscXbMYKunEDYG9WzgOdggCw3gqZGQB7tIQaHV+wGSvoxg2AvVk5D3QKAsB6K2RmAOzREmp0fMFmrKAbNwD2ZuU80CkIAOutkJkBsEdLqNHxBZuxgm7cANiblfNApyAArLdCZgbAHi2hRscXbMYKunEDYG9WzgOdggCw3gqZGQB7tIQaHV+wGSvoxg2AvVk5D3QKAsB6K2RmAOzREmp0fMFmrKAbNwD2ZuU80CkIAOutkJkBsEdLqNHxBZuxgm7cANiblfNApyAArLdCZgbAHi2hRscXbMYKunEDYG9WzgOdggCw3gqZGQB7tIQaHV+wGSvoxg2AvVk5D3QKAsB6K2RmAOzREmp0fMFmrKAbNwD2ZuU80CkIAOutkJkBsEdLqNF266FHUQqZAXDkVs4DnYIAsN4KmRkAe7SEGm0JYBsWRZMZAEdu5TzQKQgA662QmQGwR0uo0QDY1ALA3qycBzoFAWC9FTIzAPZoCTUaAJtaANiblfNAp6BZAH/vV5/a77947dq1n3mqvSXIcwuAHVsAWKTRANjUAsDerJwHOgXNAfjbNXg/88HeTUGeWwDs2ALAIo0GwKYWAPZm5TzQKWgGwJ95+x+XR8Bv/OEne7cFeW4BsGMLAIs0GgCbWgDYm5XzQKegxVPQr3/g2rVr9UHwj5bys1IjFS+8sPKtaoRSUZHhtl0w0AhVWgTw937lk72j4CAvbjgCdmxxBCzSaI6ADa25geYIWNbKeaBT0PJFWJUO7wMHeW4BsGMLAIs0GgAbWgDYn5XzQKcgAKy3QmYGwB4toUYDYEMLAPuzch7oFLQI4G+/40v7N/6IjyE5rxbQAsAijQbAhhYA9mflPNApyOhzwG8/XAgd5LkFwI4tACzSaABsaAFgf1bOA52C+CYsvRUyMwD2aAk1GgAbWgDYn5XzQKcgAKy3QmYGwB4toUYDYEMLAPuzch7oFASA9VbIzADYoyXUaABsaAFgf1bOA52CALDeCpkZAHu0hBoNgA0tAOzPynmgUxAA1lshMwNgj5ZQowGwoQWA/Vk5D3QKAsB6K2RmAOzREmo0ADa0ALA/K+eBTkEAWG+FzAyAPVpCjQbAhhYA9mflPNApCADrrZCZAbBHS6jRANjQAsD+rJwHOgUBYL0VMjMA9mgJNRoAG1oA2J+V80CnIACst0JmzhPA+t1yCo0GwIYWAPZnhR1oALwkAKy3QmYGwK5rAeAoBxoAy1phBxoALwkA662QmQGw61oAOMqBBsCyVtiBBsBLAsB6K2RmAOy6FgCOcqABsKwVdqAB8JIAsN4KmRkAu64FgKMcaAAsa4UdaAC8JACst0JmBsCua0UC4MKKRdFkBsCRW2EHGgAvCQDrrZCZswTwzMFgCo0GwIYWAPZnBR1oALwoAKy3QmYGwI5rAeA4BxoAy1pBBxoALwoA662QmfMEcNowyjEzAI7cCjrQAHhRAFhvhcwMgB3XAsBxDjQAlrWCDjQAXhQA1lshMwNgx7UAcJwDDYBlraADDYAXBYD1VsjMANhxLQAc50ADYFkr6EAD4EUBYL0VMjMAdlwLAMc50ABY1go60AB4UQBYb4XMDIAd1wLAcQ40AJa1gg40AF4UANZbITMDYMe1AHCcAw2AZa2gAw2AFwWA9VbIzADYcS0AHOdAA2BZK+hAA+BFAWC9FTIzAHZcCwDHOdAAWNYKOtAAeFEAWG+FzAyAHdcCwHEONACWtYIONABeFADWWyEzA2DHtQBwnAMNgGWtoAMNgBcFgPVWyMwA2HEtABznQANgWSvoQAPgRQFgvRUyMwB2XAsAxznQAFjWCjrQAHhRAFhvhcwMgB3XAsBxDjQAlrWCDjQAXhQA1lshMwNgx7UAcJwDDYBlraADDYAXBYD1VsjMANhxLQAc50ADYFkr6EAD4EUBYL0VMjMAdlwLAMc50ABY1go60AB4UQBYb4XMDIAd1wLAcQ40AJa1gg40AF4UANZbITMDYMe1AHCcAw2AZa2gAw2AFwWA9VbIzADYcS0AHOdAA2BZK+hAA+BFAWC9FTIzAHZcCwDHOdAAWNYKOtAAeFEAWG+FzAyAHdcCwHEONACWtYIONABeFADWWyEzA2DHtQBwnAMNgGWtoAMNgBcFgPVWyMwA2HEtABznQANgWSvoQAPgRQFgvRUyMwB2XAsAxznQAFjWCjrQAHhRAFhvhcwMgB3XAsBxDjQAlrWCDjQAXhQA1lshM5ep/dUCwCKNzjEzAI7cCjrQAHhRAFhvhcwMgB3XAsBxDjQAlrWCDjQAXhQA1lshMwNgx7UAcJwDDYBlraADDYAXBYD1VsjMANhxLQAc50ADYFkr6EAD4EUBYL0VMjMAdlwLAMc50ABY1go60AB4UQBYb4XMvCsAsNNaADjOgQbAslbQgQbAiwLAeitkZgDsuBYAjnOgAbCsFXSgAfCiALDeCpkZADuuBYDjHGgALGsFHWgAvCgArLdCZgbAjmsB4DgHGgDLWkEHGgAvCgDrrZCZAbDjWgA4zlWB3ucAACAASURBVIEGwLJW0IEGwIsCwHorZGYA7LhWPAB+PruNGwD7s4IONABeFADWWyEzA2DHtQBwnAMNgGWtoAMNgBcFgPVWyMwA2HEtABznQANgWSvoQAPgRQFgvRUyMwB2XAsAxznQAFjWCjrQPr9NCAA7swCw41oAWKTRANjQAsD+rKADDYAXBYD1VsjMANhxLQAc50ADYFkr6EAD4EUBYL0VMjMAdlwLAMc50ABY1go60AB4UQBYb4XMDIAd1wLAcQ40AJa1gg40AF4UANZbITMDYMe1AHCcAw2AZa2gAw2AFwWA9VbIzADYcS0AHOdAA2BZK+hAA+BFAWC9FTJzpgBOGkY5ZgbAkVtBB3puLwaAawFgvRUyMwB2XAsAxznQAFjWCjrQAHhRAFhvhcwMgB3XAsBxDjQAlrWCDjQAXhQA1lshM3t9PxQAizQ6x8wAOHIr6EAD4EUBYL0VMjMAdlwLAMc50ABY1go60AB4UQBYb4XMDIAd1wLAcQ40AJa1gg40AF4UANZbITMDYMe1AHCcAw2AZa2gAw2AFwWA9VbIzADYcS0AHOdAA2BZK+hAA+BFAWC9FTIzAHZcCwDHOdAAWNYKOtAAeFEAWG+FzAyAHdcCwHEONACWtYIONABeFADWWyEzA2DHtQBwnAMNgGWtoAMNgBcFgPVWyMwA2HEtABznQANgWSvwQAPgBa0EcBAVL7yQwmrKqsgyc36hyYwurHLcia0UR8B6K2RmjoAd1+IIOM6B5ghY1go80BwBLwgA662QmQGw41oAOM6BvrgADvOn+QIPNABeEADWWyEzA2DHtQBwnAMNgGWtwAMNgBcEgPVWyMwA2HEtABznQANgWSvwQAPgBQFgvRUyMwB2XAsAxznQAFjWCjzQAHhBAFhvhcwMgB3XAsBxDvSFBbDPP/ANgJMRANZbITMDYMe1AHCcA31xARwGRoEHGgAvCADrrZCZAbDjWgA4zoEGwLJW4IEGwAsCwHorZGYA7LgWAI5zoAGwrBV4oAHwggCw3gqZGQA7rgWA4xxoACxrBR5oALwgAKy3Ys0MgIUtoUbnmBkAm1oA2G0tAOzMAsBuawFgmUZb9jnpzADY1ALAbmsBYGcWAHZbCwDLNBoAG1oA2HEtAJyMALDeijUzABa2hBoNgA0tAOy4FgBORgBYb8WaGQALW0KNBsCGFgB2XAsAJyMArLdizQyAhS2hRgNgQwsAO64FgJMRANZbsWa+qABOHUY5ZgbAphYAdlsLADuzALDbWgBYptE5ZgbAphYAdlsLADuzALDbWgBYptE5ZgbAphYAdlsLADuzALDbWgBYptE5ZgbAphYAdlsLADuzALDbWgBYptE5ZgbAphYAdlsLADuzALDbWgBYptE5ZgbAphYAdlsLADuzALDbWgBYptE5ZgbAphYAdlsLADuzALDbWgBYptE5ZgbAphYAdlsLADuzALDbWgBYptE5ZgbAphYAdlsLADuzALDbWgBYptE5ZgbAplaeAA66cacgAKy3Ys0MgIUtoUbnmBkAm1oA2G0tAOzMAsBuawFgmUbnmBkAm1oA2G0tAOzMAsBuawFgmUbnmBkAm1oA2G0tAOzMAsBuawFgmUbnmBkAm1oA2G0tAOzMAsBuawFgmUbnmBkAm1oA2G0tAOzMAsBuawFgmUbnmBkAm1oA2G0tAOzMAsBuawFgmUbnmBkAm1oA2G0tAOzMAsBuawFgmUbnmBkAG1peBxoAJyMArLdizQyAhS2hRueYGQAbWgDYcS0A7MoqngfATmsBYJlG55gZABtaANhxLQDsygLAjmsBYJlG55gZABtaANhxLQDsygLAjmsBYJlG55gZABtaANhxLQDsygLAjmsBYJlG55gZABtaANhxLQDsygLAjmsBYJlG55hZfKABsKwVcqAB8LISAbC2jxd0HwWAHdcCwGEHGgA7rAWA0xEA1lsBMwNgx7UAcNiBBsAOawHgdASA9VbAzADYcS0AHHagAbDDWgA4HQFgvRUwMwB2XAsAhx1oAOywFgBORwBYbwXMDIAd1wLAYQcaADusBYDTEQDWWwEzA2DHtQBw2IEGwA5rAeB0BID1VsDMfnfMAFik0TlmBsCGVo4ADr1xpyAArLcCZgbAjmsB4LADDYAd1gLA6QgA662AmQGw41oAONKBBsCyVs4DnYIAsN4KmBkAO64FgCMdaAAsa+U80CkIAOutgJkBsONaADjSgQbAslbOA52CALDeCpgZADuuBYAjHWgALGvlPNApCADrrYCZAbDjWgA40oEGwLJWzgOdggCw3gqYGQA7rgWAIx1oACxr5TzQKQgA662AmQGw41oAONKBBsCyVs4DnYIAsN4KmBkAO64FgCMdaAAsa+U80CkIAOutgJkBsONaADjSgQbAslbOA52CALDeCpgZADuuBYAjHWgALGvlPNApCADrrYCZAbDjWgA40oEGwLJWzgOdggCw3gqYGQA7rgWAIx1oACxr5TzQKQgA662AmQGw41oAONKBBsCyVs4DnYIAsN4KmBkAO64FgCMd6AsM4CCNznmgUxAA1lsBMwNgx7UAcKQDDYBlrZwHOgUBYL0VMDMAdlwLAEc60ABY1sp5oIc6v1k0unz25lv77/zpvvpnoJPSvHRLsajqzor72AgA662AmQGw41oAONKBBsCyVs4DPdUBo9UPY6aePHB3vz8tbuiXmpHJfVQCwHorYGYA7LgWAI50oAGwrJXzQE81B+DzmzV67zx4T7vUjACwvBUwMwB2XAsARzrQAFjWynmgp2owefbmD18piqvVL9V56erAd18B+Gp3t/bW5n43zto7d4tVtynvs46ljQCw3gqYGQA7rgWAIx1oACxr5TzQU3UAvtUeAZ/fvLzfn7THvKcdQ7tbz66UzskDd9s7N78WzW2q+9gIAOutgJkBsONaMQE4t40bADuuBYB1GgP4tDr6vX+9e9u3ugqr5Gp369mVG/07N7+2t6nuYyMArLcCZgbAjmsB4EgHGgDLWjkP9FRjAJ8010X3Th7fv/7gve7W+t49ALe/7vtL9u9jIwCstwJmBsCOawHgSAcaAMtaOQ/0VBMAK6+46m6dBbDiPjYCwHorYGYA7LgWAI50oAGwrJXzQE81OQXd+9hvi9DerXMAVt3HRgBYbwXMDIAd1wLAkQ40AJa1ch7oqQ4Art73rS/CKg9kO5beqf6tLq7qbu3g2t55AGDVfWwEgPVWwMwA2HEtABzpQANgWSvngZ7qAOD9neYLsaoPEx2Ogk+694PbWw/Ebe48ALDqPutY2ggA662AmQGw41oAONKBBsCyVs4DnYIAsN4KmBkAO64FgCMdaAAsa+U80CloFsDf+9Wn9vvXP3DtHV/qbvH0BA6UI4Bt91EA2MYSajQANrMAsONaADgdzQH429d+5qn9G5/44P6LP9vd5OkJHAgAu60FgIUaDYDNLADsuBYATkczAP7M2/+4PAJ+/Xeeao6Ea3l6AgcCwG5rAWChRgNgMwsAO64FgNPR4ino7/3al/av//Yny99+tJSntRqoeKHUyveqU1eOmevQOWbOLXSOmbPduHPLvFaLAP72OzoAV/L0CmYgjoDd1uIIWKjRHAGbWRwBO67FEXA6WnEEXMnTEzgQAHZbCwALNRoAm1kA2HEtAJyOFgHMe8Ceqg0EgB3XAsDpbdwpZwbAjmsZAPgv1FpJTGEtAviNT/w6V0H7qDYQAHZcCwCnt3GnnBkAO65lAOBCrXXAlBafA9ZbsWYGwMKWUKMBsJkFgB3XAsBq1v2/KsUM4Kk8PYEDAWC3tQCwUKMBsJkFgB3XAsBq1gFgAGxoAWDHtQBweht3ypkBsONaANiZBYDd1gLAQo0GwGYWAHZcCwCrWQeAAbChBYAd1wLA6W3cKWcGwI5rAWBnFgB2WwsACzUaAJtZANhxLQCsZh0ABsCGFgB2XAsAp7dxp5wZADuutRnAZ1duVP996K5y2fJ2nbVNAFhvxZoZAAtbQo0GwGYWAHZcCwCrWbcA4AfuzgJ4HSlNBYD1VqyZAbCwJdRoAGxmAWDHtQCwmnXzAH7on11uQHv/elGxuPzn+37hVgnmorhR3fTEQ088fG9//tit1pdRH8D3r1+6tXB3T0/gQADYbS0ALNRoAGxmAWDHtQCwmnULAL5750YN4DtX9ycli8t/Ti/duv/uW+3557OHPvVY+fPD91pfRsMj4DtF8eC9ubt7egIHAsBuawFgoUYDYDMLADuuBYDVrFsC8P1fvFf9t0Tu/ffcLf9XHe5WVvljw+CTEr1XW3+ZrUYan4IuD6+Lq/q7e3oCBwLAbmsBYKFGA2AzCwA7rgWA1axbAnBJ1wrAJQKLS7fOmvPN9VHpAy2Azx7+Qn0GuvJN6Gqg6XvA1eNrT3F7egIHAsBuawFgoUYDYDMLADuuBYDVrFsE8PljH37obnt02x4B379+43AK+m7pP3xP7ui3XqnR7ydFUZ3+1p2I9vQEDgSA3dYCwEKNBsBmFgB2XAsAq1m3CODmUujqzd8SgM17wNXNZ2++1X4M6aQ6Pdz6MhoA+PxmUVQfhtqf6g6BPT2BAwFgt7UAsFCjAbCZBYAd1wLAatYtA3h/8kB9FXR1hrn85wceu1Udkn7fe2+c33zgiQbF+86X0fAq6MWrqz09gQMBYLe1YgGw38wAOLmNO+XMANhxrc0AVsnZp397K9X7uTrdvZ85/N1HOK/sowQsACzSaABsZgFgx7UAsJp1qwBcnQ6WO9DVCgDrrVgzA2BhS6jRANjMAsCOawFgNetWHwF70LH8SdFp5kPGnp7AgQCw21oAWKjRANjMAsCOawFgNeviBvDhCHhOnp7AgQCw21oAWKjRANjMAsCOawFgNetiB7CBPD2BAwFgt7UAsFCjAbCZBYAd1wLAataptY6A0jqULw9/66/4KGa+hiPCeWUfJWABYJFGA2AzCwA7rgWAlfoLtVYzU1QcAeutWDMDYGFLqNEA2MwCwI5rAWA166I+AjaTpydwIADstlZUAE650QDYzALAjmsBYDXr/geVYgJwcxp67ts4PD2BAwFgt7UAsFCjAbCZBYAd1wLAatZFD+A7l6uv4pr7W4eensCBALDbWgBYqNFZAli7kQLggQCw21oXAcDlAfD5zct8Ecfhx0gzA2BhS6jROQK4AMBmFgB2W+uCAPj+9asA+PBjpJkBsLAl1GgAbLYUAHZcCwCrWRc7gM9vXj29dKs6Ea2VpydwIADsthYAFmo0ADZbCgA7rgWA1ayLHcD7syvFZf3fAq7k6QkcCAC7rQWAhRoNgM2WAsCOawFgNeuiB/CyPD2BAwFgt7UAsFCjAbDZUjkCONiH3AMOdFoALo8+i8PfP1r6O4Q9/+zKjZkFytvnHwsA661YMwNgYUuo0QDYbCkA7LbWwAo90OkAuM/JVQCurpmaAfDsA01OQfNVlL0fI80MgIUtoUYDYLOlALDbWgMr9EAnB+A7V/cn33+9eOCJH3vvA3ebr8U4f+xDRXH1tPx/daVydUt55zs39mcP36uW+2eXm6Xb79Ao//m+X7hVw7T+Wo0nHnqivN/5Y7eU37ExvAhr5vKrSLfdBPZR8W+7ABgAA2DpagMBYLe1dqpGWwH4/nv+7D3VaeP61HJF48s1GM+uXK7v0txS/nR6dV/+b9+x+GBV/5xeunX/3bfa889nD33qsVsVrFtfD2D+HOEuz3kFwADYFsCP6wkMgI8CwG5r7VSNXgfg+vTvg/f2J+WBbvvWbUXR+++5Wx69Vkew1a/tLaV5/xfv/cmtBsDlj9V/G6v8X33nmuUNgO+elOi92vozAD6/CYCznFcADIABsHS1gQCw21o7VaPXAbh7t/bszbcOAL5eX5fVB3BzS2meP/Z7v3ivXe7kagXg1mrON5dHwtWbue1B8MNfeKxbdAbAs1/BEem2m8A+Kv5tFwADYAAsXW0gAOy21k7VaDsA3/mlywcANwesfQA3t9TU/aWr3Y/nj334obut1R4BV6eTu1PQJaw//PC96dHvGMD8PeBdnvMKgAEwAJauNlCwjTv0QCcH4Ppotfv0UPV+7oP3egBub6nM6ki5W66+FLqx2veA23u0D1Sd1u58PYAN5OkJHChbAHsLDYABMACWrjYQAHZba6dq9DoANx8B+uWbN0pMfuHmA0881FzRfOlW/wi4vaU+7P0nh4PhffVHjFqr+ucHyjufFMX3vffGefNANaxbHwAzr3on9Lym3GgAbLYUAHZba2CFHuhkALxaZz+ut5Y+/dtbqcFvJbVvnPBVlN2PgTMDYGe1di4aDYDNlgLAbmsNrNADfWEBfDI9mq11flNxqZVew78H/OCfN3+RUCtPT+BAANhtLQAs1GgAbLYUAHZba2DlPNBj1skeActo8ucIb/DnCA8/Bs4MgJ3V2rloNAA2WwoAu601sHIe6DHrADAANrQAsNtaOxeNBsBmSwFgt7UGVs4DPWadWuuAKa1B+ZPqFPT961f1d/f0BA4EgN3WAsBCjQbAZksBYLe1BlbOAz3SX6i1BpfyGvL/tHpFMMNfAOyu2kAA2G2tnYtGA2CzpQCw21oDK+eBHrMu+iPgZXl6AgcCwG5rAWChRgNgs6UAsNtaAyvngR6z7j9UCQAvWQDYbS0ALNRoAGy2FAB2W2tg5TzQY9bFDuD6BHQx+wcZPD2BAwFgt7UAsFCjMwRwcRsAG1kA2G2tnarRY9bFDeDzm/XVz/ev80Uc3Y+BMwNgZ7V2LhoNgM2WAsBuaw2snAd6zLq4Adx9A9b5Ta6Cbn8MnBkAO6u1c9FoAGy2FAB2W2tg5TzQY9ZFDeDjHwOe+y5KT0/gQADYbS0ALNRoAGy2FAB2W2tg5TzQY9ZFDeDqKzga8UUc3Y+BMwNgZ7V2LhoNgM2WAsBuaw2snAd6zDoADIANLQDsttbORaMBsNlSANhtrYGV80CPWTcL4ObPEY7ffm3+nu+Kv260VgBYb4XODICd1dq5aDQANlsKALutNbByHugx6+YBXP/933dP/46RQ/ruAfCcFTozAHZWa+ei0QDYbCkA7LbWwMp5oMesWwZwdSXU/etFRcDTovrn7KE/K3994qEnHr63P3/sVusJqgfgw3dzAeD2x8CZAbCzWjsXjQbAZksBYLe1BlbOAz1m3TKAz958a3/n6v70wXv333N3f3L5cAr6U4/d2p89fK/0Tmb+Wq+F+CYsvRU6MwB2VmvnotEA2GwpAOy21sDKeaDHrDN4D7g8AC7Je//dt9qT0Yf3gE9K9F6tbqx8QQFgvRU6MwB2VmvnotEA2GwpAOy21sDKeaDHrFs+Am7/Pa+Od68Ul24dAXz28BfqM9BFdaugALDeCp0ZADurtXPRaABsthQAdltrYOU80GPWGQG4PQKufjx98N4BwOePffjhe8JHv/VKrbu7pydwIADsthYAFmo0ADZbCgC7rTWwch7oMeuMANy+B1z+bwDg/Un1EaXGW8fMeQFgvRU6MwB2VmvnotF5Avj2apQCYLe1BlbOAz1mnRmA2yud77RXQd89v/nAE6VXXZ9VebJnoAHwjBU6MwB2VmvnotEA2GwpAOy21sDKeaDHrJsFcCABYL0VOjMAdlZr56LRANhsKQDsttbAynmgx6wDwADY0ALAbmvtXDQaAJstBYDd1hpYOQ/0mHUAGAAbWgDYba2di0YDYLOlALDbWgMr54Eesw4A21hlGwGwy1oAWKjRANhsKQDsttbAynmgx6xTax0BpQWA9Va4zADYca2di0YDYLOlALDbWgMr54Ee6S/UWkdAaQFgvRUuMwB2XGvnotEA2GwpAOy21sDKeaDHrOMIGAAbWgDYba2di0YDYLOlALDbWgMr54Ees+5/VwkAL1gA2HEtACzUaABsthQAdltrYOU80GPWAWAAbGgBYLe1di4aDYDNlgLAbmsNrJwHesw6AAyADS0A7LbWzkWjM8wMgA0tAOy21k7V6DHrADAANrQAsNtaOxeNzjAzADa0ALDbWjtVo8esA8D2ANb1Mf59VALbLgAWaXSGmQGwoQWA3dbaqRo9Zh0ABsCGFgB2W2vnotEZZgbAhhYAdltrp2r0mHUXAMABVLxQK/4VlVRB5iyUeubi8ccfX732RdqZrZR6o20UW+Z5AJ9dqT4U3P6xwcPfJtSo5zfLXZ3eof07wksrtS6Dp1cwfXEE7LgWR8BCjc4wM0fAhhZHwG5r7VSNHrNuHsB9WK4BcPXj/XdP/0qwAX33AHjOCpcZADuutXPR6AwzA2BDCwC7rbVTNXrMOiMA37m6P/n+68UDT/zYex+4e7/84e7+/LEPlce4p/VxbnNLeec7N/ZnD99rlzu/eaN19uXd6jv8WfUYDz1R3uX8sVutB4BXWdnMKwAGwP4APP+xBgAsa+U80FYAvv+eP3tPffr4yo2GxpdLvF7en125XN+luaX86fTq/vRqt9zZm29VzumD9+6/5257h/p/n3rsVsXpZikAvM7KZl4BMAC2W/3bANjMAsBua+1UjV4H4Pq93Afv7U/KA932/dvqzHJJ1PIQtjqMrX5tbynN+794709uHZa7Ud3a3WHfew/4pETv1XYpALzOymZeATAABsDS1QYCwG5r7VSNXgfg7i3b6mi2A/D1+rqsPoCbW0rz/LHf+8V7veWqf6s7lUC+dOsI4LOHv/BYtxQAXmdlM68AGAADYOlqAwFgt7V2qkbbAfjOL10+ALg5au0DuLmlMk9+6Wp/ufYIuPrx9MF7BwCfP/bhh+9pjn7rlTLB7lGensC+ALDjWgBYqNH5ZQbAphYAdltrp2r0mHVGAK4PWbuPEDXv6/YA3N5SmdWR8r4P7top/zcAcH1Gu/UA8Dorm3kFwAAYAEtXGwgAu621UzV6HYDr93KLX755o2TlF24+8ET98aLr1ZnjPoCbW+rzzf/kcDBcq73S+U57FfTd8+Yxak43SwHgdVY28wqAATAAlq42EAB2W2unavQqAK/W2Y/bLjlYqXV39/QE9gWAHdcCwEKNzi8zADa1ALDbWjtVo8esEwXwieaQdqUAsN4KlxkAO661c9Ho/DIDYFMLALuttVM1esw62SNgGQFgvRUuMwB2XGvnotH5ZQbAphYAdltrp2r0mHUAGAAbWgDYba2di0bnlxkAm1oA2G2tnarRY9aptY6A0gLAeitcZgDsuNbORaPzywyATS0A7LbWTtXoFASA9Va4zADYca2di0bnl3kDgC1Cx5HZzgLAbmvtVI1OQQBYb4XLDIAd19q5aHR+mQGwqQWA3dbaqRqdggCw3gqXGQA7rrVz0ej8MgNgUwsAu621UzU6BQFgvRUuMwB2XGvnotH5ZQbAphYAdltrp2p0CgLAeitcZgDsuNbORaPzywyATS0A7LbWTtXoFASA9Va4zADYca2di0bnlxkAG1rWmQGwjWXHwiACwHorXGYA7LjWzkWj88sMgA0tAOy41k7V6BQEgPVWuMwA2HGtnYtG55cZABtaANhxrZ2q0SkIAOutcJkBsONaOxeNzi8zADa0ALDjWjtVo1MQANZb4TIDYMe1di4anV9mAGxoAWDHtXaqRqcgAKy3wmUGwI5r7Vw0Or/MANjQAsCOa+1UjU5BAFhvhcucI4DD7aMAsO1DAmBDCwA7rrVTNToFAWC9FS4zAHZba2QJNTr6PgPgOHdiAFjYsmNhEAFgvRUuMwB2W2tkCTU6+j4D4Dh3YgBY2LJjYRABYL0VLjMAdltrZAk1Ovo+A+A4d2IAWNiyY2EQAWC9FS4zAHZba2QJNTr6PgPgOHdiAFjYsmNhEAFgvRVrZgAsbAk1OsV91LaHBMCGFgB2XGunanQKAsB6K9bMAFjYEmp0ivuobQ8JgA0tAOy41k7V6BQEgPVWrJkBsLAl1OgU91HbHhIAG1oA2HGtnarRKQgA661YMwNgYUuo0Snuo7Y9JAA2tACw41o7VaNTEADWW7FmvtAATrjRKe6jtj0kADa0ALDjWjtVo1MQANZbsWYGwMKWUKNT3Edte0gAbGgBYMe1dqpGpyAArLdizQyAhS2hRqe4j9r2kADY0ALAjmvtVI1OQQBYb8WaGQALW0KNTnEfte0hAbChBYAd19qpGp2CALDeijUzABa2hBqd4j5q20MCYEMLADuutVM1OgUBYL0Va2YALGwJNTrFfdS2hwTAhhYAdlxrp2p0CgLAeivWzABY2BJqdIr7qG0PCYANrYwBHHCgUxAA1luxZgbAwpZQo7MDcMlfAGxkAWDHtXaqRqcgAKy3Ys0MgIUtoUYDYLOlALDTWkMr3EADYBMBYL0Va2YALGwJNRoAmy0FgJ3WGlrhBhoAmwgA661YMwNgYUuo0QDYbCkA7LTW0Ao30ADYRABYb8WaGQALW0KNBsBmSwFgp7WGVriBBsAmAsB6K9bMAFjYEmp0pgDWEhgAHwSAHdfaqRqdggCw3oo1MwAWtoQaDYDNlgLATmsNrXADDYBNBID1VqyZAbCwJdRoAGy2FAB2WmtohRtoAGwiAKy3Ys0MgIUtoUYDYLOlALDTWkMr3EADYBMBYL0Va2YALGwJNRoAmy0FgJ3WGlrhBhoAmwgA661YMwNgYUuo0QDYbCkA7LTW0Ao30ADYRABYb8WaGQALW0KNBsBmSwFgp7WGVriBBsAmAsB6K9bMAFjYEmo0ADZbCgA7rTW0wg00ADYRANZbsWYGwMKWUKNT3EdtekgAbGoBYMe1dqpGpyAArLdizQyAhS2hRqe4j9r0kADY1ALAjmvtVI1OQQBYb8WaGQALW0KNTnEftekhAbCpBYAd19qpGp2CALDeijUzABa2hBqd4j5q00MCYFMLADuutVM1OgUBYL0Va2YALGwJNTrFfdSmhwTAphYAdlxrp2p0CgLAeivWzABY2BJqdIr7qE0PCYBNLQDsuNZO1egUBID1VqyZAbCwJdToFPdRmx4SAJta4TbucAMdfuNOXyJ4RwAAIABJREFUQQBYb8WaGQALW0KNTnEftekhAbCpBYAd19qpGp2CALDeijUzABa2hBqd4j5q00MCYFMLADuutVM1OgUBYL0Va2YALGwJNTrFfdSmhwTAplaOAA4/0CkIAOutWDMDYGFLqNEA2GwpAOy01tDKeaBTEADWW7FmBsDCllCjAbDZUgDYaa2hlfNApyAArLdizQyAhS2hRgNgs6UAsNNaQyvngU5BAFhvxZoZAAtbQo0GwGZLAWCntYZWzgOdggCw3oo1MwAWtoQaDYDNlgLATmsNrZwHOgUBYL0Va2YALGwJNRoAmy0FgJ3WGlo5D3QKAsB6K9bMAFjYEmo0ADZbCgA7rTW0ch7oFASA9VasmQGwsCXUaABsthQAdlpraOU80CkIAOutWDMDYGFLqNEA2GwpAOy01tDKeaBTEADWW7FmBsDCllCjAbDZUgDYaa2hlfNApyAArLdizQyAhS2hRgNgs6UAsNNaQyvngU5BAFhvxZoZAAtbQo0GwGZLAWCntYZWzgOdgpYB/MVr1679zFPtL56ewL4AsNtaO+Wm665YvPO69SEBsNlSANhpraGV80CnoGUAf+aDvV88PYF9ZQxgX6EBsEijAbDZUgDYaa2hlfNAp6BFAL/xh5/s/ebpCewLALuttVNuuu6KRZIZAG/PDIBNLQDsttbI2gBE31oE8OsfuHbtWn0Q/KOl3K/QRMULtVa+WZ222sxZhc4xc+Ibd/F4rZVrn3ZmO+W4ceeYeb0Wn53v/cone0fBnl7B9MURsNtaO+VrR3fFIsnMEfD2zBwBm1ocAbutNbI2QtGnzF6eHN4H9vQE9gWA3dbaKTddd8UiyQyAt2cGwIZWFRkAO6w1sux56F0AWG8FzwyA/ayGUKOzywyADS0A7LjWyLLnoXctAvjb7/jS/o0/4mNIzqv1BYDd1hpZQo3OLjMANrQAsONaI2sjFH3K6HPAbz9cCO3pCewLALuttVNuuu6KRZIZAG/PDIANLQDsuNbI2oREv+KbsPRW8MwA2M9qCDU6u8wA2NACwI5rjSw7FgYRANZbwTMDYD+rIdTo7DIDYEMLADuuNbLsWBhEAFhvBc8MgP2shlCjs8sMgA0tAOy41siyY2EQAWC9FTwzAPazGkKNzi4zADa0ALDjWiPLjoVBBID1VvDMANjPagg1OrvMANjQAsCOa40sOxYGEQDWW8EzA2A/qyHU6OwyA2BDCwA7rjWy7FgYRABYbwXPDID9rIZQo3PLXPEXAJtYANhxrZFlx8IgAsB6K3hmAOxnNYQanVtmAGxqAWDHtUaWHQuDCADrreCZAbCf1RBqdG6ZOwDrCAyAOwFgx7VGlh0LgwgA663gmQGwn9UQanRumQGwqQWAHdcaWXYsDCIArLeCZwbAflZDqNG5ZQbAphYAdlxrZNmxMIiSAbCmj5HvoywtAOy21sgSanRumQGwqQWAHdcaWXYsDCIArLdizQyAhS2hRueWGQCbWgDYca2RZcfCIALAeivWzABY2BJqdEaZ6xUGwKYWAHZca2TZsTCIALDeCpbZ97wCYJFGZ5S5qNYYAJtaANhxrZFlx8IgAsB6K1hmAOy41sgSanQ+mYvbAHiNBYAd1xpZdiwMIgCst4JlBsCOa40soUbnkxkAr7MAsONaI8uOhUEEgPVWsMwA2HGtkSXU6HwyA+B1FgB2XGtk2bEwiACw3gqWGQA7rjWyhBqdT2YAvM4CwI5rjSw7FgYRANZbwTIDYMe1RpZQo/PJDIDXWQDYca2RZcfCIALAeitYZgDsuNbIEmp0PpkB8DoLADuuNbLsWBhEAFhvBcsMgB3XGllCjc4nMwBeZwFgx7VGlh0LgwgA661gmQGw41ojS6jR+WQGwOusrAEcbs+dggCw3gqWGQA7rjWyhBqdT2YAvM4CwI5rjSw7FgYRANZbwTIDYMe1RpZQo7PJXDTQBcCmFgB2XGtk2bEwiACw3gqWGQA7rjWyhBqdTWYAvNICwI5rjSw7FgYRANZbwTIDYMe1RpZQo7PJDIBXWgDYca2RZcfCIALAeitYZgDsuNbIEmp0NpkbANf8BcAmFgB2XGtk2bEwiACw3gqWGQA7rjWyhBqdTWYAvNICwI5rjSw7FgYRANZbwTIDYMe1RpZQo7PJDIBXWgDYca2RZcfCIALAeitYZgDsuNbIEmp0NpkB8EoLADuuNbLsWBhEAFhvBcsMgB3XGllCjc4mswiA14eOpc/xDzQATkYAWG8FywyAHdcaWUKNziZzjd4CABtbANhxrZFlx8IgAsB6K1hmAOy41sgSanQ2mQHwSusw0P73YuEHGgDPCQDrrWCZAbDjWiNLqNHZZAbAKy0A7LjWyLJjYRABYL0VLDMAdlxrZAk1OpvMAHilBYAd1xpZdiwMIgCst4JlBsCOa40soUZnkxkAr7QAsONaI8uOhUEEgPVWsMwA2HGtkSXU6GwyN+gFwMYWAHZca2TZsTCIALDeCpYZADuuNbKEGp1N5ga9twGwqQWAHdcaWXYsDCIArLeCZQbAjmuNLKFGZ5MZAK+0ALDjWiPLjoVBBID1VrDMANhxrZEl1OhsMgPglVaOAA6YGQALWgswinUftckCwI5rjSyhRmeTGQCvtACw21pjy46FQQSA9VasmQGwsCXU6GwyA+CVFgB2W2ts2bEwiACw3oo1MwAWtoQanU1mALzSAsBua40tOxYGEQDWW7FmBsDCllCjs8kMgFdaANhtrbFlx8IgAsB6K9bMFxLAAb+vHgCvfMh8AFwoV1L3lxS1DwiA3dYaW3YsDCIArLdizQyAhS2hRgNgoxVJHsDF43oCRwej8AMNgOcEgPVWrJkBsLAl1Gh7ACe2cWcD4EIZDQCbWADYSABYb8WaGQALW0KNBsBGK5IUgBXZitsA2MACwEYCwHor1swAWNgSanQuAO7zFwCbrAgAdltrbNmxMIgAsN6KNTMAFraEGg2AjVbkAgBYlzhCGIUfaAA8JwCst2LNDICFLaFGA2CjFUkLwNNwANjIAsBGAsB6K9bMAFjYEmo0ADZZEftGe8/c/N3jsQGAjSwAbCQArLdizQyAhS2hRgNgkxUBwKZLiVjhBxoAzwkA661YMwNgYUuo0QDYZEVSB3BRZ9YRODoYhR9oADwnAKy3wmf2FBoAizQaAJusCAA2XUrECj/QAHhOAFhvhc+cI4DTbTQANlmR1AA8TgeAzawIBjoFAWC9FT4zAPayGkKNBsAmKwKATZcSsXIe6BQEgPVW+MwA2MtqCDUaAJusSDoAbnMCYCsrgoFOQQBYb4XPDIC9rIZQowGwyYoAYNOlRKycBzoFAWC9FT4zAPayGkKNBsAmK5I4gIvbANjIimCgUxAA1lvhMwNgL6sh1GgAbLIiANh0KREr54FOQQBYb4XPDIC9rIZQo3PJDIAB8LIVwcadggCw3gqfGQB7WQ2hRstkLo5/BD7SzAAYAC9bEQx0CgLAeit8ZgDsZTWEGi2SuSgeORA40syZALiLqQSwZWYA7GU17FgYRABYb4XPDIC9rIZQo2UA/MgjjwDglY5TAA/jAWBDK4KBTkFOAVwUvfNpls8tAHZba+RMG31BM0cK4Iq/AHit4w/AxbbMANjLatixMIhcArhQ/DlNAGxgAWC3tcaWUKPFANwRONLMABgAL1sRDHQKcgpgxVsoANjAAsBua40toUYDYJMVAcCmS4lYOQ90CnIP4OGmCoANLADsttbYEmo0ADZZkQwBXEcGwO5qjS07FgaRQwArN2AAbGABYLe1xpZQowUyN/xNDcAaGgHgbiEA7LbW2LJjYRABYL1lkVnGAsBua40toUbLAbglcJyZB/zNFsBrMgNgx7XGlh0Lg8gdgHtzWoysNc8tAHZba+RMG31BMwNg28zZAbgfDwCbWhEMdAoCwHprfWYhCwC7rTW2hBoNgE1WBAAbLiVjpTfQRQGAtTJ/KgZjWpguNVXSAG4+Bx09jADw1kbbLTTJ3PEXAK9zALDWSm6gp98dsX417FgYRCsBvOKBH+9pQ5XihVbO1tSZisIy+yFzgqFtRebqhnd2ivhJGEz2+vkeD3S5v3WymptVqOIpb1x8pBfYuM2Xi3rjF5efI+Djy0WBI+DBS6Q4DxIadZ+Djv5oML8j4GJwnmtro20X0h8BN4fAcW7cskfA/e++XlgNv5nVb6FxBGxqWR8BP/LIO/WHwLkfAZs/FcMxPWyu2wFcTuwj0f/BmEpF9znoyGGUIYCL4un+Xn9jo60XAsC7wXdfL6xGBAAurDIDYPMHrLYHAKyV8VMx4u9hexUAcP/bciPdR1UqlB9jMFoRADy0qlMesgB++umnOQK2zCwP4AGBAbCotXmgC78XsgDgWRk/FVMAW15XMgZwMfiuoEj3UZWU13CYrQgAHjj1QZJoracBsH1mUQAPp3l+NS4CgNUTHTGAizarJwDX28M7H9HuMgGw4VMxAfBtKQC3O6i4vyxI9xaS2Yr4fj80agAX0330xlo1fwGwbeb8AHzM1wOwOvRFA3Dh+UIWewCr9mIJyBGAp/xtN9itAB59UCPSfdRuML+Prz2j4v390N6dJqEDA/jwyditp6V6DxkrgI/8bbbvODduSQAPP/e8sBoA2MLaNtDHt9EiB/Dww0t2LAwijwC+bbVP0QE46o9K9t8BjhzA6rdDowFw0TV88/tCx4d8GgAD4MXlAPBgL+bnNF6zPawHsGYvloAAsN5amXmg/hMQM4CL2AHctXvz+0LHhwTAu0gAPJ7m+dUAwBbWpoH2/j6aJYB1e7EE5AbASv5ufC+/95ZR75xknPuo8R+MWbs9eQSwmkWxAPjYbwC8rdbYss+cMYCLXuYMAFwkA2DNXiwBeQXwpvfyxwCO+TqVbQD2+amFuAFcOABwy9/YAfyIzavVFZZ95jwAXDwOgLecxrPbiXUA1g67ficGgHuWFwBHfJCQDIC1m66LYrOWGsDHZq8dSq2VMYBlvnzECYBNPtkPgC2sDQM93IkBYCfyC+AtF9NtAfD4ElrvBwnrtif9tmv5oXitFTeA+92WAnDH3wgBPNi4HQBY6Os3AbA3AAt8Ac2GgfZ/FFFYzbr2PaUUlBaAJ7sos61p9M2DqQK4aL6SQvBbofSbru0jWluJArjoff7BG4AtN4FCJrMcgCdvKM2vRnYArr4nOxyAx30GwC6UMoBNDxLqBg0I7BjAo/giAC6Kwxuict8KlRaAdVO5ptaBvyIwKurLVIrN3/K2DsCF3SZQCL3oAMCeAFxMvifbZKmRZT/Q/gFcHGd9xQ5T/55SCnICYC1/t1xMZw3gtkFJA7golDsrwwfUWTObruUjWluqeR10O0IA9z8laXU9wiyAH9Ed5k6+Pdmoltz3X2cI4C6gZwBLzLr1QE92Yl4BvGLWAfD0KfEEYO0+qv94RdegYmItrMWqzD1rHH87gIvpufc1D6izHAC4OyObAYD7H9LY+Bn3PAGs3qgB8GGxuAAsdiGLdikrAM+8p5SCkgLwmL+PFAan4g4NWv1XhFdlngewLrfZtjvOLfWtUOIAPp6RFQDwMPU7dXujYuZLKie1jvzdDKPp39v0A+DCbhOQ+wMUAFgKwMXsmxeWjR5ZtgMtfxSxuFTvS3cAsEZLT3vzlDx+Wyv7b4VSAdjkvbDjPhcAjwsJA/jwF5DXXyRkDeBi1UGCHIAVf29zI4ANT+8AYGvLfiemArAy9RoAN0e4rRRLxQbgbTux5aUA8LKWnvbmKYkJwL1d7pHATgE82TVv3XYnsYW+lGJu07V5xN5fQF59kdAWAK/YR4kBWPHXvrZ+X70ZgLsLRS8cgJf/vIpPABe3FQAu+pk3A3j0Iffxo9k2ejf8wwS2A50KgOfeU0pBsQP42MdCwV+Do59IALzh73dPY8cJ4MFbotsBXIwzK9u97u939zcGaQBv/oMx2QFYPcpRArhJKArg8SX+YwRbA7gYXO5uOdCSRxGG73sXAHhZS09785xEBOD+LtcPgKe7ZgcAlvhM7Oymu/4Rh7nXvtefGIC1f2zEbD261VkPYNs/DiX4JxgTAbDiL4avyOwcwJMrDMcb9+EzsWtfbA+vtrMcaMmjiNGHKXVLFcOnw6zW7CmtFJQ6gJd2RAMAP61tvnIt1mR2B2BF6hgBXIwAbN3nFACsvspQGMDK91eOF4qu2y/nAuDioOqqy9HlgCsyhwDwoKXqRg/eLzY61WE30KI7sd5Rf/tNQqqlitHTAYBVWnramydlDsDWHyezAvCQvz4ArNg3OwHwmtNBaksYwKPMbgA8HsvCYBvo3bu/LWxotOYq/41/dtIlgCX/AlTEAC6K8cAXlgOtAnAxyOwAwP2eKhtdDL5TKDkAtyeZBQE8/4o6BTkA8HjbdQvg+R3RaB6fXhxyZwC2+9SCFsACn4kVBfD0mg3bPuuu/J4BsCmM0gdw722yCwfgxb/wvbiCY/zWEx8ngBVXGD4yeFmtAnCXb/bDS6NGWw207FHE5EWH6mtrCgBsoqWnvekeAJYDsDq06QY6Y82fvFn5iIq3jOID8HBjsG90oQOw/d99Vn/KfQ2A589MxgPg3kBLA1jF38FX0G7YifkB8LGp/QuSjgeQw1CpAfiYefpNAYNL4o33bwuvqFOQfwDbfp57/KkFzY5o+HiTkVwa8q0AVu2bPQF45RdgpAngYezCZBs43lsKwNptewuATT5jN7hOZfTeYP2ep6aW6J9gVADYZuMu/s1J3oXVWASwgr/DL8Cz34ltAXATeQAj9fsrx827UAJ4FMrolZbVQMseRShedIy/KcDwS3cA8NLT3nTPK4DnrkeajmRqANaFnm6h1Z9OWfFlEAsnb9Zk1rxlZNlnzfnY7QAebQzWjdZ+z9vazEsAVl9yptruD9+2qji31/clADz9ikK7jXsK4EdmjusMXlyq+WuZebITK3rBHz/cZpR5DYAfGfvHRk8+0JEwgAffYViM93KmAF56RZ2C5AFc3PYNYP3bod4BrNw5uwLw8BCouS0IgDXzuuZt6m0ANrooXAjAuhPQAQE8PDS6eAAu6heXC9u2hr9RAlh3eqeb6kLR6OEJds0LkmmjbQZa+ChC/aKjvpy7uapbOesAWKWlp30XAMAz1yNdaAD3CHzYiI2/F3np5M2KzH4BrLhS1DOA57btVZmlADw6NLpoAO427vltW8dfKQDfLvwA+JERko4AnuzIAgB4y/veisNc9e7NFMCLA52CAgDYcsesGNilXikvyphb96FlnvlgzQDYatud2UAPwzqY1xAA1s7rhms25AE83hgSBLBqvzzdM09rzXzlmVlmBwAufloxz6oTq8etOyyApwPtBsBTq1lkvB8zfKVlMdDSO7HF0+6KzLp29wcaACsVBYCL+ozVhQfwVBcfwP1Tr8N91HwtIQDPfMhdHMDjDzgbAfhpxTQkDGDDF5da/l4AANfBFZeTGr3SshhoNwBemXkRwJNr3gHwoXu+AdyenTp+C079hSuaV8W6yxe6R5i0cTnzwVIfHV1wAOvn1R7Ayq/fnEQ8Anj5Y9GTbSEyABt8y8zokxqqa3OUABb8G8g7zwAefjpFv3Hr+WuXefkoQpPaCMAzry6V270SwIanOtYP9OxOzDSzBwAvNzoFXQwAP6J6M79YDeDh15gnCWDDb4VavHxBJLMjAB8O/XrW0jY13RTkj4zsv5PCCsDtqclJss9OzlwnC+Dhs3J8OsZ/wa/47EUH8MJXjLSFFKFFB9o8s3MAmwx0CrogAFZa+s8FavaHhbKNy5k7S/sFDbbbrjrzdgAvv3tinHl2Xq0vmpwD8COZAnjy5YXK9wZLAI+PgWMEcPHTRgAebQLtm4lNoP41iEkBeHbjVllqAJud6pAdaHsAr33RMQ9g1XeuAOBd176oAay5frBrKgAehV7K7ALAmq/f7DS6qMMAwIqBld8xr83sDMCjXXM6AH5kOJuTy3aKYZ7i8HsYACtiOwKw9lzeoI4q9OqBTgHAyu88A8C7rn2xAPi3lBOpBfDWfZT+G5Jst10LACu+orAY/1kYg8sXTDMvvOiwvGZDHsA+dswhAKwINgbw7FeeGWTehQLw9KTl+CVH93ePLjiAH1ECZ/JegwyAxY8ibAGsnOn9KOj8XiwBhQCw1XuDyveM5q9H+tgqAG//ulwhAPfmdTOAD5M7+NSCIIAXMrsBcIOeFQA2e8G8tI5LG7c8gJV/oG6QWQ3gAYFTAnD/jyCrdtmF5ugHAO88Adgws0MAq58MANw+74NmafoYFsDq7yqIEcCazMYAHmyqvbfMDDZdocx2ANZ+//WhtYNL7i4EgJebOX061KcmP9ts44flNmYeW8EBrBrpiw5gZbLPas90bADw0k7MEsDrM2sArMMvAG6f90GzNH2MEcACXxYktO32Abw6tOqvl3Wxj2+ZLW+6hpnnvpZRE1kCwGVzR9YsgJUza9HohY1704uOpWauBfDhSrW0AHz8MlXlLlvzbmhSAF46vaOwtKE1ZzouLIAnf/B5ttEp6OICuPgfP6Yl8LSUwHcVLMLIM4DH2+pnj2+ZLW+6UpldAXhizWxTpm8ZLa1jAAAr/j5dP/PM0eABwBszTywRAJdb9gKANZjS7ICFAWzyPprNQFsCWHMxyxDAmkavHOhlAE9D+wPwysvdU1AQAFt9bBAAG267bZXJrkq/7VoDeP5rGTWd9g1g47eMltbREMB2meebuR7ATw8+srN54x49CVsHegbA3ear7nOeAFbvyD47+GvHMgBe3okFBHDZfAC88LSPmqXpY3QALi4cgBVf0LBm0zXKrP/DQNvOWIkC2PyajcV1XNi4XQJY+TUGswB+urlSbWPmqeUYwN3Xi2j6rGlmQgBev3EXmh1ZfbWd8q2G6ABscdp9MtLrL3dPQVkC2Mm39RnAyGzbPcyrdi9l8t3tys+Hmm+6Rpn1kaMB8JprNpb6Mu6mLrM/AGv3y81WPnm/ISoA664wrP9Kna7P+rOxYn3epQTgw2ehda+0Vg10zABuEgLghad9YR/lD8DFx0oAaw+BTS7gTxvAa3ZSlgCe+VrkbfO6PrMOwKuu2VjqyziZNrPNiw5dMM0ZWRMAC2SeWuPNXB7Ajyj+Quxh29ZMdEIAXr9xzwL4aeXrbVsAm+zEJqk9APjwUhIAz29qS/so2wtV1rNoFsCjT9BJXChqcjToB8C6z2pcbAArCTzD39WNLibJtJnlAaz8FKX+rUGpzApLBMDF35kD8EyfcwRwoduPdW/2K66svBAAPp7+OeYDwPOb2tI+KhYAm3yCLmEAr/yspB2Ajf5iW0AAV/slwR2zUwAv/K1N9SUs+QFYdywYCsArB9oNgOdDrxhow52YZwAPX10A4PlNbWkf5Q3A5VZrDGCRj0rKbbvdvOpP0y0BeO2VolYALlwBeP13jh6ntf8nKWW/orCYJtNmlgWw9hpSAOwqsyiA23nOGcA2F3U8Uh9JjA/uAfDs054QgHXfVwGAR6G1ADbcR62eV2sAK07FhQGw7IsO5Vuii28NSmRWWWoArxzoDQD2ktklgFWp5zbuKrM6dSgAj1MvAlj5qsMEwGs+ygGAdw4A3IeRDYD1L5g11+87+Dvt/gG89ijBBsDG+yhvAFa97hDbMReqZNrMXo76kwRwew2WHYAL7UQnA2D19wlFAmDDnZgvAG8e6BQkCuDlt8l8AbjaaucBrP6qoIgAXPPX6iro1afpLABcmAN45byu/85Rg8/EGoWeWcdCnWxTnwUAbL9fDgrg4qcBsGmjG/6mAeCif15xy1F/k1x1IAGAZze1xX2UJYBXHwwaAFh9/f78vBbjzy8dk19YAHd/zXC4jmbfeDY/r9PM9gAu1KkTAbBNZi2NLiyA9ceCwpnNN+61ANZ8mjIOAJvuxMaxjwB+/vjFbZtOu9fBlWd4APDspra4j1r7ZQUuAay8fn9+Xh/XfY+18ba7DKNuXm0BbHGhyiyA26tsBgwuDD/vPT+v09DWAFZPq9SOefCNXwBYFdofgD1kBsBWA10FLXo/bwSwMjUAnumjwXUq3gEs+4L5cc2u5uIDuELwcRWN3+ufm1dFaGsYuT0dW2iTbejz5swA2FXmFad3DF5pbQJw0ezFlKmFAWx8VaUXAGs2bwA800dnAJ65ZkPdxrp7jgCsWnXzbdc5gLUXim4F8OEouFjT55l5VYS2O0hwDKPRN15HAuCN1+aEBHDZ4UwBrLuUxSuAFe8odandAHj9hWf6txsA8MymlgmAFeu+edudRLYFcGFzoYohgGsEFz0euQDw+n2UWxgV47844QDANn90Q0+jiwrgzSwCwLXq03ibjiLUA93uqwehbQGs3boB8MymturIaM23uG0BsOh+WQPgFVcEGwO4ybwewDavOowBPBdszhqEFgdwIQ/g47d5rAi95UUHAF4MnSOAi4+5AbCCwGt2YsqBBsA2EgTwuiMjlwBu2ucMwJN1B8ALlmMAyzfa8BsJtvR5G4ALXzAaWZMnxhuAt7NI6s9OXgQATwi85mMNzgHcbd3T1ABYv6k5A/DcNRtBADxa+VXbrm7HfHhnZhOAC6vz7s4BPEg9CyPt5XYOz9LNNHpVaDMAH78BJlMAVy3OE8DrN253AN60E1MOtA7A1ld+A+Cp5jY11wA2b6N7AA/WfvuLx2q3XH1lam87nsk8M6+FVWgArGv0qtBGR/3HS2C2ANjf6djx6mtCmwC42G0AcPGxKAG84qpKi41bILR+oIcfLFyT+bZqoLsDh0Fouyu/AbBWM5ua0XcVeAFw2z+HAL4tD+A6aLHbCGC70EkD2MmRkUMAd20enpm0BfDWt8kW+jJdfU1oAwDXrzwkAOw6sysA6y+rNACwbei5gZ58sFAAwM8PzuNt++gVAJ5oZlNbCeAVf8krQgD3137ltqvcMXcvH4vjJ5+bzJbzGhuA+6mjO0jwCeBmgz7i1/LPTiYJ4Gr7fv7iA3j8MR97AB911yPlAAAUDUlEQVS/zcANgA8rv/aD/bcVA60D8Pr3vQGwXv3tSvEegqZZSssXgN3sl4/p1267cwAu91DdAfA2AK8L7QPAxSTzuM2bDxLiArD6qL9t75G/VgAuvMFobG0HcN3i1QCWYJFh5nUDPQFw/9OwXe5YAXx79Mn+1QCul9/3UwoA+GMAWKvedvV4oXgTYUUfjQF8gJFhG7t3ENzul+1fPGqvX+jpwgH4tiMAO9oxOwZwXwDYJPSgzxv3ywuZtwF4cClSl7ub6XUbd//DlNahFwZ6+Fm7tQAu6qSyAC7kGp2CNgB4+Db+agAb/2GCOAHcrf76F4/OAFzYhvYB4GPsGQCv3kfFDGDVafcpfze+750OgAc9XgtgERb5BHDv7dXnhxu3KnY4AJtu2+pX1CoAP9+7lHTje0qK0AB40MfJidg1fXQE4MMldK73y/U1JdYvHvuZp7tlGwAP5jUTABc+Gm0a2hLAQa7NCQbgJu2FBfDxvaTJLX/nQgK45O1+N9iwi96vL+i/0M/kFTUAHms36mMxOg5c00fDj9AdrtmIDcC3rb6W8fZ0x6zYK+cF4PE+yu7zZtEBWHHaXR7AbmE0scIAeNTnmAA8/jjtYYJHH/deD2CZ0C4Hur2iUBLAoxcdAHik3aSPw3fxV/XR7Ar+eAFsu+0uA/iY2QuMvAD4EHvc56KwBXDhbMfsCMAK/m593zthAJu/8T3u87b98kLmLQAuXjjOcNH/XP/xYw3WALYL7W6gu09sFPvhhr0FwMUYwOPQAHjcR9U35oYE8PFD3LHslxd3zJkAuIs9vjan9+7RWgDH1ejFo/5CBMBFjABe/usqh8v7Iwfw2os6dAB+fvC5/vUAnmzcsQH4drc5F6MNu5hcVWn/ogMAD7VT9VE7lAt9NAJwMT+v4zYe+RvNfnkJwGr+rgXweF5TAXB/dlcCuEgOwAr+br441unR4MSyBvDgAHglgIVY5AbAg68EeP6FYW+L4xnolQAeX0oaI4APlB1t0dYAnpzSAsAj7ST7uAjg7gD4ogH4dtF9jFoMwNN5XRHaKYAfffTRYcPVF8f291E+MnsB8Oi0e/oA1v9xqCmAlV9HYQNgBYs27ZfnM0sC+PC5/t5FHRcIwP2/uKAG8Morv6evtMapAbBYH8v98nBo253UaGjXAbjH32j2y/3M3aZbRusArL4E68IA+NFHP/7xQ+zDi47d6E9PDPdRtm/2y8FICsCDo341fze+1RAtgIvihemnYbsdcrwAXv+xhjkAH0G8EsCFVGjxgT7qUS2ALT96pcoMgAfaifWx2i9PAVy+qBpewL90zYYRgMPul/swOqCoeaGoBnA/s+m8bnrV4RTAHz8C+Hb3xTlFl7+wB3ARM4CPjR5s2wIA9no6dmKtAfDzQgBW9XnTfnk28xYAF1MY9UZ6zUArN+7oAPzxQgng4xe9FasALN7oFBQUwNOvZWz/JkErgzNW71S3MKb98sHqsagGUCEGYNWVZytCOwRwlblP4LrP3fdtFiP+rslcKDNLHRltBHD/qH+3a78dWHMCeuv73i5Px04scwDXMGo/IlGM+bsGwGoWRQTg2/0jBjWA+6e0VLHNBtoqtPRA92QA4O0vOgDwQDupPtY75kcHbxPtFQcJ6wA84G80++XOevTRA4sefbQ9BNxr+bsdRjEAuOHvEcC3u1dW6p2UeeZC+WZ/JAB+tJe5ifuCJrTEtTkf+y1XMJpaegDfHn0z7QHA9etoewBrXmiNOi2W2eaD/f1P/MoAWBc6KgBXW3mhBLDVxu2g0SkoLIBHX8s45e8qABeRA7hh0aPNj+23uCn4uxrAm2HkHMAdjR6tXnkY7KMWMxea9xpiAnCXWb9fXg9gv0eDE2vK3x6A+9+AXLSh29cd3T8dgtYAWN3n0cuOUAB+tFZxfFmpbPTwlNYygHUDbQMj4YHuqd7K5zbuVe976zN/zLrRKSgQgLsjo+5k8