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<h1 class="title toc-ignore">Chapter 4: Clustering and classification</h1>
<h4 class="date"><em>2020-11-19</em></h4>
</div>
<hr />
<div id="description-of-data" class="section level1" number="1">
<h1 number="1"><span class="header-section-number">1</span> Description of data</h1>
<p>The data used in this excercise contains information collected by the U.S. Census Service concerning housing in the area of Boston Mass. It has been previous released to the public domain and has been used extensively to benchmark differen algorithms.</p>
<p>The data first appeared in: Harrison, D. and Rubinfeld, D.L. `Hedonic prices and the demand for clean air’, J. Environ. Economics & Management, vol.5, 81-102, 1978.</p>
<p>The data was originally used to relate housing price with various predictors.</p>
<hr />
<div id="variable-decoding" class="section level2" number="1.1">
<h2 number="1.1"><span class="header-section-number">1.1</span> Variable decoding</h2>
<p>For an explanation of the individual variables, please, refer to the following:</p>
<hr />
<table>
<colgroup>
<col width="18%" />
<col width="81%" />
</colgroup>
<thead>
<tr class="header">
<th>Variable name</th>
<th>Explanation</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><em>crim</em></td>
<td>per capita crime rate by town/suburb.</td>
</tr>
<tr class="even">
<td><em>zn</em></td>
<td>proportion of residential land zoned for lots over 25,000 sq.ft.</td>
</tr>
<tr class="odd">
<td><em>indus</em></td>
<td>proportion of non-retail business acres per town.</td>
</tr>
<tr class="even">
<td><em>chas</em></td>
<td>Charles River dummy variable (= 1 if tract bounds river; 0 otherwise).</td>
</tr>
<tr class="odd">
<td><em>nox</em></td>
<td>nitrogen oxides concentration (parts per 10 million).</td>
</tr>
<tr class="even">
<td><em>rm</em></td>
<td>average number of rooms per dwelling.</td>
</tr>
<tr class="odd">
<td><em>age</em></td>
<td>proportion of owner-occupied units built prior to 1940.</td>
</tr>
<tr class="even">
<td><em>dis</em></td>
<td>weighted mean of distances to five Boston employment centres.</td>
</tr>
<tr class="odd">
<td><em>rad</em></td>
<td>index of accessibility to radial highways.</td>
</tr>
<tr class="even">
<td><em>tax</em></td>
<td>full-value property-tax rate per $10,000.</td>
</tr>
<tr class="odd">
<td><em>ptratio</em></td>
<td>pupil-teacher ratio by town.</td>
</tr>
<tr class="even">
<td><em>black</em></td>
<td>1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town.</td>
</tr>
<tr class="odd">
<td><em>lstat</em></td>
<td>lower status of the population (percent).</td>
</tr>
<tr class="even">
<td><em>medv</em></td>
<td>median value of owner-occupied homes in $1000s.</td>
</tr>
</tbody>
</table>
<hr />
</div>
<div id="interactive-table" class="section level2" number="1.2">
<h2 number="1.2"><span class="header-section-number">1.2</span> Interactive table</h2>
<pre class="r"><code>#Read the Boston data
library(MASS)</code></pre>
<pre><code>##
## Attaching package: 'MASS'</code></pre>
<pre><code>## The following object is masked from 'package:dplyr':
##
## select</code></pre>
<pre><code>## The following object is masked from 'package:plotly':
##
## select</code></pre>
<pre><code>## The following object is masked from 'package:gtsummary':
##
## select</code></pre>
<pre class="r"><code>data("Boston")
#Draw an interactive table that can be used to view the data and its dimensions
library(DT)
datatable(Boston)</code></pre>
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class=\"display\">\n <thead>\n <tr>\n <th> <\/th>\n <th>crim<\/th>\n <th>zn<\/th>\n <th>indus<\/th>\n <th>chas<\/th>\n <th>nox<\/th>\n <th>rm<\/th>\n <th>age<\/th>\n <th>dis<\/th>\n <th>rad<\/th>\n <th>tax<\/th>\n <th>ptratio<\/th>\n <th>black<\/th>\n <th>lstat<\/th>\n <th>medv<\/th>\n <\/tr>\n <\/thead>\n<\/table>","options":{"columnDefs":[{"className":"dt-right","targets":[1,2,3,4,5,6,7,8,9,10,11,12,13,14]},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
