diff --git a/docs/labs/03.QualitativeVariable.html b/docs/labs/03.QualitativeVariable.html
index 9e26146..ea2b925 100644
--- a/docs/labs/03.QualitativeVariable.html
+++ b/docs/labs/03.QualitativeVariable.html
@@ -9,7 +9,7 @@
 <meta name="author" content="Zi Ye">
 <meta name="dcterms.date" content="2024-11-21">
 
-<title>3&nbsp; Correlation and Multiple Linear Regression with Qualitative Variables – Exploring the Social World - Quantitative Block: Statistics</title>
+<title>3&nbsp; Lab: Correlation and Multiple Linear Regression with Qualitative Variables – Exploring the Social World - Quantitative Block: Statistics</title>
 <style>
 code{white-space: pre-wrap;}
 span.smallcaps{font-variant: small-caps;}
@@ -118,7 +118,7 @@
       <button type="button" class="quarto-btn-toggle btn" data-bs-toggle="collapse" role="button" data-bs-target=".quarto-sidebar-collapse-item" aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Toggle sidebar navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
         <i class="bi bi-layout-text-sidebar-reverse"></i>
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-        <nav class="quarto-page-breadcrumbs" aria-label="breadcrumb"><ol class="breadcrumb"><li class="breadcrumb-item"><a href="../labs/03.QualitativeVariable.html"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Correlation and Multiple Linear Regression with Qualitative Variables</span></a></li></ol></nav>
+        <nav class="quarto-page-breadcrumbs" aria-label="breadcrumb"><ol class="breadcrumb"><li class="breadcrumb-item"><a href="../labs/03.QualitativeVariable.html"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Lab: Correlation and Multiple Linear Regression with Qualitative Variables</span></a></li></ol></nav>
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@@ -180,7 +180,7 @@
         <li class="sidebar-item">
   <div class="sidebar-item-container"> 
   <a href="../labs/03.QualitativeVariable.html" class="sidebar-item-text sidebar-link active">
- <span class="menu-text"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Correlation and Multiple Linear Regression with Qualitative Variables</span></span></a>
+ <span class="menu-text"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Lab: Correlation and Multiple Linear Regression with Qualitative Variables</span></span></a>
   </div>
 </li>
         <li class="sidebar-item">
@@ -224,7 +224,7 @@ <h2 id="toc-title">Table of contents</h2>
 
 <header id="title-block-header" class="quarto-title-block default">
 <div class="quarto-title">
-<h1 class="title"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Correlation and Multiple Linear Regression with Qualitative Variables</span></h1>
+<h1 class="title"><span class="chapter-number">3</span>&nbsp; <span class="chapter-title">Lab: Correlation and Multiple Linear Regression with Qualitative Variables</span></h1>
 </div>
 