645T6fecufeG3ynuoWO9lFbMvdYVL92LKYfoFNl3gIj09CuAPxol7kFcDOyM9cCm2YudO81BG30EMAtgR/9eKF/a3DtxbF+jwan1gyAHy26b3/SwujIX/Pz7rpte8t+eSbzyq+2a7fv5tXF8zoAj15RLwJYv3HHBOBjdomNW7sT29LoFLQM4Nc/cO0dX+p+2bqPmhwZ9d4OVLyVsDyvxzaO8OtkHyUBo+olcwciFX/XAlh/2G8MIzcAfvTI34bA3ciqrvteA+D5V1rhGj1837vfaqFrczyfjp1aCwCuP4BybO/4IzlH/poCeOaF1jC1UOb+NwoZX+DQEViVuZ/bEMDFbOjVMBIc6KG68Iod93GkjTPP7LkHI50fgN/4xAf3X/zZ7ret+6gxgPu748kL5vEZq5l9VDHeKU/3URIvmO0z92HUi76ceQuMTEO7APCjo8TH3//pxyfnOsan3WfnddLqWBo92bZ7nVYd9hdCp9237KP0MNpNLQV/e6GbCwt7QcdfSrEWwOOhHgO4l1om8+Ab/ZZPaZnsxKZHEarYxgO9/lWH2ECPfn901ca9MNBLmX9rXeYLBeDXf+ep/fd+9an2t637qPGpyX7/xvM6PWOlaWOhwq9iH2XZRonMKv5ON11l5pltV5HbascsD+Axfvv6p03y3jdQTvdRuszKVsfS6Ml+uZd5+gZLUax5a3AJRgKZFwE8/sbZUejJbviFaVhzACs6PQHwsdUimYf5JHZig9zLAFZt3YpXHV2rQwK4n366cReTjXtb5o+ty3yhAPy9X/vS/vXf/mT504+W6i95QTX7bF1Q5Zg5y9BkziPzXOjQq+ZMc42OVotr/e13dACutOYFsxfLZalYM7t8EveT0HGsYgqNji/YjJXgxp1j5s1WzgOdglYcAVcK/9x6LBVrZgAsbAk1Or5gM1aCG3eOmQGwjbURij5l/x5wHE87+ygBCwCLNDq+YDNWght3jpkBsI21EYo+ZXAV9K+rr4KO42lnHyVgAWCRRscXbMZKcOPOMTMAtrG2MdGr7D8HHMfTzj5KwALAIo2OL9iMleDGnWNmAGxjbUKiX9l/E1YcTzv7KAELAIs0Or5gM1aCG3eOmQGwjWXHwiACwHor1swAWNgSanR8wWasBDfuHDMDYBvLjoVBBID1VqyZAbCwJdTo+ILNWAlu3DlmBsA2lh0LgwgA661YMwNgYUuo0fEFm7ES3LhzzAyAbSw7FgYRANZbsWYGwMKWUKPjCzZjJbhx55gZANtYdiwMIgCst2LNDICFLaFGxxdsxkpw484xMwC2sexYGEQAWG/FmhkAC1tCjY4v2IyV4MadY2YAbGPZsTCIALDeijUzABa2hBodX7AZK8GNO8fMANjGsmNhEAFgvRVrZgAsbAk1Or5gM1aCG3eOmQGwjWXHwiACwHor1swAWNgSanR8wWasBDfuHDMDYBvLjoVBBID1VqyZAbCwJdTo+ILNWAlu3DlmBsA2lh0LgwgA661YMwNgYUuo0fEFm7ES3LhzzAyAbSw7FgYRANZbsWYGwMKWUKPjCzZjJbhx55gZANtYdiwMIgCst2LNDICFLaFGxxdsxkpw484xMwC2sexYGEQAWG/FmhkAC1tCjY4v2IyV4MadY2YAbGPZsTCIALDeijUzABa2hBodX7AZK8GNO8fMANjGsmNhEAFgvRVrZgAsbAk1Or5gM1aCG3eOmQGwjWXHwiACwHor1swAWNgSanR8wWasBDfuHDMDYBvLjoVBBID1VqyZAbCwJdTo+ILNWAlu3DlmBsA2lh0LgwgA661YMwNgYUuo0fEFm7ES3LhzzAyAbSw7FgYRANZbsWYGwMKWUKPjCzZjJbhx55gZANtYdiwMIgCst2LNDICFLaFGxxdsxkpw484xMwC2sexYGEQAWG/FmhkAC1tCjY4v2IyV4MadY2YAbGPZsTCIVgK4px+NfSkHpaLP7OCZin7to2l0NGtvt1Q0K+KxVPSZHSwVy3rEsVRoAeA1S0WfGQDLLBXLBudzqWhWxGOp6DMDYMdLhRYAXrNU9JkBsMxSsWxwPpeKZkU8loo+MwB2vFRo2QMYIYQQQtYCwAghhFAAAWCEEEIogAAwQgghFEAAGCGEEAogOwB/71efqv99/QPX3vElw2WO9/3itWvXfuapdcusqGRTqNJCqKgz24bOMbOD0DlmZqATbHSOmeOWFYC/3T45b3zig/sv/qzZMr37fuaDhnWOy6yoZFOo0kKoqDPbhs4xs4PQOWZmoA1XI6ZG55g5ctkA+DNv/+PmJcfrv/PU4dXHko73feMPP2lY6LjMiko2hfaLoeLObBk6x8wuQueYmYE2XI+IGp1j5ti16RT0937tS/vXf9vsuTre9/UPXLt2zegVznGZFZVsCjULzoeKObN16Bwzy4fOMTMDnWKjc8wctzYB+NvvME98vO/3fuWThi9xjsusqGRTqNZCqJgzW4fOMbN86BwzM9ApNjrHzHFrJYA/c+1adZJ95UuOaqnRfY1O8m98wWxeqFlQEyqBzNahc8wsGzrHzAz0ilWJo9E5Zk5Cm46A7U7w1zJ6dje+ZWReqNZCqJgzW4fOMbN86BwzM9ApNjrHzHFrE4Df+MSvr7jErbtvdabgjT8yeZ6Oy6yoZFOo1kKomDNbh84xs3zoHDMz0Ck2OsfMccsewNX/13/Iq1rqi9euvd3sRMFxmdUfG1xXqNJCqKgz24bOMbOD0DlmZqATbHSOmeMW34SFEEIIBRAARgghhAIIACOEEEIBBIARQgihAALACCGEUAABYIQQQiiAADBCCCEUQAAYobU6v1k0unz25lv77/zpvvpnoJPSvHRLsajqzor79Kr0Hma8ZFsdIZSmADBCNjrAsPphTMaTB+7u96fFDf1SBo98fvPq4bG0S5s8IEIoTgFghGw0B+DzmzV67zx4T7uUwSO3AL5//cbYWfmACKE4BYARslFDvrM3f/hKUVytfqnOGLcHqy06mx/rW5v73Thr79wtVt2mvE/vUSoAV/e43LK+tEv/7KHfLR54onmYO6W1P7kc4ElACG0RAEbIRh2Ab7VHwOc3SwKetMe8py1D992tZ1dK5+SBu+2dm1+L5jbVfZpl68e409yj+n/p1MfD1Z2uXD5UPy3p3R50I4QSEgBGyEZjAFcU7J0urq7CKhHZ3Xp25Ub/zs2v7W2q+1RqL8Iq3foepzWa/+ZeW7V356rq2UN3dWuKEIpUABghG40BfNJcF331eI/71x+8191a37sH4PbXfX/J/n0qHU9kn1YH1p1zWl8ZPbjzyWXOQCOUoAAwQjaaAFh5xVV36yyAFfeppATw/euXBo/Q/PvQpzgDjVB6AsAI2WhyCnr6ed3erXMAVt2nUg/A1T2aU9A1i09HR8DnN/8RZ6ARSk8AGCEbHQBcvwNbXYRVorFj6Z1Lt5oLsLpbO162dx4AWHWfSkcA9y7CqiqcXRnf+aTgDDRC6QkAI2SjA4D3d5ovxKqumTocBZ907we3tx6I29x5AGDVffb7yYeZLndmcen3rt8Y3rm+JAshlJgAMELJi2ugEUpRABih5HVydfk+CKHYBIARSlz1N3gghJITAEYIIYQCCAAjhBBCAQSAEUIIoQACwAghhFAAAWCEEEIogAAwQgghFEAAGCGEEAogAIwQQggFEABGCCGk0Xe++uKLX/+u+f1ffqn67yv6JV5+sdRfqb3zr313+Nt5/46vlgt++bWjrX4Qzc1xCgAjhBBS6/yr39yfv/qS+f2/VjH0/ldm7vDd6lG/pTTPxoVO+ze8XC70nRe/pfQ0i8QuAIwQQkitGqX3y0Pgv64PW6tfy/+f/tUrL52/Uh+Olrd/o77naf3P2UuvfqMBaW2cfWV/v0Tmq6/d/+qLX/5Wc4fqvyVLmwc8/auvvvjS8XHLZV9pb3/lpbOXzsqfK1a/8q1uVY53Oasev7lz++BNxW59khAARgghpNHLX/9m9c+rL333/OXXanyW/3/1y9/dv1zjtbq9fzh7+o3yxv3pa61RQfVr3yqPest7/+sDQPenX+ke8OWvDB63XO6v9tUNVYXyUUpQl/9roH34b3uX0uh+qh+8XZWX1QfXcQoAI4QQ0un0q1/75v5+ycPq5G5JyJqLr1XwLdXc3jvkfPW1869WbGyNEsB/efra2Tf2p1/+V+0dqreAv/7d9gHrE9Ll8t3jVvD8m795ua5Q/lbZpVUfANf3ac8wV3dp3i+u71w/eFtx+DZy7ALACCGE9PrXL36rxl75n4qQDRebt1pPK5z2z/m+8t0Gq61x/vX73zh97dVyqb95pQLk4TKr9gHv1/98o/e4r7z4tb98sf6p/H911rk8pm7e1W0ObV/9RnuXymt+ah68rTjz9nOEAsAIIYSUao5zX/1GzcuXX6vfqv3ydysiNoe94yuemjv8fy91xvnX/vpbp//ypQqbzRFsx8f2Ac/Gj1vd3lYob2zOTDcHwA26S+94l/an5sHbipPruKIWAEYIIaTU+Vf/VX3l8Vn1lmwNxPNXXqrhe/aV755/9bXqvO/p14/3r/H36te+se+MV76+P/3aa+Wy9Vu9Rz62D1jevn+1/7jlMucvN1djnbWFXuyR9Ttffa13l+6n+sHbiqcJXYIFgBFCCOn0na+9+OKXv1mfa/76d0sev/j1v27esd2/Wl8Efdp9Srg9Iq7+e/bi0Xj5GxVn6wuXj3eof6j9l//lV0eP+8qLX/7Lr3TvCZ++2KC8XaBc5Jv77i6n9UXQ1U/tgzePeJrSRdAAGCGEUBDpPg/cV1qHtCsFgBFCCIXQ8hVT91/8+tJdUhYARgghhAIIACOEEEIBBIARQgihAALACCGEUAABYIQQQiiAADBCCCEUQAAYIYQQCqD/H+OHl9wD/QOLAAAAAElFTkSuQmCC" /><!-- --></p>
<p>The plot above shows the density of distribution of the shares of
each type of title sentimental category for each day of the week, in
other words, how much density is covered by each type of sentimental
titled article for each day. Again, the trend would be the same for each
type of the data, depending on various situations that drive these
articles, and its publications.</p>
<h1 id="modelling">Modelling</h1>
<p>Firstly, we are checking for the skewness in the data set for the
response variable that is <strong>“shares”</strong>. For that we are
plotting the distribution for the data of that variable below:</p>
<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(newspopData) <span class="sc">+</span> <span class="fu">geom_density</span>(<span class="fu">aes</span>(<span class="at">x =</span> shares))<span class="sc">+</span> </span>
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">&quot;Shares Predictor Distribution in Dataset&quot;</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>From the plot above showing distribution of shares, we can see that
the distribution is left-skewed. To mitigate this, we are taking a log
transform of that variable.</p>
<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(newspopData) <span class="sc">+</span> <span class="fu">geom_density</span>(<span class="fu">aes</span>(<span class="at">x =</span> <span class="fu">log</span>(shares)))<span class="sc">+</span></span>
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">&quot;Logarithmic transformation of shares distribution&quot;</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>As seen from the plot above, after doing the log transformation,
shares distribution can be estimated as a normal distribution, which
will be better for the models that we would be fitting for this project.
Hence, for all the models that are built in this project, the target
response variable is the log transform <strong>(“logShares”)</strong> of
the original shares variable.</p>
<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">42</span>)</span>
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a><span class="co"># Removing mutated variables from the data set</span></span>
<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a>lmData <span class="ot">&lt;-</span> newspopData <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="sc">-</span>day, <span class="sc">-</span>title_Sentiment_Class, <span class="sc">-</span>content_Sentiment_Class, <span class="sc">-</span>article_popularity_index)</span>
<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a>lmData<span class="sc">$</span>logShares <span class="ot">&lt;-</span> <span class="fu">log</span>(lmData<span class="sc">$</span>shares)</span>
<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-8"><a href="#cb25-8" aria-hidden="true" tabindex="-1"></a><span class="co"># train test split</span></span>
<span id="cb25-9"><a href="#cb25-9" aria-hidden="true" tabindex="-1"></a>index <span class="ot">&lt;-</span> <span class="fu">createDataPartition</span>(newspopData<span class="sc">$</span>shares, <span class="at">p =</span> <span class="fl">0.7</span>, <span class="at">list =</span> <span class="cn">FALSE</span>)</span>
<span id="cb25-10"><a href="#cb25-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-11"><a href="#cb25-11" aria-hidden="true" tabindex="-1"></a><span class="co"># Removing the shares variable because we are using logShares as response</span></span>
<span id="cb25-12"><a href="#cb25-12" aria-hidden="true" tabindex="-1"></a>trainDf <span class="ot">&lt;-</span> lmData[index, ] <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="sc">-</span>shares)</span>
<span id="cb25-13"><a href="#cb25-13" aria-hidden="true" tabindex="-1"></a>testDf  <span class="ot">&lt;-</span> lmData[<span class="sc">-</span>index, ] <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="sc">-</span>shares)</span></code></pre></div>