<hr />
</div>
</div>
<div id="graphical-overview-and-summary" class="section level1" number="2">
<h1 number="2"><span class="header-section-number">2</span> Graphical overview and summary</h1>
<hr />
<div id="summary-table-of-variables" class="section level2" number="2.1">
<h2 number="2.1"><span class="header-section-number">2.1</span> Summary table of variables</h2>
<pre class="r"><code>library(gtsummary)
#First print out a summary table of all variables
my_table <- tbl_summary(Boston,
digits = all_continuous() ~ 2,
type = all_continuous() ~ "continuous2",
statistic = list(all_continuous() ~ c("{mean} ({sd})",
"{median} ({p25}, {p75})",
"{min}, {max}"),
all_categorical() ~ "{n} / {N} ({p}%)"))
#Add some missing elements to the table and print it out
my_table %>% bold_labels()</code></pre>
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<div id="tftepjlxks" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;"><table class="gt_table">
<thead class="gt_col_headings">
<tr>
<th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1"><strong>Characteristic</strong></th>
<th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1"><strong>N = 506</strong></th>
</tr>
</thead>
<tbody class="gt_table_body">
<tr>
<td class="gt_row gt_left" style="font-weight: bold;">crim</td>
<td class="gt_row gt_center"></td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Mean (SD)</td>
<td class="gt_row gt_center">3.61 (8.60)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Median (IQR)</td>
<td class="gt_row gt_center">0.26 (0.08, 3.68)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Range</td>
<td class="gt_row gt_center">0.01, 88.98</td>
</tr>
<tr>
<td class="gt_row gt_left" style="font-weight: bold;">zn</td>
<td class="gt_row gt_center"></td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Mean (SD)</td>
<td class="gt_row gt_center">11.36 (23.32)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Median (IQR)</td>
<td class="gt_row gt_center">0.00 (0.00, 12.50)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Range</td>
<td class="gt_row gt_center">0.00, 100.00</td>
</tr>
<tr>
<td class="gt_row gt_left" style="font-weight: bold;">indus</td>
<td class="gt_row gt_center"></td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Mean (SD)</td>
<td class="gt_row gt_center">11.14 (6.86)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Median (IQR)</td>
<td class="gt_row gt_center">9.69 (5.19, 18.10)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Range</td>
<td class="gt_row gt_center">0.46, 27.74</td>
</tr>
<tr>
<td class="gt_row gt_left" style="font-weight: bold;">chas</td>
<td class="gt_row gt_center">35 / 506 (6.9%)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="font-weight: bold;">nox</td>
<td class="gt_row gt_center"></td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Mean (SD)</td>
<td class="gt_row gt_center">0.55 (0.12)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Median (IQR)</td>
<td class="gt_row gt_center">0.54 (0.45, 0.62)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Range</td>
<td class="gt_row gt_center">0.38, 0.87</td>
</tr>
<tr>
<td class="gt_row gt_left" style="font-weight: bold;">rm</td>
<td class="gt_row gt_center"></td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Mean (SD)</td>
<td class="gt_row gt_center">6.28 (0.70)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Median (IQR)</td>
<td class="gt_row gt_center">6.21 (5.89, 6.62)</td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Range</td>
<td class="gt_row gt_center">3.56, 8.78</td>
</tr>
<tr>
<td class="gt_row gt_left" style="font-weight: bold;">age</td>
<td class="gt_row gt_center"></td>
</tr>
<tr>
<td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Mean (SD)</td>
<td class="gt_row gt_center">68.57 (28.15)</td>
</tr>