 
@@ -278,81 +278,99 @@ <h2 data-number="3.1" class="anchored" data-anchor-id="analysis-categorical-vari
 <p>Check your working directory by</p>
 <div class="cell">
 <div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">getwd</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
-<div class="cell-output cell-output-stdout">
-<pre><code>[1] "C:/Users/ziye/Documents/GitHub/stats/labs"</code></pre>
-</div>
 </div>
 <p>Check the relative path of your data folder on your PC/laptop, make sure you know the relative path of your data from your workding directory, returned by <code>getwd()</code>.</p>
 <p><strong>Library knowledge used in today:</strong></p>
-<p>dplyr: a basic library provides a suite of functions for data manipulation</p>
-<p>ggplot2: a widely-used data visualisation library to help you create nice plots through layered plotting.</p>
-<p>tidyverse: a collection of R packages designed for data science, offering a cohesive framework for data manipulation, visualization, and analysis. Containing dyplyr, ggplot2 and other basic libraries.</p>
-<p>broom: a part of the tidyverse and is designed to convert statistical analysis results into tidy data frames.</p>
+<ul>
+<li><p><strong><code>dplyr</code></strong>: a basic library provides a suite of functions for data manipulation</p></li>
+<li><p><strong><code>ggplot2</code></strong>: a widely-used data visualisation library to help you create nice plots through layered plotting.</p></li>
+<li><p><strong><code>tidyverse</code></strong>: a collection of R packages designed for data science, offering a cohesive framework for data manipulation, visualization, and analysis. Containing dyplyr, ggplot2 and other basic libraries.</p></li>
+<li><p><strong><code>broom</code></strong>: a part of the tidyverse and is designed to convert statistical analysis results into tidy data frames.</p></li>
+<li><p><strong><code>forcats</code></strong>: designed to work with factors, which are used to represent categorical data. It simplifies the process of creating, modifying, and ordering factors.</p></li>
+<li><p><strong><code>vcd</code></strong>: visualise and analyse categorical data.</p></li>
+</ul>
 <section id="data-overview" class="level3" data-number="3.1.1">
 <h3 data-number="3.1.1" class="anchored" data-anchor-id="data-overview"><span class="header-section-number">3.1.1</span> Data overview</h3>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span>(<span class="sc">!</span><span class="fu">require</span>(<span class="st">"dplyr"</span>))</span>
-<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">install.packages</span>(<span class="st">"dplyr"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span>(<span class="sc">!</span><span class="fu">require</span>(<span class="st">"dplyr"</span>))</span>
+<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">install.packages</span>(<span class="st">"dplyr"</span>,<span class="at">dependencies =</span> T)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
-<pre><code>Warning: package 'dplyr' was built under R version 4.3.2</code></pre>
+<pre><code>Loading required package: dplyr</code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Load necessary libraries </span></span>
-<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span>(<span class="sc">!</span><span class="fu">require</span>(<span class="st">"ggplot2"</span>))</span>
-<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">install.packages</span>(<span class="st">"ggplot2"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
-<pre><code>Warning: package 'ggplot2' was built under R version 4.3.2</code></pre>
-</div>
-<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(dplyr) </span>
-<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
-</div>
-<p>Or we can use library <code>tidyverse</code> which complies <code>ggplot2</code>, <code>dplyr</code> and other foundamental libraries together already, remember you need first install the package if you haven’t by using <code>install.packages("tidyverse")</code>.</p>
-<div class="cell">
-<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span>(<span class="sc">!</span><span class="fu">require</span>(<span class="st">"tidyverse"</span>))</span>
-<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">install.packages</span>(<span class="st">"tidyverse"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
-<div class="cell-output cell-output-stderr">
-<pre><code>Warning: package 'tidyverse' was built under R version 4.3.2</code></pre>
+<pre><code>
+Attaching package: 'dplyr'</code></pre>
 </div>
 <div class="cell-output cell-output-stderr">
-<pre><code>Warning: package 'tibble' was built under R version 4.3.2</code></pre>
+<pre><code>The following objects are masked from 'package:stats':
+
+    filter, lag</code></pre>
 </div>
 <div class="cell-output cell-output-stderr">
-<pre><code>Warning: package 'tidyr' was built under R version 4.3.2</code></pre>
+<pre><code>The following objects are masked from 'package:base':
+
+    intersect, setdiff, setequal, union</code></pre>
 </div>
+<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Load necessary libraries </span></span>
+<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span>(<span class="sc">!</span><span class="fu">require</span>(<span class="st">"ggplot2"</span>))</span>
+<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">install.packages</span>(<span class="st">"ggplot2"</span>,<span class="at">dependencies =</span> T)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
-<pre><code>Warning: package 'readr' was built under R version 4.3.2</code></pre>
+<pre><code>Loading required package: ggplot2</code></pre>
 </div>
+<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span>(<span class="sc">!</span><span class="fu">require</span>(<span class="st">"broom"</span>))</span>
+<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">install.packages</span>(<span class="st">"broom"</span>,<span class="at">dependencies =</span> T)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
-<pre><code>Warning: package 'purrr' was built under R version 4.3.2</code></pre>
+<pre><code>Loading required package: broom</code></pre>
 </div>
-<div class="cell-output cell-output-stderr">
-<pre><code>Warning: package 'stringr' was built under R version 4.3.2</code></pre>
+<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(dplyr) </span>
+<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2)</span>
+<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(broom)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
+<p>Or we can use library <code>tidyverse</code> which includes <code>ggplot2</code>, <code>dplyr,broom</code> and other foundamental libraries together already, remember you need first install the package if you haven’t by using <code>install.packages("tidyverse")</code>.</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span>(<span class="sc">!</span><span class="fu">require</span>(<span class="st">"tidyverse"</span>))</span>
+<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">install.packages</span>(<span class="st">"tidyverse"</span>,<span class="at">dependencies =</span> T)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
-<pre><code>Warning: package 'forcats' was built under R version 4.3.2</code></pre>
+<pre><code>Loading required package: tidyverse</code></pre>
 </div>
 <div class="cell-output cell-output-stderr">
-<pre><code>Warning: package 'lubridate' was built under R version 4.3.2</code></pre>
-</div>
-<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidyverse)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<pre><code>── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
+✔ forcats   1.0.0     ✔ stringr   1.5.1
+✔ lubridate 1.9.3     ✔ tibble    3.2.1
+✔ purrr     1.0.2     ✔ tidyr     1.3.1
+✔ readr     2.1.5     
+── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
+✖ dplyr::filter() masks stats::filter()
+✖ dplyr::lag()    masks stats::lag()
+ℹ Use the conflicted package (&lt;http://conflicted.r-lib.org/&gt;) to force all conflicts to become errors</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidyverse)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>We will also use forcat library, so</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span>(<span class="sc">!</span><span class="fu">require</span>(<span class="st">"forcats"</span>))</span>
+<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">install.packages</span>(<span class="st">"forcats"</span>)</span>
+<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(forcats)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>Exactly as you did in previous weeks, we first load in the dataset:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>frs_data <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="st">"../data/FamilyResourceSurvey/FRS16-17_labels.csv"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>frs_data <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="st">"../data/FamilyResourceSurvey/FRS16-17_labels.csv"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>Recall in previous weeks, we used the following code to overview the dataset. Familiar yourself again by using them:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="fu">View</span>(frs_data)</span>
-<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a><span class="fu">glimpse</span>(frs_data)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="fu">View</span>(frs_data)</span>
+<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a><span class="fu">glimpse</span>(frs_data)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>and also <code>summary()</code> to produce summaries of each variable</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb20"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(frs_data)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(frs_data)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>You may notice that for the numeric variables such as <em>hh_income_gross</em> (household gross income) and <em>work_hours</em>(worked hours per week), the <code>summary()</code> offers useful descriptive statistics. While for the qualitative information, such as <em>age_group</em> (age group), <em>highest_qual (</em>Highest educational qualification), <em>marital_status (</em>Marital status) and <em>nssec (</em>Socio-economic status), the <code>summary()</code> function is not that useful by providing mean or median values.</p>
 <p>Performing descriptive analysis for categorical variables or qualitative variables, we focus on summarising the frequency and distribution of categories within the variable. This analysis helps understand the composition and diversity of categories in the data, which is especially useful for identifying patterns, common categories, or potential data imbalances.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb21"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Frequency count</span></span>