<h2 id="variable-selection">Variable Selection</h2>
<p>For variable selection we used p-test values to consider significant
coefficients from the linear model fit. For a confidence interval of
95%, the significant predictors are used to fit a Linear and a Lasso
regression model. For the significant parameter selection, our NULL and
Alternate hypothesis is explained below:<br />
H~0: All coefficients have zero slope<br />
H~a: At-least one predictor variable has a non-zero slope</p>
<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a>modelLmVar <span class="ot">&lt;-</span> <span class="fu">lm</span>(logShares<span class="sc">~</span>. ,<span class="at">data =</span> trainDf)</span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-3"><a href="#cb26-3" aria-hidden="true" tabindex="-1"></a><span class="co"># getting p-values </span></span>
<span id="cb26-4"><a href="#cb26-4" aria-hidden="true" tabindex="-1"></a>pVal <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(<span class="fu">summary</span>(modelLmVar)<span class="sc">$</span>coefficients[,<span class="dv">4</span>])</span>
<span id="cb26-5"><a href="#cb26-5" aria-hidden="true" tabindex="-1"></a>pVal<span class="sc">$</span>row_names <span class="ot">&lt;-</span> <span class="fu">row.names</span>(pVal)</span>
<span id="cb26-6"><a href="#cb26-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-7"><a href="#cb26-7" aria-hidden="true" tabindex="-1"></a><span class="co"># checking if slope of intercept is significant (i.e. &lt;&lt;&lt; 0.05)</span></span>
<span id="cb26-8"><a href="#cb26-8" aria-hidden="true" tabindex="-1"></a>pVal <span class="ot">&lt;-</span> pVal <span class="sc">%&gt;%</span> <span class="fu">filter</span>(pVal[,<span class="dv">1</span>] <span class="sc">&lt;</span> <span class="fl">0.05</span>)</span>
<span id="cb26-9"><a href="#cb26-9" aria-hidden="true" tabindex="-1"></a>cols <span class="ot">=</span> <span class="fu">c</span>()</span>
<span id="cb26-10"><a href="#cb26-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-11"><a href="#cb26-11" aria-hidden="true" tabindex="-1"></a><span class="co"># remove intercept term and store all significant intercepts in &quot;cols&quot; variable </span></span>
<span id="cb26-12"><a href="#cb26-12" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> (pVal[,<span class="dv">2</span>][<span class="dv">1</span>] <span class="sc">==</span> <span class="st">&quot;(Intercept)&quot;</span>){</span>
<span id="cb26-13"><a href="#cb26-13" aria-hidden="true" tabindex="-1"></a>  cols <span class="ot">=</span> pVal[,<span class="dv">2</span>][<span class="sc">-</span><span class="dv">1</span>]</span>
<span id="cb26-14"><a href="#cb26-14" aria-hidden="true" tabindex="-1"></a>}<span class="cf">else</span>{</span>
<span id="cb26-15"><a href="#cb26-15" aria-hidden="true" tabindex="-1"></a>  cols <span class="ot">=</span> pVal[,<span class="dv">2</span>]</span>
<span id="cb26-16"><a href="#cb26-16" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb26-17"><a href="#cb26-17" aria-hidden="true" tabindex="-1"></a>cols</span></code></pre></div>
<pre><code>##  [1] &quot;n_non_stop_words&quot;         
##  [2] &quot;n_non_stop_unique_tokens&quot; 
##  [3] &quot;num_imgs&quot;                 
##  [4] &quot;kw_max_avg&quot;               
##  [5] &quot;kw_avg_avg&quot;               
##  [6] &quot;weekday_is_tuesday&quot;       
##  [7] &quot;weekday_is_wednesday&quot;     
##  [8] &quot;weekday_is_thursday&quot;      
##  [9] &quot;weekday_is_friday&quot;        
## [10] &quot;global_sentiment_polarity&quot;
## [11] &quot;min_positive_polarity&quot;</code></pre>
<h2 id="multiple-linear-regression-model">Multiple Linear Regression
Model</h2>
<p>Linear regression is a regression model that uses a straight line to
describe a relationship between two or more predictor and a response
variable. Out of the 54 predictor variables in the data set, the
predictors that were deemed significant from the step above are used in
this model, with a response variable of logShares.</p>
<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb28-1"><a href="#cb28-1" aria-hidden="true" tabindex="-1"></a>trControl <span class="ot">&lt;-</span> <span class="fu">trainControl</span>(<span class="at">method =</span> <span class="st">&#39;repeatedcv&#39;</span>, <span class="at">number =</span> <span class="dv">10</span>)</span>
<span id="cb28-2"><a href="#cb28-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-3"><a href="#cb28-3" aria-hidden="true" tabindex="-1"></a><span class="co"># model training</span></span>
<span id="cb28-4"><a href="#cb28-4" aria-hidden="true" tabindex="-1"></a>modelLm <span class="ot">&lt;-</span> <span class="fu">train</span>(logShares <span class="sc">~</span> .,</span>
<span id="cb28-5"><a href="#cb28-5" aria-hidden="true" tabindex="-1"></a>              <span class="at">data =</span> trainDf <span class="sc">%&gt;%</span> </span>
<span id="cb28-6"><a href="#cb28-6" aria-hidden="true" tabindex="-1"></a>              <span class="fu">select</span>(<span class="fu">all_of</span>(cols), logShares),</span>
<span id="cb28-7"><a href="#cb28-7" aria-hidden="true" tabindex="-1"></a>              <span class="at">method =</span> <span class="st">&quot;lm&quot;</span>,</span>
<span id="cb28-8"><a href="#cb28-8" aria-hidden="true" tabindex="-1"></a>              <span class="at">preProcess =</span> <span class="fu">c</span>(<span class="st">&#39;center&#39;</span>, <span class="st">&#39;scale&#39;</span>),</span>
<span id="cb28-9"><a href="#cb28-9" aria-hidden="true" tabindex="-1"></a>              <span class="at">trControl =</span> trControl)</span>
<span id="cb28-10"><a href="#cb28-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-11"><a href="#cb28-11" aria-hidden="true" tabindex="-1"></a>title <span class="ot">=</span> <span class="fu">toupper</span>(<span class="fu">str_replace_all</span>(params<span class="sc">$</span>data_channel, <span class="st">&quot;_&quot;</span>, <span class="st">&quot; &quot;</span>))</span>
<span id="cb28-12"><a href="#cb28-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb28-13"><a href="#cb28-13" aria-hidden="true" tabindex="-1"></a><span class="co"># variable importance for linear model</span></span>
<span id="cb28-14"><a href="#cb28-14" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(<span class="fu">varImp</span>(modelLm), </span>
<span id="cb28-15"><a href="#cb28-15" aria-hidden="true" tabindex="-1"></a>     <span class="at">main =</span> <span class="fu">paste</span>(<span class="st">&quot;Variable importance Plot for &quot;</span>, <span class="st">&quot;</span><span class="sc">\n</span><span class="st">&quot;</span>, title))</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a>lmPredict <span class="ot">&lt;-</span> <span class="fu">predict</span>(modelLm, <span class="at">newdata =</span> testDf <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="fu">all_of</span>(cols), logShares))</span>
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a>lmRes <span class="ot">&lt;-</span> <span class="fu">postResample</span>(lmPredict, <span class="at">obs =</span> testDf<span class="sc">$</span>logShares)</span>
<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb29-5"><a href="#cb29-5" aria-hidden="true" tabindex="-1"></a><span class="co"># Adjusted R-square</span></span>
<span id="cb29-6"><a href="#cb29-6" aria-hidden="true" tabindex="-1"></a>n <span class="ot">&lt;-</span> <span class="fu">dim</span>(testDf)[<span class="dv">1</span>]</span>
<span id="cb29-7"><a href="#cb29-7" aria-hidden="true" tabindex="-1"></a>p <span class="ot">&lt;-</span> <span class="fu">dim</span>(testDf <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="fu">all_of</span>(cols)))[<span class="dv">2</span>]</span>
<span id="cb29-8"><a href="#cb29-8" aria-hidden="true" tabindex="-1"></a>adjR2Linear <span class="ot">&lt;-</span>  <span class="dv">1</span><span class="sc">-</span>(((<span class="dv">1</span><span class="sc">-</span>lmRes[<span class="dv">2</span>]<span class="sc">^</span><span class="dv">2</span>)<span class="sc">*</span>(n<span class="dv">-1</span>))<span class="sc">/</span>(n<span class="sc">-</span>p<span class="dv">-1</span>))  </span>
<span id="cb29-9"><a href="#cb29-9" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb29-10"><a href="#cb29-10" aria-hidden="true" tabindex="-1"></a>lmRes</span></code></pre></div>
<pre><code>##      RMSE  Rsquared       MAE 
## 0.9173554 0.0321371 0.7096754</code></pre>
<h2 id="lasso-regression">Lasso Regression</h2>
<p>LASSO or the Least Absolute Shrinkage and Selection Operator is a
special type of linear model that uses penalty based shrinkage.