-<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_data<span class="sc">$</span>age_group)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb20"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Frequency count</span></span>
+<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_data<span class="sc">$</span>age_group)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
   0-4 05-10 11-15 16-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 
@@ -360,7 +378,7 @@ <h3 data-number="3.1.1" class="anchored" data-anchor-id="data-overview"><span cl
 65-69 70-74   75+ 
  2990  2354  3743 </code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb23"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_data<span class="sc">$</span>highest_qual)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb22"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_data<span class="sc">$</span>highest_qual)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
 A-level or equivalent       Degree or above       Dependent child 
@@ -368,7 +386,7 @@ <h3 data-number="3.1.1" class="anchored" data-anchor-id="data-overview"><span cl
    GCSE or equivalent             Not known                 Other 
                  9729                  6820                  2882 </code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb25"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_data<span class="sc">$</span>marital_status)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb24"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_data<span class="sc">$</span>marital_status)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
                           Cohabiting Divorced/civil partnership dissolved 
@@ -378,7 +396,7 @@ <h3 data-number="3.1.1" class="anchored" data-anchor-id="data-overview"><span cl
                               Single                              Widowed 
                                16663                                 2326 </code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb27"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_data<span class="sc">$</span>nssec)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb26"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_data<span class="sc">$</span>nssec)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
                               Dependent child 
@@ -409,34 +427,49 @@ <h3 data-number="3.1.1" class="anchored" data-anchor-id="data-overview"><span cl
 </div>
 <p>By using ggplot2, it is easy to create some nice descriptive charts for the categorical variables, such like what you did for the continuous variables last week.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb29"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(frs_data, <span class="fu">aes</span>(<span class="at">x =</span> highest_qual)) <span class="sc">+</span></span>
-<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_bar</span>(<span class="at">fill=</span><span class="st">"brown"</span>,<span class="at">width=</span><span class="fl">0.5</span>) <span class="sc">+</span></span>
-<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of Highest Qualification in FRS"</span>, <span class="at">x =</span> <span class="st">"Highest Qualification"</span>, <span class="at">y =</span> <span class="st">"Count"</span>)<span class="sc">+</span><span class="co">#set text info</span></span>
-<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_classic</span>()<span class="co">#choose theme type, try theme_bw(), theme_minimal() see differences</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb28"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb28-1"><a href="#cb28-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(frs_data, <span class="fu">aes</span>(<span class="at">x =</span> highest_qual)) <span class="sc">+</span></span>
+<span id="cb28-2"><a href="#cb28-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_bar</span>(<span class="at">fill=</span><span class="st">"brown"</span>,<span class="at">width=</span><span class="fl">0.5</span>) <span class="sc">+</span></span>
+<span id="cb28-3"><a href="#cb28-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of Highest Qualification in FRS"</span>, <span class="at">x =</span> <span class="st">"Highest Qualification"</span>, <span class="at">y =</span> <span class="st">"Count"</span>)<span class="sc">+</span><span class="co">#set text info</span></span>
+<span id="cb28-4"><a href="#cb28-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_classic</span>()<span class="co">#choose theme type, try theme_bw(), theme_minimal() see differences</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output-display">
 <div>
 <figure class="figure">
-<p><img src="03.QualitativeVariable_files/figure-html/unnamed-chunk-8-1.png" class="img-fluid figure-img" width="672"></p>
+<p><img src="03.QualitativeVariable_files/figure-html/unnamed-chunk-9-1.png" class="img-fluid figure-img" width="672"></p>
 </figure>
 </div>
 </div>
 </div>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb30"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(frs_data, <span class="fu">aes</span>(<span class="at">x =</span> health)) <span class="sc">+</span></span>
-<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_bar</span>(<span class="at">fill=</span><span class="st">"skyblue"</span>) <span class="sc">+</span></span>
-<span id="cb30-3"><a href="#cb30-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_text</span>(<span class="at">stat =</span> <span class="st">"count"</span>, <span class="fu">aes</span>(<span class="at">label =</span> ..count..),<span class="at">vjust =</span> <span class="sc">-</span><span class="fl">0.3</span>,<span class="at">colour =</span> <span class="st">"grey"</span>)<span class="sc">+</span> <span class="co">#add text</span></span>
-<span id="cb30-4"><a href="#cb30-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of Health in FRS"</span>, <span class="at">x =</span> <span class="st">"Health"</span>, <span class="at">y =</span> <span class="st">"Count"</span>)<span class="sc">+</span><span class="co">#set text info</span></span>
-<span id="cb30-5"><a href="#cb30-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_minimal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb29"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(frs_data, <span class="fu">aes</span>(<span class="at">x =</span> health)) <span class="sc">+</span></span>
+<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_bar</span>(<span class="at">fill=</span><span class="st">"skyblue"</span>) <span class="sc">+</span></span>
+<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_text</span>(<span class="at">stat =</span> <span class="st">"count"</span>, <span class="fu">aes</span>(<span class="at">label =</span> ..count..),<span class="at">vjust =</span> <span class="sc">-</span><span class="fl">0.3</span>,<span class="at">colour =</span> <span class="st">"grey"</span>)<span class="sc">+</span> <span class="co">#add text</span></span>
+<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of Health in FRS"</span>, <span class="at">x =</span> <span class="st">"Health"</span>, <span class="at">y =</span> <span class="st">"Count"</span>)<span class="sc">+</span><span class="co">#set text info</span></span>
+<span id="cb29-5"><a href="#cb29-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_minimal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output-display">
 <div>
 <figure class="figure">
-<p><img src="03.QualitativeVariable_files/figure-html/unnamed-chunk-9-1.png" class="img-fluid figure-img" width="672"></p>
+<p><img src="03.QualitativeVariable_files/figure-html/unnamed-chunk-10-1.png" class="img-fluid figure-img" width="672"></p>
+</figure>
+</div>
+</div>
+</div>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb30"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(frs_data, <span class="fu">aes</span>(<span class="at">x =</span> nssec)) <span class="sc">+</span> </span>
+<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_bar</span>(<span class="at">fill =</span> <span class="st">"yellow4"</span>) <span class="sc">+</span> </span>
+<span id="cb30-3"><a href="#cb30-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of NSSEC in FRS"</span>, <span class="at">x =</span> <span class="st">"NSSEC"</span>, <span class="at">y =</span> <span class="st">"Count"</span>) <span class="sc">+</span></span>
+<span id="cb30-4"><a href="#cb30-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">coord_flip</span>()<span class="sc">+</span> <span class="co">#Flip the Axes, add a # in front of this line, to make the code in gray and you will see why we would better flip the axes at here</span></span>
+<span id="cb30-5"><a href="#cb30-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">theme_bw</span>() </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output-display">
+<div>
+<figure class="figure">
+<p><img src="03.QualitativeVariable_files/figure-html/unnamed-chunk-11-1.png" class="img-fluid figure-img" width="672"></p>
 </figure>
 </div>
 </div>
 </div>
+<p>If we want to reorder the Y axis by from highest to lowest, we use the functions in <code>forcats</code> library. <code>fct_infreq()</code>: orders by the value’s frequency of the variable <code>nssec</code>. <code>fct_rev()</code>: reverses the order to go from highest to lowest.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb31"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(frs_data, <span class="fu">aes</span>(<span class="at">x =</span> nssec)) <span class="sc">+</span> </span>
+<div class="sourceCode cell-code" id="cb31"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(frs_data, <span class="fu">aes</span>(<span class="at">x =</span> <span class="fu">fct_rev</span>(<span class="fu">fct_infreq</span>(nssec)))) <span class="sc">+</span> </span>
 <span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_bar</span>(<span class="at">fill =</span> <span class="st">"yellow4"</span>) <span class="sc">+</span> </span>
 <span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of NSSEC in FRS"</span>, <span class="at">x =</span> <span class="st">"NSSEC"</span>, <span class="at">y =</span> <span class="st">"Count"</span>) <span class="sc">+</span></span>
 <span id="cb31-4"><a href="#cb31-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">coord_flip</span>()<span class="sc">+</span> <span class="co">#Flip the Axes, add a # in front of this line, to make the code in gray and you will see why we would better flip the axes at here</span></span>
@@ -444,7 +477,7 @@ <h3 data-number="3.1.1" class="anchored" data-anchor-id="data-overview"><span cl
 <div class="cell-output-display">
 <div>
 <figure class="figure">
-<p><img src="03.QualitativeVariable_files/figure-html/unnamed-chunk-10-1.png" class="img-fluid figure-img" width="672"></p>
+<p><img src="03.QualitativeVariable_files/figure-html/unnamed-chunk-12-1.png" class="img-fluid figure-img" width="672"></p>
 </figure>
 </div>
 </div>
@@ -478,7 +511,7 @@ <h3 data-number="3.1.2" class="anchored" data-anchor-id="correlation"><span clas
 <div class="cell">
 <div class="sourceCode cell-code" id="cb35"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb35-1"><a href="#cb35-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Install the 'vcd' package if not installed </span></span>
 <span id="cb35-2"><a href="#cb35-2" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span>(<span class="sc">!</span><span class="fu">require</span>(<span class="st">"vcd"</span>))   </span>
-<span id="cb35-3"><a href="#cb35-3" aria-hidden="true" tabindex="-1"></a><span class="fu">install.packages</span>(<span class="st">"vcd"</span>, <span class="at">repos =</span> <span class="st">"https://cran.r-project.org"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<span id="cb35-3"><a href="#cb35-3" aria-hidden="true" tabindex="-1"></a><span class="fu">install.packages</span>(<span class="st">"vcd"</span>, <span class="at">repos =</span> <span class="st">"https://cran.r-project.org"</span>, <span class="at">dependencies =</span> T)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stderr">
 <pre><code>Loading required package: vcd</code></pre>
 </div>
@@ -490,8 +523,11 @@ <h3 data-number="3.1.2" class="anchored" data-anchor-id="correlation"><span clas
 </div>
 <div class="sourceCode cell-code" id="cb39"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb39-1"><a href="#cb39-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(vcd)  </span>
 <span id="cb39-2"><a href="#cb39-2" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb39-3"><a href="#cb39-3" aria-hidden="true" tabindex="-1"></a><span class="co"># Calculate Cramér's V </span></span>
-<span id="cb39-4"><a href="#cb39-4" aria-hidden="true" tabindex="-1"></a><span class="fu">assocstats</span>(<span class="fu">table</span>(frs_data<span class="sc">$</span>health, frs_data<span class="sc">$</span>happy))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<span id="cb39-3"><a href="#cb39-3" aria-hidden="true" tabindex="-1"></a><span class="co"># creat the crosstable </span></span>
+<span id="cb39-4"><a href="#cb39-4" aria-hidden="true" tabindex="-1"></a>crosstab <span class="ot">&lt;-</span> <span class="fu">table</span>(frs_data<span class="sc">$</span>health, frs_data<span class="sc">$</span>happy)</span>
+<span id="cb39-5"><a href="#cb39-5" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb39-6"><a href="#cb39-6" aria-hidden="true" tabindex="-1"></a><span class="co"># Calculate Cramér's V </span></span>
+<span id="cb39-7"><a href="#cb39-7" aria-hidden="true" tabindex="-1"></a><span class="fu">assocstats</span>(crosstab)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>                   X^2 df P(&gt; X^2)
 Likelihood Ratio 54036 60        0
@@ -501,6 +537,17 @@ <h3 data-number="3.1.2" class="anchored" data-anchor-id="correlation"><span clas
 Contingency Coeff.: 0.713 
 Cramer's V        : 0.454 </code></pre>
 </div>
+<div class="sourceCode cell-code" id="cb41"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb41-1"><a href="#cb41-1" aria-hidden="true" tabindex="-1"></a><span class="co">#you can also directly calculate the assoication between variables</span></span>
+<span id="cb41-2"><a href="#cb41-2" aria-hidden="true" tabindex="-1"></a><span class="fu">assocstats</span>(<span class="fu">table</span>(frs_data<span class="sc">$</span>health, frs_data<span class="sc">$</span>age_group))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>                   X^2 df P(&gt; X^2)
+Likelihood Ratio 26557 75        0
+Pearson          23854 75        0
+
+Phi-Coefficient   : NA 
+Contingency Coeff.: 0.592 
+Cramer's V        : 0.329 </code></pre>
+</div>
 </div>
 <div style="background-color: #FFFBCC; padding: 10px; border-radius: 5px; border: 1px solid #E1C948;">
 <p><strong>Research Question 1. Which of our selected person-level variables is most strongly correlated with an individual’s health status?</strong></p>
@@ -563,38 +610,38 @@ <h2 data-number="3.2" class="anchored" data-anchor-id="implementing-a-linear-reg
 <p>The practical is split into two main parts. The first focuses on implementing a linear regression model with a qualitative independent variable. <strong>Note that</strong> you need first to set the reference category (baseline) as the outcomes of the model reflects the <strong>differences</strong> between categories with the baseline. The second part focuses prediction based the estimated linear regression model.</p>
 <p>First we load the UK district-level census dataset.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb41"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb41-1"><a href="#cb41-1" aria-hidden="true" tabindex="-1"></a><span class="co"># load data</span></span>
-<span id="cb41-2"><a href="#cb41-2" aria-hidden="true" tabindex="-1"></a>LAcensus <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="st">"../data/Census2011/UK_DistrictPercentages.csv"</span>) <span class="co"># Local authority level</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb43"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb43-1"><a href="#cb43-1" aria-hidden="true" tabindex="-1"></a><span class="co"># load data</span></span>
+<span id="cb43-2"><a href="#cb43-2" aria-hidden="true" tabindex="-1"></a>LAcensus <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="st">"../data/Census2011/UK_DistrictPercentages.csv"</span>) <span class="co"># Local authority level</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>Using the district-level census dataset “<strong>UK_DistrictPercentages.csv</strong>”. the variable “Region” (labelled as Government Office Region) is used to explore regional inequality in health.</p>
 <p>Familiar yourself with the dataset by using the same codes as last week:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb42"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb42-1"><a href="#cb42-1" aria-hidden="true" tabindex="-1"></a><span class="co">#view the data </span></span>
-<span id="cb42-2"><a href="#cb42-2" aria-hidden="true" tabindex="-1"></a><span class="fu">View</span>(LAcensus)  </span>
-<span id="cb42-3"><a href="#cb42-3" aria-hidden="true" tabindex="-1"></a><span class="fu">glimpse</span>(LAcensus)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb44"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb44-1"><a href="#cb44-1" aria-hidden="true" tabindex="-1"></a><span class="co">#view the data </span></span>
+<span id="cb44-2"><a href="#cb44-2" aria-hidden="true" tabindex="-1"></a><span class="fu">View</span>(LAcensus)  </span>
+<span id="cb44-3"><a href="#cb44-3" aria-hidden="true" tabindex="-1"></a><span class="fu">glimpse</span>(LAcensus)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>The names() function returns all the column names.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb43"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb43-1"><a href="#cb43-1" aria-hidden="true" tabindex="-1"></a><span class="fu">names</span>(df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb45"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb45-1"><a href="#cb45-1" aria-hidden="true" tabindex="-1"></a><span class="fu">names</span>(df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>The dim() function can merely returns the number of rows and number of columns.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb44"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb44-1"><a href="#cb44-1" aria-hidden="true" tabindex="-1"></a><span class="fu">dim</span>(LAcensus) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb46"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb46-1"><a href="#cb46-1" aria-hidden="true" tabindex="-1"></a><span class="fu">dim</span>(LAcensus) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>[1] 406 128</code></pre>
 </div>
 </div>
 <p>There are 406 rows and 130 columns in the dataset. It would be very hard to scan throught the data if we use so many variables altogether. Therefore, we can select several columns to tailor for this practical. You can of course include other variables you are interested in also by their names:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb46"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb46-1"><a href="#cb46-1" aria-hidden="true" tabindex="-1"></a>df <span class="ot">&lt;-</span> LAcensus <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="fu">c</span>(<span class="st">"pct_Long_term_ill"</span>,</span>
-<span id="cb46-2"><a href="#cb46-2" aria-hidden="true" tabindex="-1"></a>                            <span class="st">"pct_No_qualifications"</span>,</span>
-<span id="cb46-3"><a href="#cb46-3" aria-hidden="true" tabindex="-1"></a>                            <span class="st">"pct_Males"</span>,</span>
-<span id="cb46-4"><a href="#cb46-4" aria-hidden="true" tabindex="-1"></a>                            <span class="st">"pct_Higher_manager_prof"</span>,</span>
-<span id="cb46-5"><a href="#cb46-5" aria-hidden="true" tabindex="-1"></a>                            <span class="st">"Region"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb48"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb48-1"><a href="#cb48-1" aria-hidden="true" tabindex="-1"></a>df <span class="ot">&lt;-</span> LAcensus <span class="sc">%&gt;%</span> <span class="fu">select</span>(<span class="fu">c</span>(<span class="st">"pct_Long_term_ill"</span>,</span>
+<span id="cb48-2"><a href="#cb48-2" aria-hidden="true" tabindex="-1"></a>                            <span class="st">"pct_No_qualifications"</span>,</span>
+<span id="cb48-3"><a href="#cb48-3" aria-hidden="true" tabindex="-1"></a>                            <span class="st">"pct_Males"</span>,</span>
+<span id="cb48-4"><a href="#cb48-4" aria-hidden="true" tabindex="-1"></a>                            <span class="st">"pct_Higher_manager_prof"</span>,</span>
+<span id="cb48-5"><a href="#cb48-5" aria-hidden="true" tabindex="-1"></a>                            <span class="st">"Region"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>Simply descriptive of this new data</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb47"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb47-1"><a href="#cb47-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb49"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb49-1"><a href="#cb49-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code> pct_Long_term_ill pct_No_qualifications   pct_Males    
  Min.   :11.20     Min.   : 6.721        Min.   :47.49  
@@ -618,7 +665,7 @@ <h2 data-number="3.2" class="anchored" data-anchor-id="implementing-a-linear-reg
 </div>