Shrinkage here means converging data values to a central point, or where
the absolute magnitude of the coefficients are shrunk to a 0 based on L1
regularization penalty method which adds a penalty factor(lambda) for
every misclassified or wrongly predicted values.</p>
<p>LASSO generally works well with models having less variable
parameters. From the above process, we have narrowed down a few most
influencing and statistically significant variables which we will be
using for this model as well.</p>
<p>The caret package is used to train the model here using the
<strong>lasso</strong> method. The prediction metrics are then derived
using the postResample function. The same predictor and response
variable from the model above are used here as well.</p>
<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">43</span>)</span>
<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a><span class="co"># train</span></span>
<span id="cb31-4"><a href="#cb31-4" aria-hidden="true" tabindex="-1"></a>fitControl <span class="ot">&lt;-</span> <span class="fu">trainControl</span>(<span class="at">method =</span> <span class="st">&quot;repeatedcv&quot;</span>,<span class="at">number =</span> <span class="dv">5</span>)</span>
<span id="cb31-5"><a href="#cb31-5" aria-hidden="true" tabindex="-1"></a>fitLASSO <span class="ot">&lt;-</span> <span class="fu">train</span>(logShares <span class="sc">~</span> . ,</span>
<span id="cb31-6"><a href="#cb31-6" aria-hidden="true" tabindex="-1"></a>                  <span class="at">data=</span>trainDf,</span>
<span id="cb31-7"><a href="#cb31-7" aria-hidden="true" tabindex="-1"></a>                  <span class="at">method =</span> <span class="st">&quot;lasso&quot;</span>, </span>
<span id="cb31-8"><a href="#cb31-8" aria-hidden="true" tabindex="-1"></a>                  <span class="at">trControl =</span> fitControl,</span>
<span id="cb31-9"><a href="#cb31-9" aria-hidden="true" tabindex="-1"></a>                  <span class="at">preProcess =</span> <span class="fu">c</span>(<span class="st">&quot;center&quot;</span>, <span class="st">&quot;scale&quot;</span>)</span>
<span id="cb31-10"><a href="#cb31-10" aria-hidden="true" tabindex="-1"></a>                )</span>
<span id="cb31-11"><a href="#cb31-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-12"><a href="#cb31-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-13"><a href="#cb31-13" aria-hidden="true" tabindex="-1"></a>predLASSO <span class="ot">&lt;-</span> <span class="fu">predict</span>(fitLASSO, <span class="at">newdata =</span> testDf)</span>
<span id="cb31-14"><a href="#cb31-14" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-15"><a href="#cb31-15" aria-hidden="true" tabindex="-1"></a>coeff <span class="ot">&lt;-</span> <span class="fu">predict</span>(fitLASSO<span class="sc">$</span>finalModel, <span class="at">type =</span> <span class="st">&quot;coef&quot;</span>, <span class="at">mode =</span> <span class="st">&quot;fraction&quot;</span>,</span>
<span id="cb31-16"><a href="#cb31-16" aria-hidden="true" tabindex="-1"></a>                 <span class="at">s =</span> fitLASSO<span class="sc">$</span>bestTune<span class="sc">$</span>fraction, testDf)</span>
<span id="cb31-17"><a href="#cb31-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-18"><a href="#cb31-18" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-19"><a href="#cb31-19" aria-hidden="true" tabindex="-1"></a>lassoRes <span class="ot">&lt;-</span> <span class="fu">postResample</span>(predLASSO, <span class="at">obs =</span> testDf<span class="sc">$</span>logShares)</span>
<span id="cb31-20"><a href="#cb31-20" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-21"><a href="#cb31-21" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-22"><a href="#cb31-22" aria-hidden="true" tabindex="-1"></a><span class="co"># Adjusted R-square</span></span>
<span id="cb31-23"><a href="#cb31-23" aria-hidden="true" tabindex="-1"></a>n <span class="ot">&lt;-</span> <span class="fu">dim</span>(testDf)[<span class="dv">1</span>]</span>
<span id="cb31-24"><a href="#cb31-24" aria-hidden="true" tabindex="-1"></a>p <span class="ot">&lt;-</span> <span class="fu">dim</span>(testDf)[<span class="dv">2</span>]</span>
<span id="cb31-25"><a href="#cb31-25" aria-hidden="true" tabindex="-1"></a>adjR2Lasso <span class="ot">&lt;-</span>  <span class="dv">1</span><span class="sc">-</span>(((<span class="dv">1</span><span class="sc">-</span>lassoRes[<span class="dv">2</span>]<span class="sc">^</span><span class="dv">2</span>)<span class="sc">*</span>(n<span class="dv">-1</span>))<span class="sc">/</span>(n<span class="sc">-</span>p<span class="dv">-1</span>))</span>
<span id="cb31-26"><a href="#cb31-26" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-27"><a href="#cb31-27" aria-hidden="true" tabindex="-1"></a>lassoRes</span></code></pre></div>
<pre><code>##      RMSE  Rsquared       MAE 
## 0.9047553 0.0560580 0.6982046</code></pre>
<h2 id="random-forest">Random Forest</h2>
<p>Before building the random forest model, seeing at the data, the data
set is high dimensional, hence, it would be easier to select the “best”
subsets of variables for random forest ensemble tree learning method to
make the process more efficient. More details about Random Forest is
given before the model is formulated.</p>
<h2 id="best-variable-selection-principal-component-analysis">Best
Variable Selection: Principal Component Analysis</h2>
<p>Since the data set includes a large number of variables, it becomes
important to select the best subsets of the data that defines the data
set and variations in the data set for number of shares. To get these
variables, here we are conducting Principal Component Analysis (PCA).
PCA standardizes the variables, and represent new variables/PCs that are
a function of the original variables from the data set.</p>
<p>Again, to keep the models separate, we are again splitting the data
into train and test data set, and removing the categorical variables
that were added previously in the data. After that the PCs are
formulated.</p>
<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">200</span>)</span>
<span id="cb33-2"><a href="#cb33-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb33-3"><a href="#cb33-3" aria-hidden="true" tabindex="-1"></a>newspopData<span class="sc">$</span>logShares <span class="ot">&lt;-</span> <span class="fu">log</span>(newspopData<span class="sc">$</span>shares)</span>
<span id="cb33-4"><a href="#cb33-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb33-5"><a href="#cb33-5" aria-hidden="true" tabindex="-1"></a>trainIndex <span class="ot">&lt;-</span> <span class="fu">createDataPartition</span>(newspopData<span class="sc">$</span>shares, <span class="at">p =</span> <span class="fl">0.7</span>, <span class="at">list =</span> <span class="cn">FALSE</span>)</span>
<span id="cb33-6"><a href="#cb33-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb33-7"><a href="#cb33-7" aria-hidden="true" tabindex="-1"></a>trainData <span class="ot">&lt;-</span> newspopData[trainIndex, ]</span>
<span id="cb33-8"><a href="#cb33-8" aria-hidden="true" tabindex="-1"></a>testData <span class="ot">&lt;-</span> newspopData[<span class="sc">-</span>trainIndex, ]</span></code></pre></div>
<p>Creating new PCs, and plotting the cumulative variance graph:</p>
<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb34-1"><a href="#cb34-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Removing shares, logShares and mutated variables to form PCs</span></span>
<span id="cb34-2"><a href="#cb34-2" aria-hidden="true" tabindex="-1"></a>PCs <span class="ot">&lt;-</span> <span class="fu">prcomp</span>(trainData <span class="sc">%&gt;%</span> </span>
<span id="cb34-3"><a href="#cb34-3" aria-hidden="true" tabindex="-1"></a>                <span class="fu">select</span>(<span class="sc">-</span>shares, <span class="sc">-</span>logShares, <span class="sc">-</span>day, </span>
<span id="cb34-4"><a href="#cb34-4" aria-hidden="true" tabindex="-1"></a>                       <span class="sc">-</span>title_Sentiment_Class, </span>
<span id="cb34-5"><a href="#cb34-5" aria-hidden="true" tabindex="-1"></a>                       <span class="sc">-</span>content_Sentiment_Class,</span>
<span id="cb34-6"><a href="#cb34-6" aria-hidden="true" tabindex="-1"></a>                       <span class="sc">-</span>article_popularity_index), </span>
<span id="cb34-7"><a href="#cb34-7" aria-hidden="true" tabindex="-1"></a>                        <span class="at">center=</span><span class="cn">TRUE</span>, <span class="at">scale=</span><span class="cn">TRUE</span>)</span>
<span id="cb34-8"><a href="#cb34-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb34-9"><a href="#cb34-9" aria-hidden="true" tabindex="-1"></a><span class="co"># cumulative variance</span></span>
<span id="cb34-10"><a href="#cb34-10" aria-hidden="true" tabindex="-1"></a>var <span class="ot">=</span> <span class="fu">cumsum</span>(PCs<span class="sc">$</span>sdev<span class="sc">**</span><span class="dv">2</span><span class="sc">/</span><span class="fu">sum</span>(PCs<span class="sc">$</span>sdev<span class="sc">**</span><span class="dv">2</span>))</span>
<span id="cb34-11"><a href="#cb34-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb34-12"><a href="#cb34-12" aria-hidden="true" tabindex="-1"></a><span class="fu">show</span>(<span class="fu">plot</span>(var, <span class="at">xlab =</span> <span class="st">&quot;Principal Component&quot;</span>, </span>
<span id="cb34-13"><a href="#cb34-13" aria-hidden="true" tabindex="-1"></a>          <span class="at">ylab =</span> <span class="st">&quot;Cum. Prop of Variance Explained&quot;</span>, <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>), <span class="at">type =</span> <span class="st">&#39;b&#39;</span>))</span></code></pre></div>
<pre><code>## NULL</code></pre>
<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb36-1"><a href="#cb36-1" aria-hidden="true" tabindex="-1"></a>pt <span class="ot">&lt;-</span> <span class="fu">min</span>(<span class="fu">which</span>(var <span class="sc">&gt;</span> <span class="fl">0.80</span>))</span>
<span id="cb36-2"><a href="#cb36-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb36-3"><a href="#cb36-3" aria-hidden="true" tabindex="-1"></a><span class="fu">points</span>(pt, var[pt], <span class="at">col=</span><span class="st">&quot;red&quot;</span>, <span class="at">cex=</span><span class="dv">2</span>, <span class="at">pch=</span><span class="dv">20</span>)</span>
<span id="cb36-4"><a href="#cb36-4" aria-hidden="true" tabindex="-1"></a><span class="fu">text</span>(<span class="dv">8</span>, <span class="fl">0.8</span>, <span class="at">col=</span><span class="st">&quot;red&quot;</span>, <span class="fu">paste0</span>(<span class="fu">round</span>(<span class="dv">100</span><span class="sc">*</span>var[pt],<span class="dv">2</span>), <span class="st">&quot;% variance </span><span class="sc">\n</span><span class="st">is explained by &quot;</span>, pt, <span class="st">&quot; </span><span class="sc">\n</span><span class="st">number of PC(s)&quot;</span>))</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>From the above graph, we can see that at least 80% variance is
explained by 21 PCs, and hence for the subsequent steps, 21 PCs will be
used.</p>
<p>Now, we are creating the training data for Random Forest Ensemble
model.</p>
<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Creating training data PCs without the logShares variables</span></span>
<span id="cb37-2"><a href="#cb37-2" aria-hidden="true" tabindex="-1"></a>treeTrainData <span class="ot">&lt;-</span> <span class="fu">predict</span>(PCs, <span class="at">newdata =</span> trainData <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="sc">-</span>shares, <span class="sc">-</span>logShares)) <span class="sc">%&gt;%</span> </span>
<span id="cb37-3"><a href="#cb37-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">as_tibble</span>() <span class="sc">%&gt;%</span> </span>
<span id="cb37-4"><a href="#cb37-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">select</span>(PC1<span class="sc">:</span><span class="fu">paste0</span>(<span class="st">&quot;PC&quot;</span>, pt))</span>
<span id="cb37-5"><a href="#cb37-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb37-6"><a href="#cb37-6" aria-hidden="true" tabindex="-1"></a>treeTrainData<span class="sc">$</span>logShares <span class="ot">&lt;-</span> trainData<span class="sc">$</span>logShares</span>
<span id="cb37-7"><a href="#cb37-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb37-8"><a href="#cb37-8" aria-hidden="true" tabindex="-1"></a><span class="co"># This the final training data that will be used to train random forest model</span></span>
<span id="cb37-9"><a href="#cb37-9" aria-hidden="true" tabindex="-1"></a>treeTrainData</span></code></pre></div>
<pre><code>## # A tibble: 1,472 × 22
##      PC1   PC2     PC3     PC4    PC5    PC6
##    &lt;dbl&gt; &lt;dbl&gt;   &lt;dbl&gt;   &lt;dbl&gt;  &lt;dbl&gt;  &lt;dbl&gt;
##  1 -1.84 2.74  -3.64    3.46    1.35  -2.01 
##  2 -4.38 1.88   0.722  -0.832   0.735  0.133
##  3 -4.53 0.714  0.0971 -1.52    0.585  0.170
##  4 -4.56 1.58   0.150  -0.357   0.772  0.200
##  5 -2.63 4.61  -1.88   -0.565   0.512 -1.21 
##  6 -3.25 1.39  -1.01    0.0392  1.88   1.52 
##  7 -1.92 2.23  -3.54    3.96    1.47  -2.40 
##  8 -4.45 1.13   0.568  -0.391   0.582 -0.550
##  9 -4.55 0.610 -0.851   1.20    0.452  1.00 
## 10 -5.22 0.958  0.473   0.516  -0.692  0.311
## # … with 1,462 more rows, and 16 more
## #   variables: PC7 &lt;dbl&gt;, PC8 &lt;dbl&gt;,
## #   PC9 &lt;dbl&gt;, PC10 &lt;dbl&gt;, PC11 &lt;dbl&gt;,
## #   PC12 &lt;dbl&gt;, PC13 &lt;dbl&gt;, PC14 &lt;dbl&gt;,
## #   PC15 &lt;dbl&gt;, PC16 &lt;dbl&gt;, PC17 &lt;dbl&gt;,
## #   PC18 &lt;dbl&gt;, PC19 &lt;dbl&gt;, PC20 &lt;dbl&gt;,
## #   PC21 &lt;dbl&gt;, logShares &lt;dbl&gt;</code></pre>
<h3 id="random-forest-model">Random Forest Model:</h3>
<p>Random Forest model is a tree based ensemble learning method where
the training data set is sampled into smaller data sets, and some
variables from the data set are included in the smaller sampled data. A
tree is fitted to that data. This method is repeated several times, and
finally a model is finalized that will be an average of all these
sampled tree models. Since Random Forest takes only a subset of
variables in any given sampling, it creates really strong model to
predict on with unknown variables since the sampled data is able to
explain variance much better with fewer variables.</p>
<p>We are using train() function from caret package to train the Random
Forest model using the <strong>rf</strong> method. Pre-processing is
done by centering and scaling the data, and a 3 fold cross validation is
also used. (The value 3 is selected to have some computation ease).