 <p>Simply use the function table() would return you the answer.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb49"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb49-1"><a href="#cb49-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(df<span class="sc">$</span>Region) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb51"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb51-1"><a href="#cb51-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(df<span class="sc">$</span>Region) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
  1  2  3  4  5  6  7  8  9 10 11 12 
@@ -629,22 +676,22 @@ <h2 data-number="3.2" class="anchored" data-anchor-id="implementing-a-linear-reg
 <p>The <code>table()</code> function tells us that this data frame contains 12 regions, and the number of LAs belongs to each region.</p>
 <p>Now, for better interpration of our regions with their real name rather than the code, we can create a new column named “<em>Region_label</em>” by using the following code. **R can only include the categorical variables in the <strong>factor</strong> type, so we set the new column <em>Region_label</em> in <code>factor()</code></p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb51"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb51-1"><a href="#cb51-1" aria-hidden="true" tabindex="-1"></a>df<span class="sc">$</span>Region_label <span class="ot">&lt;-</span> <span class="fu">factor</span>(df<span class="sc">$</span>Region,<span class="fu">c</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">12</span>),<span class="at">labels=</span><span class="fu">c</span>(<span class="st">"East Midlands"</span>,</span>
-<span id="cb51-2"><a href="#cb51-2" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"East of England"</span>,</span>
-<span id="cb51-3"><a href="#cb51-3" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"London"</span>,</span>
-<span id="cb51-4"><a href="#cb51-4" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"North East"</span>,</span>
-<span id="cb51-5"><a href="#cb51-5" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"North West"</span>,</span>
-<span id="cb51-6"><a href="#cb51-6" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"South East"</span>,</span>
-<span id="cb51-7"><a href="#cb51-7" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"South West"</span>,</span>
-<span id="cb51-8"><a href="#cb51-8" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"West Midlands"</span>,</span>
-<span id="cb51-9"><a href="#cb51-9" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"Yorkshire and the Humber"</span>,</span>
-<span id="cb51-10"><a href="#cb51-10" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"Wales"</span>,</span>
-<span id="cb51-11"><a href="#cb51-11" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"Scotland"</span>,</span>
-<span id="cb51-12"><a href="#cb51-12" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"Northern Ireland"</span>)) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb53"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb53-1"><a href="#cb53-1" aria-hidden="true" tabindex="-1"></a>df<span class="sc">$</span>Region_label <span class="ot">&lt;-</span> <span class="fu">factor</span>(df<span class="sc">$</span>Region,<span class="fu">c</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">12</span>),<span class="at">labels=</span><span class="fu">c</span>(<span class="st">"East Midlands"</span>,</span>
+<span id="cb53-2"><a href="#cb53-2" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"East of England"</span>,</span>
+<span id="cb53-3"><a href="#cb53-3" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"London"</span>,</span>
+<span id="cb53-4"><a href="#cb53-4" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"North East"</span>,</span>
+<span id="cb53-5"><a href="#cb53-5" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"North West"</span>,</span>
+<span id="cb53-6"><a href="#cb53-6" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"South East"</span>,</span>
+<span id="cb53-7"><a href="#cb53-7" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"South West"</span>,</span>
+<span id="cb53-8"><a href="#cb53-8" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"West Midlands"</span>,</span>
+<span id="cb53-9"><a href="#cb53-9" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"Yorkshire and the Humber"</span>,</span>
+<span id="cb53-10"><a href="#cb53-10" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"Wales"</span>,</span>
+<span id="cb53-11"><a href="#cb53-11" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"Scotland"</span>,</span>
+<span id="cb53-12"><a href="#cb53-12" aria-hidden="true" tabindex="-1"></a>                                                     <span class="st">"Northern Ireland"</span>)) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>If you re-run the table() function, the output is now more readable:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb52"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb52-1"><a href="#cb52-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(df<span class="sc">$</span>Region_label)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb54"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb54-1"><a href="#cb54-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(df<span class="sc">$</span>Region_label)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
            East Midlands          East of England                   London 
@@ -664,13 +711,13 @@ <h3 data-number="3.2.1" class="anchored" data-anchor-id="include-the-categorical
 <p>Implement the regression model with the newly created categorical variables - <em>Region_label</em> in our case. R will automatically handle the qualitative variable as dummy variables so you don’t need to concern any of that. But you need to let R knows which category of your qualitative variable is your reference category or the baseline. Here we will use London as our first go. <strong>Note:</strong> We choose London as the baseline category so the London region will be <u><strong>excluded</strong></u> in the independent variable list.</p>
 <p>Therefore, first, we set London as the reference:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb54"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb54-1"><a href="#cb54-1" aria-hidden="true" tabindex="-1"></a>df<span class="sc">$</span>Region_label <span class="ot">&lt;-</span> <span class="fu">relevel</span>(df<span class="sc">$</span>Region_label, <span class="at">ref =</span> <span class="st">"London"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb56"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb56-1"><a href="#cb56-1" aria-hidden="true" tabindex="-1"></a>df<span class="sc">$</span>Region_label <span class="ot">&lt;-</span> <span class="fu">fct_relevel</span>(df<span class="sc">$</span>Region_label,  <span class="st">"London"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>Similar to last week, we build our linear regression model, but also include the <em>Region_label</em> variable into the model.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb55"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb55-1"><a href="#cb55-1" aria-hidden="true" tabindex="-1"></a>model <span class="ot">&lt;-</span> <span class="fu">lm</span>(pct_Long_term_ill <span class="sc">~</span> pct_Males <span class="sc">+</span> pct_No_qualifications <span class="sc">+</span> pct_Higher_manager_prof <span class="sc">+</span> Region_label, <span class="at">data =</span> df)</span>
-<span id="cb55-2"><a href="#cb55-2" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb55-3"><a href="#cb55-3" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(model)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb57"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb57-1"><a href="#cb57-1" aria-hidden="true" tabindex="-1"></a>model <span class="ot">&lt;-</span> <span class="fu">lm</span>(pct_Long_term_ill <span class="sc">~</span> pct_Males <span class="sc">+</span> pct_No_qualifications <span class="sc">+</span> pct_Higher_manager_prof <span class="sc">+</span> Region_label, <span class="at">data =</span> df)</span>
+<span id="cb57-2"><a href="#cb57-2" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb57-3"><a href="#cb57-3" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(model)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
 Call:
@@ -801,13 +848,13 @@ <h3 data-number="3.2.1" class="anchored" data-anchor-id="include-the-categorical
 <h3 data-number="3.2.2" class="anchored" data-anchor-id="change-the-baseline-category"><span class="header-section-number">3.2.2</span> <strong>Change the baseline category</strong></h3>
 <p>If you would like to learn about differences in long-term illness between East of England and other regions in the UK, you need to change the baseline category (from London) to the East of England region (with variable name “Region_2”).</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb57"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb57-1"><a href="#cb57-1" aria-hidden="true" tabindex="-1"></a>df<span class="sc">$</span>Region_label <span class="ot">&lt;-</span> <span class="fu">relevel</span>(df<span class="sc">$</span>Region_label, <span class="at">ref =</span> <span class="st">"East of England"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb59"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb59-1"><a href="#cb59-1" aria-hidden="true" tabindex="-1"></a>df<span class="sc">$</span>Region_label <span class="ot">&lt;-</span> <span class="fu">fct_relevel</span>(df<span class="sc">$</span>Region_label, <span class="st">"East of England"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>The regression model is specified again as follows:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb58"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb58-1"><a href="#cb58-1" aria-hidden="true" tabindex="-1"></a>model1 <span class="ot">&lt;-</span> <span class="fu">lm</span>(pct_Long_term_ill <span class="sc">~</span> pct_Males <span class="sc">+</span> pct_No_qualifications <span class="sc">+</span> pct_Higher_manager_prof <span class="sc">+</span> Region_label, <span class="at">data =</span> df)</span>
-<span id="cb58-2"><a href="#cb58-2" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb58-3"><a href="#cb58-3" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(model1)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb60"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb60-1"><a href="#cb60-1" aria-hidden="true" tabindex="-1"></a>model1 <span class="ot">&lt;-</span> <span class="fu">lm</span>(pct_Long_term_ill <span class="sc">~</span> pct_Males <span class="sc">+</span> pct_No_qualifications <span class="sc">+</span> pct_Higher_manager_prof <span class="sc">+</span> Region_label, <span class="at">data =</span> df)</span>
+<span id="cb60-2"><a href="#cb60-2" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb60-3"><a href="#cb60-3" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(model1)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
 Call:
@@ -905,42 +952,49 @@ <h3 data-number="3.2.3" class="anchored" data-anchor-id="recode-the-region-varia
 </table>
 <p>Here we use mutate() function in R to make it happen:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb60"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb60-1"><a href="#cb60-1" aria-hidden="true" tabindex="-1"></a>df <span class="ot">&lt;-</span> df <span class="sc">%&gt;%</span> <span class="fu">mutate</span>(<span class="at">New_region_label =</span> <span class="fu">if_else</span>(<span class="sc">!</span>Region_label <span class="sc">%in%</span> <span class="fu">c</span>(<span class="st">"London"</span>,<span class="st">"Wales"</span>,<span class="st">"Scotland"</span>,<span class="st">"Northern Ireland"</span>), <span class="st">"Other regions in England"</span>,Region_label))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb62"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb62-1"><a href="#cb62-1" aria-hidden="true" tabindex="-1"></a>df <span class="ot">&lt;-</span> df <span class="sc">%&gt;%</span> <span class="fu">mutate</span>(<span class="at">New_region_label =</span> <span class="fu">fct_other</span>(Region_label, <span class="at">keep=</span><span class="fu">c</span>(<span class="st">"London"</span>,<span class="st">"Wales"</span>,<span class="st">"Scotland"</span>,<span class="st">"Northern Ireland"</span>), <span class="at">other_level=</span><span class="st">"Other regions in England"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>This code may looks a bit complex. You can simply type ?mutate in your console. Now in your right hand Help window, the R studio offers your the explanation of the mutate function. This is a common way you can use R studio to help you learn what the function ca<code>ate()</code> creates new columns that are functions of existing variables. Therefore, the <code>df %&gt;% mutate()</code> means add a new column into the current dataframe <code>df</code>; the <code>New_region_label</code> in the <code>mutate()</code> function indicates the name of this new column is <code>New_region_label</code>. The right side of the <code>New_region_label =</code> indicates the value we want to assign to the <code>New_region_label</code> in each row.</p>
 <p>The right side of <code>New_region_label</code> is</p>
-<p><code>if_else(!Region_label %in% c("London","Wales","Scotland","Northern Ireland"), "Other regions in England",Region_label))</code></p>
-<p>By using the code, the <code>if_else()</code> function checks whether each value in the <code>Region_label</code> column is <strong>not</strong> (<code>!</code>)one of the specified regions: “London”, “Wales”, “Scotland”, or “Northern Ireland”. If the region is not in this list, the value is replaced with the label “Other regions in England”. If the region is one of these four, the original value in <code>Region_label</code> is retained. This process categorizes regions that are outside of the four specified ones into a new group labeled “Other regions in England”, while preserving the original labels for the specified regions.</p>
+<p><code>fct_other(Region_label, keep=c("London","Wales","Scotland","Northern Ireland"), other_level="Other regions in England")</code></p>
+<p>By using the code, the <code>fct_other()</code> function checks whether each value in the <code>Region_label</code> column is one of the <strong>keep</strong> regions: “London”, “Wales”, “Scotland”, or “Northern Ireland”. If the region is not in this list, the value is replaced with the label “Other regions in England”. If the region is one of these four, the original value in <code>Region_label</code> is kept. This process categorizes regions that are outside of the four specified ones into a new group labeled “Other regions in England”, while preserving the original labels for the specified regions.</p>
 <p>Now we use the same way to examine our new column <code>New_region_label</code>:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb61"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb61-1"><a href="#cb61-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(df<span class="sc">$</span>New_region_label)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb63"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb63-1"><a href="#cb63-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(df<span class="sc">$</span>New_region_label)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
-                  London         Northern Ireland Other regions in England 
-                      33                       26                      293 
-                Scotland                    Wales 
-                      32                       22 </code></pre>
+                  London                    Wales                 Scotland 
+                      33                       22                       32 
+        Northern Ireland Other regions in England 
+                      26                      293 </code></pre>
 </div>
 </div>
 <p>Comparing with the <code>Region_label</code>, we now can see the mutate worked:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb63"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb63-1"><a href="#cb63-1" aria-hidden="true" tabindex="-1"></a>df[,<span class="fu">c</span>(<span class="st">"Region_label"</span>,<span class="st">"New_region_label"</span>)]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb65"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb65-1"><a href="#cb65-1" aria-hidden="true" tabindex="-1"></a>df[,<span class="fu">c</span>(<span class="st">"Region_label"</span>,<span class="st">"New_region_label"</span>)]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>Now you will have a new qualitative variable named <code>New_region_label</code> in which the UK is divided into five regions: London, Other regions in England, Wales, Scotland and Northern Ireland.</p>
 <p><em>Based on the newly generated qualitative variable</em> <code>New_region_label</code>, we can now build our new linear regression model. Don’t forget:</p>
 <p>(1) R need to deal with the categorical variables in regression model in the factor type;</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb64"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb64-1"><a href="#cb64-1" aria-hidden="true" tabindex="-1"></a>df<span class="sc">$</span>New_region_label <span class="ot">=</span> <span class="fu">as.factor</span>(df<span class="sc">$</span>New_region_label)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb66"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb66-1"><a href="#cb66-1" aria-hidden="true" tabindex="-1"></a><span class="fu">class</span>(df<span class="sc">$</span>New_region_label)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>[1] "factor"</code></pre>
+</div>
+</div>
+<p>The <code>class()</code> returns the type of the variable. The <code>New_region_label</code> is already a factor variable. If not, we need to convert it by the <code>as.factor()</code>, as we used above.</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb68"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb68-1"><a href="#cb68-1" aria-hidden="true" tabindex="-1"></a>df<span class="sc">$</span>New_region_label <span class="ot">=</span> <span class="fu">as.factor</span>(df<span class="sc">$</span>New_region_label)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>2) Let R know which region you want to use as the baseline category. Here I will use London again, but of course you can choose other regions.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb65"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb65-1"><a href="#cb65-1" aria-hidden="true" tabindex="-1"></a>df<span class="sc">$</span>New_region_label <span class="ot">&lt;-</span> <span class="fu">relevel</span>(df<span class="sc">$</span>New_region_label, <span class="at">ref =</span> <span class="st">"London"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb69"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb69-1"><a href="#cb69-1" aria-hidden="true" tabindex="-1"></a>df<span class="sc">$</span>New_region_label <span class="ot">&lt;-</span> <span class="fu">fct_relevel</span>(df<span class="sc">$</span>New_region_label, <span class="st">"London"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>The linear regression window is set up below. This time we include <code>New_region_label</code> rather than <code>Region_label</code> as the region variable:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb66"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb66-1"><a href="#cb66-1" aria-hidden="true" tabindex="-1"></a>model2 <span class="ot">&lt;-</span> <span class="fu">lm</span>(pct_Long_term_ill <span class="sc">~</span> pct_Males <span class="sc">+</span> pct_No_qualifications <span class="sc">+</span> pct_Higher_manager_prof <span class="sc">+</span> New_region_label, <span class="at">data =</span> df)</span>
-<span id="cb66-2"><a href="#cb66-2" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb66-3"><a href="#cb66-3" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(model2)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb70"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb70-1"><a href="#cb70-1" aria-hidden="true" tabindex="-1"></a>model2 <span class="ot">&lt;-</span> <span class="fu">lm</span>(pct_Long_term_ill <span class="sc">~</span> pct_Males <span class="sc">+</span> pct_No_qualifications <span class="sc">+</span> pct_Higher_manager_prof <span class="sc">+</span> New_region_label, <span class="at">data =</span> df)</span>
+<span id="cb70-2"><a href="#cb70-2" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb70-3"><a href="#cb70-3" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(model2)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
 Call:
@@ -957,19 +1011,19 @@ <h3 data-number="3.2.3" class="anchored" data-anchor-id="recode-the-region-varia
 pct_Males                                -0.834471   0.113398  -7.359 1.07e-12
 pct_No_qualifications                     0.472354   0.032764  14.417  &lt; 2e-16
 pct_Higher_manager_prof                   0.000497   0.040851   0.012 0.990300
+New_region_labelWales                     4.345262   0.471088   9.224  &lt; 2e-16
+New_region_labelScotland                  0.143672   0.442989   0.324 0.745863
 New_region_labelNorthern Ireland          0.264425   0.474074   0.558 0.577314
 New_region_labelOther regions in England  1.071719   0.312746   3.427 0.000674
-New_region_labelScotland                  0.143672   0.442989   0.324 0.745863
-New_region_labelWales                     4.345262   0.471088   9.224  &lt; 2e-16
                                             