Lastly, the model is tried for a number of values for the tuning
parameter “mtry”, out of which the best mtry value is selected.</p>
<p>Training the model:</p>
<div class="sourceCode" id="cb39"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb39-1"><a href="#cb39-1" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">400</span>)</span>
<span id="cb39-2"><a href="#cb39-2" aria-hidden="true" tabindex="-1"></a>trctrl <span class="ot">&lt;-</span> <span class="fu">trainControl</span>(<span class="at">method =</span> <span class="st">&quot;repeatedcv&quot;</span>, <span class="at">number =</span> <span class="dv">3</span>)</span>
<span id="cb39-3"><a href="#cb39-3" aria-hidden="true" tabindex="-1"></a>randomForest <span class="ot">&lt;-</span> <span class="fu">train</span>(logShares <span class="sc">~</span>., <span class="at">data =</span> treeTrainData, </span>
<span id="cb39-4"><a href="#cb39-4" aria-hidden="true" tabindex="-1"></a>                      <span class="at">method =</span> <span class="st">&quot;rf&quot;</span>,</span>
<span id="cb39-5"><a href="#cb39-5" aria-hidden="true" tabindex="-1"></a>                      <span class="at">trControl=</span>trctrl,</span>
<span id="cb39-6"><a href="#cb39-6" aria-hidden="true" tabindex="-1"></a>                      <span class="at">preProcess =</span> <span class="fu">c</span>(<span class="st">&quot;center&quot;</span>, <span class="st">&quot;scale&quot;</span>),</span>
<span id="cb39-7"><a href="#cb39-7" aria-hidden="true" tabindex="-1"></a>                      <span class="at">tuneGrid =</span> <span class="fu">expand.grid</span>(<span class="at">mtry =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">as.integer</span>(pt<span class="sc">/</span><span class="dv">3</span>)))</span>
<span id="cb39-8"><a href="#cb39-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb39-9"><a href="#cb39-9" aria-hidden="true" tabindex="-1"></a>randomForest</span></code></pre></div>
<pre><code>## Random Forest 
## 
## 1472 samples
##   21 predictor
## 
## Pre-processing: centered (21), scaled (21) 
## Resampling: Cross-Validated (3 fold, repeated 1 times) 
## Summary of sample sizes: 981, 983, 980 
## Resampling results across tuning parameters:
## 
##   mtry  RMSE       Rsquared    MAE      
##   1     0.9153664  0.02243316  0.7056881
##   2     0.9159739  0.02430438  0.7074691
##   3     0.9162671  0.02617734  0.7074963
##   4     0.9188450  0.02376155  0.7103767
##   5     0.9190373  0.02434655  0.7108327
##   6     0.9199683  0.02441688  0.7110105
##   7     0.9191692  0.02664557  0.7119071
## 
## RMSE was used to select the optimal
##  model using the smallest value.
## The final value used for the model was mtry
##  = 1.</code></pre>
<p>Testing the model on the test data set to see the metrics of
evaluation. The predict() function is used to create both PC based
testing data, and to predict the logShares using the Random Forest
model. Further, the postResample() function is used to extract metrics
such as RMSE, R-Squared, and MAE, represented below.</p>
<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb41-1"><a href="#cb41-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Creating test data PCs</span></span>
<span id="cb41-2"><a href="#cb41-2" aria-hidden="true" tabindex="-1"></a>treeTestData <span class="ot">&lt;-</span> <span class="fu">predict</span>(PCs, <span class="at">newdata =</span> testData <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="sc">-</span>shares, <span class="sc">-</span>logShares)) <span class="sc">%&gt;%</span> </span>
<span id="cb41-3"><a href="#cb41-3" aria-hidden="true" tabindex="-1"></a>                         <span class="fu">as_tibble</span>() <span class="sc">%&gt;%</span> </span>
<span id="cb41-4"><a href="#cb41-4" aria-hidden="true" tabindex="-1"></a>                         <span class="fu">select</span>(PC1<span class="sc">:</span><span class="fu">paste0</span>(<span class="st">&quot;PC&quot;</span>, pt))</span>
<span id="cb41-5"><a href="#cb41-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb41-6"><a href="#cb41-6" aria-hidden="true" tabindex="-1"></a><span class="co"># Completing the test data</span></span>
<span id="cb41-7"><a href="#cb41-7" aria-hidden="true" tabindex="-1"></a>treeTestData<span class="sc">$</span>logShares <span class="ot">&lt;-</span> testData<span class="sc">$</span>logShares</span>
<span id="cb41-8"><a href="#cb41-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb41-9"><a href="#cb41-9" aria-hidden="true" tabindex="-1"></a>rfPredict <span class="ot">&lt;-</span> <span class="fu">predict</span>(randomForest, <span class="at">newdata =</span> treeTestData)</span>
<span id="cb41-10"><a href="#cb41-10" aria-hidden="true" tabindex="-1"></a>randomFRes <span class="ot">&lt;-</span> <span class="fu">postResample</span>(rfPredict, <span class="at">obs =</span> treeTestData<span class="sc">$</span>logShares)</span>
<span id="cb41-11"><a href="#cb41-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb41-12"><a href="#cb41-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb41-13"><a href="#cb41-13" aria-hidden="true" tabindex="-1"></a><span class="co"># Adjusted R-square</span></span>
<span id="cb41-14"><a href="#cb41-14" aria-hidden="true" tabindex="-1"></a>n <span class="ot">&lt;-</span> <span class="fu">dim</span>(treeTestData)[<span class="dv">1</span>]</span>
<span id="cb41-15"><a href="#cb41-15" aria-hidden="true" tabindex="-1"></a>p <span class="ot">&lt;-</span> <span class="fu">dim</span>(treeTestData)[<span class="dv">2</span>] <span class="sc">-</span> <span class="dv">1</span></span>
<span id="cb41-16"><a href="#cb41-16" aria-hidden="true" tabindex="-1"></a>adjR2Rf <span class="ot">&lt;-</span>  <span class="dv">1</span><span class="sc">-</span>(((<span class="dv">1</span><span class="sc">-</span>randomFRes[<span class="dv">2</span>]<span class="sc">^</span><span class="dv">2</span>)<span class="sc">*</span>(n<span class="dv">-1</span>))<span class="sc">/</span>(n<span class="sc">-</span>p<span class="dv">-1</span>))</span>
<span id="cb41-17"><a href="#cb41-17" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb41-18"><a href="#cb41-18" aria-hidden="true" tabindex="-1"></a>randomFRes</span></code></pre></div>
<pre><code>##       RMSE   Rsquared        MAE 
## 0.96673542 0.03525394 0.72522972</code></pre>
<h2 id="boosted-tree-model">Boosted Tree Model</h2>
<p>Boosting is another tree based approach for improving the predictions
resulting from a decision tree. Like other tree models, boosting can be
applied for classification and regression. Boosting works in
<strong>sequentially</strong>: each tree is grown using information from
previously grown trees. In this project, we are using
<strong>gbm</strong> method within caret train function.</p>
<p>An additional input tunegrid also provided to train function, which
will find best hyper parameter combinations of number of trees, and
depth.</p>
<p>Here, all the available parameters are used as predictor variables,
and logShares is the target response variable.</p>
<div class="sourceCode" id="cb43"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb43-1"><a href="#cb43-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Training the model</span></span>
<span id="cb43-2"><a href="#cb43-2" aria-hidden="true" tabindex="-1"></a>boostedTree <span class="ot">&lt;-</span> <span class="fu">train</span>(logShares <span class="sc">~</span>., <span class="at">data =</span> trainData <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="sc">-</span>shares), <span class="at">method =</span> <span class="st">&quot;gbm&quot;</span>,</span>
<span id="cb43-3"><a href="#cb43-3" aria-hidden="true" tabindex="-1"></a>                     <span class="at">trControl =</span> <span class="fu">trainControl</span>(<span class="at">method =</span> <span class="st">&quot;repeatedcv&quot;</span>, <span class="at">number =</span> <span class="dv">3</span>),</span>
<span id="cb43-4"><a href="#cb43-4" aria-hidden="true" tabindex="-1"></a>                     <span class="at">preProcess =</span> <span class="fu">c</span>(<span class="st">&quot;center&quot;</span>, <span class="st">&quot;scale&quot;</span>),</span>
<span id="cb43-5"><a href="#cb43-5" aria-hidden="true" tabindex="-1"></a>                     <span class="at">tuneGrid =</span> <span class="fu">expand.grid</span>(<span class="at">n.trees =</span> <span class="fu">c</span>(<span class="dv">25</span>, <span class="dv">50</span>, <span class="dv">100</span>, <span class="dv">150</span>, <span class="dv">200</span>),</span>
<span id="cb43-6"><a href="#cb43-6" aria-hidden="true" tabindex="-1"></a>                                            <span class="at">interaction.depth =</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>,</span>
<span id="cb43-7"><a href="#cb43-7" aria-hidden="true" tabindex="-1"></a>                                            <span class="at">shrinkage =</span> <span class="fl">0.1</span>,</span>
<span id="cb43-8"><a href="#cb43-8" aria-hidden="true" tabindex="-1"></a>                                            <span class="at">n.minobsinnode =</span> <span class="dv">10</span>),</span>
<span id="cb43-9"><a href="#cb43-9" aria-hidden="true" tabindex="-1"></a>                     <span class="at">verbose =</span> <span class="cn">FALSE</span>)</span>
<span id="cb43-10"><a href="#cb43-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb43-11"><a href="#cb43-11" aria-hidden="true" tabindex="-1"></a><span class="co"># Best combination of tuning hyperparameters</span></span>
<span id="cb43-12"><a href="#cb43-12" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(boostedTree<span class="sc">$</span>bestTune)</span></code></pre></div>
<pre><code>##    n.trees interaction.depth shrinkage
## 12      50                 3       0.1
##    n.minobsinnode
## 12             10</code></pre>
<div class="sourceCode" id="cb45"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb45-1"><a href="#cb45-1" aria-hidden="true" tabindex="-1"></a>boostedTPredict <span class="ot">&lt;-</span> <span class="fu">predict</span>(boostedTree, <span class="at">newdata =</span> testData <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="sc">-</span>shares))</span>
<span id="cb45-2"><a href="#cb45-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb45-3"><a href="#cb45-3" aria-hidden="true" tabindex="-1"></a>boostedTRes <span class="ot">&lt;-</span> <span class="fu">postResample</span>(boostedTPredict, <span class="at">obs =</span> (testData <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="sc">-</span>shares))<span class="sc">$</span>logShares)</span>
<span id="cb45-4"><a href="#cb45-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb45-5"><a href="#cb45-5" aria-hidden="true" tabindex="-1"></a><span class="co"># plot</span></span>
<span id="cb45-6"><a href="#cb45-6" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(boostedTree, <span class="at">xlab =</span> <span class="st">&quot;Max Tree Depth &quot;</span>, </span>
<span id="cb45-7"><a href="#cb45-7" aria-hidden="true" tabindex="-1"></a>     <span class="at">ylab =</span> <span class="st">&quot;Root Mean Square Error (Found through CV)&quot;</span>, </span>
<span id="cb45-8"><a href="#cb45-8" aria-hidden="true" tabindex="-1"></a>     <span class="at">main =</span> <span class="st">&quot;All Predictors - Minimizing RMSE&quot;</span>)</span></code></pre></div>
<p><img 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" /><!-- --></p>
<div class="sourceCode" id="cb46"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb46-1"><a href="#cb46-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Adjusted R-square</span></span>
<span id="cb46-2"><a href="#cb46-2" aria-hidden="true" tabindex="-1"></a>n <span class="ot">&lt;-</span> <span class="fu">dim</span>(testData)[<span class="dv">1</span>]</span>
<span id="cb46-3"><a href="#cb46-3" aria-hidden="true" tabindex="-1"></a>p <span class="ot">&lt;-</span> <span class="fu">dim</span>(testData)[<span class="dv">2</span>] <span class="sc">-</span> <span class="dv">1</span></span>
<span id="cb46-4"><a href="#cb46-4" aria-hidden="true" tabindex="-1"></a>adjR2Boosted <span class="ot">&lt;-</span>  <span class="dv">1</span><span class="sc">-</span>(((<span class="dv">1</span><span class="sc">-</span>boostedTRes[<span class="dv">2</span>]<span class="sc">^</span><span class="dv">2</span>)<span class="sc">*</span>(n<span class="dv">-1</span>))<span class="sc">/</span>(n<span class="sc">-</span>p<span class="dv">-1</span>))</span>
<span id="cb46-5"><a href="#cb46-5" aria-hidden="true" tabindex="-1"></a> </span>
<span id="cb46-6"><a href="#cb46-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb46-7"><a href="#cb46-7" aria-hidden="true" tabindex="-1"></a>boostedTRes</span></code></pre></div>
<pre><code>##      RMSE  Rsquared       MAE 
## 0.4657117 0.7848593 0.2731229</code></pre>
<p>From the plot we can visualize the best combinations of parameters
that were used to find minimum RMSE value using Boosted tree algorithm,
which can also be seen by using <strong>(boostedTree$bestTune)</strong>
function.</p>
<h2 id="model-comparision">Model Comparision</h2>