 (Intercept)                              ***
 pct_Males                                ***
 pct_No_qualifications                    ***
 pct_Higher_manager_prof                     
+New_region_labelWales                    ***
+New_region_labelScotland                    
 New_region_labelNorthern Ireland            
 New_region_labelOther regions in England ***
-New_region_labelScotland                    
-New_region_labelWales                    ***
 ---
 Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 
@@ -1001,21 +1055,21 @@ <h2 data-number="3.4" class="anchored" data-anchor-id="income-inequality-with-re
 <p>To explore income inequality, we need to work with a data set excluding dependent children. In addition, we look at individuals who are the representative persons of households. Therefore, we will select cases (or samples) that meet both conditions.</p>
 <p>We want R to select persons only if they are the representative persons of households and they are not dependent children. The involved variables are <code>hrp</code> and <code>Dependent</code> for the categories “Household Reference Person” and “independent”, you can select the appropriate cases. We also want to exclude the health variable reported as “Not known”.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb68"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb68-1"><a href="#cb68-1" aria-hidden="true" tabindex="-1"></a>frs_df <span class="ot">&lt;-</span> frs_data <span class="sc">%&gt;%</span> <span class="fu">filter</span>(hrp<span class="sc">==</span><span class="st">"HRP"</span> <span class="sc">&amp;</span> dependent<span class="sc">==</span><span class="st">"Independent"</span> <span class="sc">&amp;</span> health<span class="sc">!=</span><span class="st">"Not known"</span>) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb72"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb72-1"><a href="#cb72-1" aria-hidden="true" tabindex="-1"></a>frs_df <span class="ot">&lt;-</span> frs_data <span class="sc">%&gt;%</span> <span class="fu">filter</span>(hrp<span class="sc">==</span><span class="st">"HRP"</span> <span class="sc">&amp;</span> dependent<span class="sc">==</span><span class="st">"Independent"</span> <span class="sc">&amp;</span> health<span class="sc">!=</span><span class="st">"Not known"</span>) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>Then, we create a new numeric variable <code>Net_inc_perc</code> indicate net income per capita as our dependent variable:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb69"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb69-1"><a href="#cb69-1" aria-hidden="true" tabindex="-1"></a>frs_df<span class="sc">$</span>Net_inc_perc <span class="ot">=</span> frs_df<span class="sc">$</span>hh_income_net <span class="sc">/</span> frs_df<span class="sc">$</span>hh_size</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb73"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb73-1"><a href="#cb73-1" aria-hidden="true" tabindex="-1"></a>frs_df<span class="sc">$</span>Net_inc_perc <span class="ot">=</span> frs_df<span class="sc">$</span>hh_income_net <span class="sc">/</span> frs_df<span class="sc">$</span>hh_size</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>Our two qualitative independent variables “<code>sex</code>” and “<code>health</code>”. Let’s first know what they look like:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb70"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb70-1"><a href="#cb70-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_df<span class="sc">$</span>sex)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb74"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb74-1"><a href="#cb74-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_df<span class="sc">$</span>sex)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
 Female   Male 
   7647   9180 </code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb72"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb72-1"><a href="#cb72-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_df<span class="sc">$</span>health)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb76"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb76-1"><a href="#cb76-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(frs_df<span class="sc">$</span>health)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
       Bad      Fair      Good  Very Bad Very Good 
@@ -1024,13 +1078,13 @@ <h2 data-number="3.4" class="anchored" data-anchor-id="income-inequality-with-re
 </div>
 <p>Remember what we did in the Region long-term illness practical previously before we put the qualitative variable into the regression model? Yes. First, make sure they are in factor type and Second, decide the reference category. Here, I will use Male and Fair health status as my base categories. You can decide what you wish to use. This time, I use the following codes to combine these two steps in one line.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb74"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb74-1"><a href="#cb74-1" aria-hidden="true" tabindex="-1"></a>frs_df<span class="sc">$</span>sex <span class="ot">&lt;-</span> <span class="fu">relevel</span>(<span class="fu">as.factor</span>(frs_df<span class="sc">$</span>sex), <span class="at">ref =</span> <span class="st">"Male"</span>)</span>
-<span id="cb74-2"><a href="#cb74-2" aria-hidden="true" tabindex="-1"></a>frs_df<span class="sc">$</span>health <span class="ot">&lt;-</span> <span class="fu">relevel</span>(<span class="fu">as.factor</span>(frs_df<span class="sc">$</span>health), <span class="at">ref =</span> <span class="st">"Fair"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb78"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb78-1"><a href="#cb78-1" aria-hidden="true" tabindex="-1"></a>frs_df<span class="sc">$</span>sex <span class="ot">&lt;-</span> <span class="fu">relevel</span>(<span class="fu">as.factor</span>(frs_df<span class="sc">$</span>sex), <span class="at">ref =</span> <span class="st">"Male"</span>)</span>
+<span id="cb78-2"><a href="#cb78-2" aria-hidden="true" tabindex="-1"></a>frs_df<span class="sc">$</span>health <span class="ot">&lt;-</span> <span class="fu">relevel</span>(<span class="fu">as.factor</span>(frs_df<span class="sc">$</span>health), <span class="at">ref =</span> <span class="st">"Fair"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>Implement the regression model with the two qualitative independent variables.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb75"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb75-1"><a href="#cb75-1" aria-hidden="true" tabindex="-1"></a>model_frs <span class="ot">&lt;-</span> <span class="fu">lm</span>(Net_inc_perc <span class="sc">~</span> sex <span class="sc">+</span> health, <span class="at">data =</span> frs_df)</span>
-<span id="cb75-2"><a href="#cb75-2" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(model_frs)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb79"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb79-1"><a href="#cb79-1" aria-hidden="true" tabindex="-1"></a>model_frs <span class="ot">&lt;-</span> <span class="fu">lm</span>(Net_inc_perc <span class="sc">~</span> sex <span class="sc">+</span> health, <span class="at">data =</span> frs_df)</span>
+<span id="cb79-2"><a href="#cb79-2" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(model_frs)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
 Call:
@@ -1058,8 +1112,8 @@ <h2 data-number="3.4" class="anchored" data-anchor-id="income-inequality-with-re
 </div>
 <p>The result can be formatted by:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb77"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb77-1"><a href="#cb77-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(broom)</span>
-<span id="cb77-2"><a href="#cb77-2" aria-hidden="true" tabindex="-1"></a><span class="fu">tidy</span>(model_frs)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb81"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb81-1"><a href="#cb81-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(broom)</span>
+<span id="cb81-2"><a href="#cb81-2" aria-hidden="true" tabindex="-1"></a><span class="fu">tidy</span>(model_frs)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code># A tibble: 6 × 5
   term            estimate std.error statistic  p.value
@@ -1093,14 +1147,14 @@ <h2 data-number="3.5" class="anchored" data-anchor-id="extension-activities"><sp
 <p>the model of London will be: <em>pct_Long_term_ill</em> (%) <em>= 47.218+ (-0.834)* 49 + 0.472 * 23 + 1.072*0+ 4.345* 0 = 17.208</em></p>
 <p>You can also make a new object like</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb79"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb79-1"><a href="#cb79-1" aria-hidden="true" tabindex="-1"></a>obj_London <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(<span class="at">pct_Males =</span> <span class="dv">49</span>, <span class="at">pct_No_qualifications=</span><span class="dv">23</span>,<span class="at">pct_Higher_manager_prof =</span><span class="dv">11</span>, <span class="at">New_region_label =</span><span class="st">"London"</span>)</span>
-<span id="cb79-2"><a href="#cb79-2" aria-hidden="true" tabindex="-1"></a>obj_Wales <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(<span class="at">pct_Males =</span> <span class="dv">49</span>, <span class="at">pct_No_qualifications=</span><span class="dv">23</span>,<span class="at">pct_Higher_manager_prof =</span><span class="dv">11</span>, <span class="at">New_region_label =</span><span class="st">"Wales"</span>)</span>
-<span id="cb79-3"><a href="#cb79-3" aria-hidden="true" tabindex="-1"></a><span class="fu">predict</span>(model2,obj_London)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb83"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb83-1"><a href="#cb83-1" aria-hidden="true" tabindex="-1"></a>obj_London <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(<span class="at">pct_Males =</span> <span class="dv">49</span>, <span class="at">pct_No_qualifications=</span><span class="dv">23</span>,<span class="at">pct_Higher_manager_prof =</span><span class="dv">11</span>, <span class="at">New_region_label =</span><span class="st">"London"</span>)</span>
+<span id="cb83-2"><a href="#cb83-2" aria-hidden="true" tabindex="-1"></a>obj_Wales <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(<span class="at">pct_Males =</span> <span class="dv">49</span>, <span class="at">pct_No_qualifications=</span><span class="dv">23</span>,<span class="at">pct_Higher_manager_prof =</span><span class="dv">11</span>, <span class="at">New_region_label =</span><span class="st">"Wales"</span>)</span>
+<span id="cb83-3"><a href="#cb83-3" aria-hidden="true" tabindex="-1"></a><span class="fu">predict</span>(model2,obj_London)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>       1 
 17.19808 </code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb81"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb81-1"><a href="#cb81-1" aria-hidden="true" tabindex="-1"></a><span class="fu">predict</span>(model2,obj_Wales)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb85"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb85-1"><a href="#cb85-1" aria-hidden="true" tabindex="-1"></a><span class="fu">predict</span>(model2,obj_Wales)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>       1 
 21.54334 </code></pre>
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index b8a5c6f..cf8a61b 100644
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diff --git a/labs/03.QualitativeVariable.qmd b/labs/03.QualitativeVariable.qmd
index f1fbb6b..b5258a7 100644
--- a/labs/03.QualitativeVariable.qmd
+++ b/labs/03.QualitativeVariable.qmd
@@ -1,5 +1,5 @@
 ---
-title: "Correlation and Multiple Linear Regression with Qualitative Variables"
+title: "Lab: Correlation and Multiple Linear Regression with Qualitative Variables"
 author: "Zi Ye"
 date: "`r Sys.Date()`"
 output: html_document
@@ -41,7 +41,7 @@ Recall in Week 7, you get familiar to R by using the Family Resource Survey data
 