<div class="sourceCode" id="cb48"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb48-1"><a href="#cb48-1" aria-hidden="true" tabindex="-1"></a>model_types <span class="ot">=</span> <span class="fu">c</span>(<span class="st">&quot;Linear&quot;</span>, <span class="st">&quot;Ensemble&quot;</span>)</span>
<span id="cb48-2"><a href="#cb48-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb48-3"><a href="#cb48-3" aria-hidden="true" tabindex="-1"></a>modelComparisonDf <span class="ot">=</span> <span class="fu">tibble</span>(<span class="at">model =</span> <span class="fu">c</span>(<span class="st">&quot;Linear Model&quot;</span>), <span class="at">model_type =</span> <span class="fu">c</span>(model_types[<span class="dv">1</span>]), <span class="at">RMSE =</span> <span class="fu">c</span>(<span class="fu">round</span>(lmRes[[<span class="dv">1</span>]],<span class="dv">3</span>)), <span class="at">R_Squared =</span> <span class="fu">c</span>(<span class="fu">round</span>(lmRes[[<span class="dv">2</span>]], <span class="dv">4</span>)), <span class="at">Adj_R2 =</span> <span class="fu">c</span>(<span class="fu">round</span>(adjR2Linear,<span class="dv">4</span>)) )</span>
<span id="cb48-4"><a href="#cb48-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb48-5"><a href="#cb48-5" aria-hidden="true" tabindex="-1"></a>modelComparisonDf <span class="ot">&lt;-</span> <span class="fu">rbind</span>(modelComparisonDf, <span class="fu">c</span>(<span class="st">&quot;LASSO&quot;</span>, model_types[<span class="dv">1</span>], <span class="fu">round</span>(lassoRes[[<span class="dv">1</span>]],<span class="dv">3</span>), <span class="fu">round</span>(lassoRes[[<span class="dv">2</span>]],<span class="dv">4</span>), <span class="fu">round</span>(adjR2Lasso,<span class="dv">4</span>)))</span>
<span id="cb48-6"><a href="#cb48-6" aria-hidden="true" tabindex="-1"></a>modelComparisonDf <span class="ot">&lt;-</span> <span class="fu">rbind</span>(modelComparisonDf, <span class="fu">c</span>(<span class="st">&quot;Random Forest&quot;</span>, model_types[<span class="dv">2</span>], <span class="fu">round</span>(randomFRes[[<span class="dv">1</span>]],<span class="dv">3</span>), <span class="fu">round</span>(randomFRes[[<span class="dv">2</span>]],<span class="dv">4</span>), <span class="fu">round</span>(adjR2Rf,<span class="dv">4</span>)))</span>
<span id="cb48-7"><a href="#cb48-7" aria-hidden="true" tabindex="-1"></a>modelComparisonDf <span class="ot">&lt;-</span> <span class="fu">rbind</span>(modelComparisonDf, <span class="fu">c</span>(<span class="st">&quot;Boosted Trees&quot;</span>, model_types[<span class="dv">2</span>], <span class="fu">round</span>(boostedTRes[[<span class="dv">1</span>]],<span class="dv">3</span>), <span class="fu">round</span>(boostedTRes[[<span class="dv">2</span>]],<span class="dv">4</span>), <span class="fu">round</span>(adjR2Boosted,<span class="dv">4</span>)))</span>
<span id="cb48-8"><a href="#cb48-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb48-9"><a href="#cb48-9" aria-hidden="true" tabindex="-1"></a>knitr<span class="sc">::</span><span class="fu">kable</span>(modelComparisonDf)</span></code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">model</th>
<th align="left">model_type</th>
<th align="left">RMSE</th>
<th align="left">R_Squared</th>
<th align="left">Adj_R2</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Linear Model</td>
<td align="left">Linear</td>
<td align="left">0.917</td>
<td align="left">0.0321</td>
<td align="left">-0.0168</td>
</tr>
<tr class="even">
<td align="left">LASSO</td>
<td align="left">Linear</td>
<td align="left">0.905</td>
<td align="left">0.0561</td>
<td align="left">-0.091</td>
</tr>
<tr class="odd">
<td align="left">Random Forest</td>
<td align="left">Ensemble</td>
<td align="left">0.967</td>
<td align="left">0.0353</td>
<td align="left">-0.0334</td>
</tr>
<tr class="even">
<td align="left">Boosted Trees</td>
<td align="left">Ensemble</td>
<td align="left">0.466</td>
<td align="left">0.7849</td>
<td align="left">0.5768</td>
</tr>
</tbody>
</table>
<div class="sourceCode" id="cb49"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb49-1"><a href="#cb49-1" aria-hidden="true" tabindex="-1"></a>bestLinearModel <span class="ot">=</span> <span class="st">&quot;&quot;</span></span>
<span id="cb49-2"><a href="#cb49-2" aria-hidden="true" tabindex="-1"></a>bestLinearRMSE <span class="ot">=</span> <span class="st">&quot;&quot;</span></span>
<span id="cb49-3"><a href="#cb49-3" aria-hidden="true" tabindex="-1"></a>bestLinearR2 <span class="ot">=</span> <span class="st">&quot;&quot;</span></span>
<span id="cb49-4"><a href="#cb49-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb49-5"><a href="#cb49-5" aria-hidden="true" tabindex="-1"></a>bestEnsembleModel <span class="ot">=</span> <span class="st">&quot;&quot;</span></span>
<span id="cb49-6"><a href="#cb49-6" aria-hidden="true" tabindex="-1"></a>bestEnsembleRMSE <span class="ot">=</span> <span class="st">&quot;&quot;</span></span>
<span id="cb49-7"><a href="#cb49-7" aria-hidden="true" tabindex="-1"></a>bestEnsembleR2 <span class="ot">=</span> <span class="st">&quot;&quot;</span></span>
<span id="cb49-8"><a href="#cb49-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb49-9"><a href="#cb49-9" aria-hidden="true" tabindex="-1"></a>bestOverallModel <span class="ot">=</span> <span class="st">&quot;&quot;</span></span>
<span id="cb49-10"><a href="#cb49-10" aria-hidden="true" tabindex="-1"></a>bestOverallRMSE <span class="ot">=</span> <span class="st">&quot;&quot;</span></span>
<span id="cb49-11"><a href="#cb49-11" aria-hidden="true" tabindex="-1"></a>bestOverallR2 <span class="ot">=</span> <span class="st">&quot;&quot;</span></span>
<span id="cb49-12"><a href="#cb49-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb49-13"><a href="#cb49-13" aria-hidden="true" tabindex="-1"></a>lineardf <span class="ot">&lt;-</span> modelComparisonDf <span class="sc">%&gt;%</span> <span class="fu">filter</span>(model_type <span class="sc">==</span> <span class="st">&quot;Linear&quot;</span>)</span>
<span id="cb49-14"><a href="#cb49-14" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb49-15"><a href="#cb49-15" aria-hidden="true" tabindex="-1"></a>ensembleDf <span class="ot">&lt;-</span> modelComparisonDf <span class="sc">%&gt;%</span> <span class="fu">filter</span>(model_type <span class="sc">==</span> <span class="st">&quot;Ensemble&quot;</span>)</span>
<span id="cb49-16"><a href="#cb49-16" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb49-17"><a href="#cb49-17" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> (<span class="fu">length</span>(<span class="fu">unique</span>(lineardf<span class="sc">$</span>R_Squared)) <span class="sc">&gt;</span> <span class="dv">1</span>){</span>
<span id="cb49-18"><a href="#cb49-18" aria-hidden="true" tabindex="-1"></a>  bestLinearModel <span class="ot">&lt;-</span> lineardf[<span class="fu">which.min</span>(lineardf<span class="sc">$</span>RMSE),][[<span class="dv">1</span>]]</span>
<span id="cb49-19"><a href="#cb49-19" aria-hidden="true" tabindex="-1"></a>  bestLinearRMSE <span class="ot">&lt;-</span> lineardf[<span class="fu">which.min</span>(lineardf<span class="sc">$</span>RMSE),][[<span class="dv">3</span>]]</span>
<span id="cb49-20"><a href="#cb49-20" aria-hidden="true" tabindex="-1"></a>  bestLinearR2 <span class="ot">&lt;-</span> lineardf[<span class="fu">which.min</span>(lineardf<span class="sc">$</span>RMSE),][[<span class="dv">4</span>]]</span>
<span id="cb49-21"><a href="#cb49-21" aria-hidden="true" tabindex="-1"></a>} <span class="cf">else</span>{</span>
<span id="cb49-22"><a href="#cb49-22" aria-hidden="true" tabindex="-1"></a>  bestLinearModel <span class="ot">&lt;-</span> lineardf[<span class="fu">which.max</span>(lineardf<span class="sc">$</span>Adj_R2),][[<span class="dv">1</span>]]</span>
<span id="cb49-23"><a href="#cb49-23" aria-hidden="true" tabindex="-1"></a>  bestLinearRMSE <span class="ot">&lt;-</span> lineardf[<span class="fu">which.max</span>(lineardf<span class="sc">$</span>Adj_R2),][[<span class="dv">3</span>]]</span>
<span id="cb49-24"><a href="#cb49-24" aria-hidden="true" tabindex="-1"></a>  bestLinearR2 <span class="ot">&lt;-</span> lineardf[<span class="fu">which.max</span>(lineardf<span class="sc">$</span>Adj_R2),][[<span class="dv">4</span>]]</span>
<span id="cb49-25"><a href="#cb49-25" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb49-26"><a href="#cb49-26" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb49-27"><a href="#cb49-27" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb49-28"><a href="#cb49-28" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> (<span class="fu">length</span>(<span class="fu">unique</span>(ensembleDf<span class="sc">$</span>R_Squared)) <span class="sc">&gt;</span> <span class="dv">1</span>){</span>
<span id="cb49-29"><a href="#cb49-29" aria-hidden="true" tabindex="-1"></a>  bestEnsembleModel <span class="ot">&lt;-</span> ensembleDf[<span class="fu">which.min</span>(ensembleDf<span class="sc">$</span>RMSE),][[<span class="dv">1</span>]]</span>
<span id="cb49-30"><a href="#cb49-30" aria-hidden="true" tabindex="-1"></a>  bestEnsembleRMSE <span class="ot">&lt;-</span> ensembleDf[<span class="fu">which.min</span>(ensembleDf<span class="sc">$</span>RMSE),][[<span class="dv">3</span>]]</span>
<span id="cb49-31"><a href="#cb49-31" aria-hidden="true" tabindex="-1"></a>  bestEnsembleR2 <span class="ot">&lt;-</span> ensembleDf[<span class="fu">which.min</span>(ensembleDf<span class="sc">$</span>RMSE),][[<span class="dv">4</span>]]</span>
<span id="cb49-32"><a href="#cb49-32" aria-hidden="true" tabindex="-1"></a>} <span class="cf">else</span>{</span>
<span id="cb49-33"><a href="#cb49-33" aria-hidden="true" tabindex="-1"></a>  bestEnsembleModel <span class="ot">&lt;-</span> ensembleDf[<span class="fu">which.max</span>(ensembleDf<span class="sc">$</span>Adj_R2),][[<span class="dv">1</span>]]</span>
<span id="cb49-34"><a href="#cb49-34" aria-hidden="true" tabindex="-1"></a>  bestEnsembleRMSE <span class="ot">&lt;-</span> ensembleDf[<span class="fu">which.max</span>(ensembleDf<span class="sc">$</span>Adj_R2),][[<span class="dv">3</span>]]</span>
<span id="cb49-35"><a href="#cb49-35" aria-hidden="true" tabindex="-1"></a>  bestEnsembleR2 <span class="ot">&lt;-</span> ensembleDf[<span class="fu">which.max</span>(ensembleDf<span class="sc">$</span>Adj_R2),][[<span class="dv">4</span>]]</span>
<span id="cb49-36"><a href="#cb49-36" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb49-37"><a href="#cb49-37" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb49-38"><a href="#cb49-38" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb49-39"><a href="#cb49-39" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> (<span class="fu">length</span>(<span class="fu">unique</span>(modelComparisonDf<span class="sc">$</span>R_Squared)) <span class="sc">&gt;</span> <span class="dv">1</span>){</span>
<span id="cb49-40"><a href="#cb49-40" aria-hidden="true" tabindex="-1"></a>  bestOverallModel <span class="ot">&lt;-</span> modelComparisonDf[<span class="fu">which.min</span>(modelComparisonDf<span class="sc">$</span>RMSE),][[<span class="dv">1</span>]]</span>
<span id="cb49-41"><a href="#cb49-41" aria-hidden="true" tabindex="-1"></a>  bestOverallRMSE <span class="ot">&lt;-</span> modelComparisonDf[<span class="fu">which.min</span>(modelComparisonDf<span class="sc">$</span>RMSE),][[<span class="dv">3</span>]]</span>
<span id="cb49-42"><a href="#cb49-42" aria-hidden="true" tabindex="-1"></a>  bestOverallR2 <span class="ot">&lt;-</span> modelComparisonDf[<span class="fu">which.min</span>(modelComparisonDf<span class="sc">$</span>RMSE),][[<span class="dv">4</span>]]</span>
<span id="cb49-43"><a href="#cb49-43" aria-hidden="true" tabindex="-1"></a>} <span class="cf">else</span>{</span>
<span id="cb49-44"><a href="#cb49-44" aria-hidden="true" tabindex="-1"></a>  bestOverallModel <span class="ot">&lt;-</span> modelComparisonDf[<span class="fu">which.max</span>(modelComparisonDf<span class="sc">$</span>Adj_R2),][[<span class="dv">1</span>]]</span>
<span id="cb49-45"><a href="#cb49-45" aria-hidden="true" tabindex="-1"></a>  bestOverallRMSE <span class="ot">&lt;-</span> modelComparisonDf[<span class="fu">which.max</span>(modelComparisonDf<span class="sc">$</span>Adj_R2),][[<span class="dv">3</span>]]</span>
<span id="cb49-46"><a href="#cb49-46" aria-hidden="true" tabindex="-1"></a>  bestOverallR2 <span class="ot">&lt;-</span> modelComparisonDf[<span class="fu">which.max</span>(modelComparisonDf<span class="sc">$</span>Adj_R2),][[<span class="dv">4</span>]]</span>
<span id="cb49-47"><a href="#cb49-47" aria-hidden="true" tabindex="-1"></a>}</span></code></pre></div>
<h2 id="conclusion">Conclusion</h2>
<p>Selection of best model is based on comparing the lowest prediction
RMSE value across all models.</p>
<p>For the data set for <strong>LIFESTYLE</strong>:</p>
<p>The best linear model is LASSO with RMSE value of 0.905, and R
Squared value of 0.0561.</p>
<p>The best ensemble method is Boosted Trees with RMSE value of 0.466,
and R Squared value of 0.7849.</p>
<p>The best overall model is Boosted Trees with RMSE value of 0.466, and
R Squared value of 0.7849.</p>

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