 Check your working directory by
 
-```{r}
+```{r,results='hide',message=FALSE}
 getwd()
 ```
 
@@ -49,36 +49,54 @@ Check the relative path of your data folder on your PC/laptop, make sure you kno
 
 **Library knowledge used in today:**
 
-dplyr: a basic library provides a suite of functions for data manipulation
+-   **`dplyr`**: a basic library provides a suite of functions for data manipulation
+
+-   **`ggplot2`**: a widely-used data visualisation library to help you create nice plots through layered plotting.
+
+-   **`tidyverse`**: a collection of R packages designed for data science, offering a cohesive framework for data manipulation, visualization, and analysis. Containing dyplyr, ggplot2 and other basic libraries.
 
-ggplot2: a widely-used data visualisation library to help you create nice plots through layered plotting.
+-   **`broom`**: a part of the tidyverse and is designed to convert statistical analysis results into tidy data frames.
 
-tidyverse: a collection of R packages designed for data science, offering a cohesive framework for data manipulation, visualization, and analysis. Containing dyplyr, ggplot2 and other basic libraries.
+-   **`forcats`**: designed to work with factors, which are used to represent categorical data. It simplifies the process of creating, modifying, and ordering factors.
 
-broom: a part of the tidyverse and is designed to convert statistical analysis results into tidy data frames.
+-   **`vcd`**: visualise and analyse categorical data.
 
 ### Data overview
 
-```{r,results='hide',message=FALSE}
+```{r,warning=FALSE}
 if(!require("dplyr"))
-  install.packages("dplyr")
+  install.packages("dplyr",dependencies = T)
 # Load necessary libraries 
 if(!require("ggplot2"))
-  install.packages("ggplot2")
+  install.packages("ggplot2",dependencies = T)
+if(!require("broom"))
+  install.packages("broom",dependencies = T)
+
 
 library(dplyr) 
-library(ggplot2) 
+library(ggplot2)
+library(broom)
+
 ```
 
-Or we can use library `tidyverse` which complies `ggplot2`, `dplyr` and other foundamental libraries together already, remember you need first install the package if you haven't by using `install.packages("tidyverse")`.
+Or we can use library `tidyverse` which includes `ggplot2`, `dplyr,broom` and other foundamental libraries together already, remember you need first install the package if you haven't by using `install.packages("tidyverse")`.
 
-```{r,results='hide',message=FALSE}
+```{r,warning=FALSE}
 if(!require("tidyverse"))
-  install.packages("tidyverse")
+  install.packages("tidyverse",dependencies = T)
 
 library(tidyverse)
 ```
 
+We will also use forcat library, so
+
+```{r,warning=FALSE}
+if(!require("forcats"))
+  install.packages("forcats")
+
+library(forcats)
+```
+
 Exactly as you did in previous weeks, we first load in the dataset:
 
 ```{r}
@@ -137,6 +155,18 @@ ggplot(frs_data, aes(x = nssec)) +
  
 ```
 
+If we want to reorder the Y axis by from highest to lowest, we use the functions in `forcats` library. `fct_infreq()`: orders by the value's frequency of the variable `nssec`. `fct_rev()`: reverses the order to go from highest to lowest.
+
+```{r}
+ggplot(frs_data, aes(x = fct_rev(fct_infreq(nssec)))) + 
+  geom_bar(fill = "yellow4") + 
+  labs(title = "Histogram of NSSEC in FRS", x = "NSSEC", y = "Count") +
+  coord_flip()+ #Flip the Axes, add a # in front of this line, to make the code in gray and you will see why we would better flip the axes at here
+  theme_bw() 
+ 
+
+```
+
 You can change the variables in ggplot() to make your own histogram chart for the variables you are interested in. You will learn more of visualisation methods in Week11's practical.
 
 ### Correlation
@@ -162,11 +192,17 @@ If you see a warning message of Chi-squared approximation may be incorrect. This
 ```{r}
 # Install the 'vcd' package if not installed 
 if(!require("vcd"))   
-install.packages("vcd", repos = "https://cran.r-project.org")
+install.packages("vcd", repos = "https://cran.r-project.org", dependencies = T)
 library(vcd)  
 
+# creat the crosstable 
+crosstab <- table(frs_data$health, frs_data$happy)
+
 # Calculate Cramér's V 
-assocstats(table(frs_data$health, frs_data$happy))
+assocstats(crosstab)
+
+#you can also directly calculate the assoication between variables
+assocstats(table(frs_data$health, frs_data$age_group))
 ```
 
 ::: {style="background-color: #FFFBCC; padding: 10px; border-radius: 5px; border: 1px solid #E1C948;"}
@@ -289,7 +325,7 @@ Implement the regression model with the newly created categorical variables - *R
 Therefore, first, we set London as the reference:
 
 ```{r}
-df$Region_label <- relevel(df$Region_label, ref = "London")
+df$Region_label <- fct_relevel(df$Region_label,  "London")
 ```
 
 Similar to last week, we build our linear regression model, but also include the *Region_label* variable into the model.
@@ -347,7 +383,7 @@ Now, complete the following table.
 If you would like to learn about differences in long-term illness between East of England and other regions in the UK, you need to change the baseline category (from London) to the East of England region (with variable name “Region_2”).
 
 ```{r}
-df$Region_label <- relevel(df$Region_label, ref = "East of England")
+df$Region_label <- fct_relevel(df$Region_label, "East of England")
 ```
 
 The regression model is specified again as follows:
@@ -381,16 +417,16 @@ In many real-word studies, we might not be interested in health inequality acros
 Here we use mutate() function in R to make it happen:
 
 ```{r}
-df <- df %>% mutate(New_region_label = if_else(!Region_label %in% c("London","Wales","Scotland","Northern Ireland"), "Other regions in England",Region_label))
+df <- df %>% mutate(New_region_label = fct_other(Region_label, keep=c("London","Wales","Scotland","Northern Ireland"), other_level="Other regions in England"))
 ```
 
 This code may looks a bit complex. You can simply type ?mutate in your console. Now in your right hand Help window, the R studio offers your the explanation of the mutate function. This is a common way you can use R studio to help you learn what the function ca`ate()` creates new columns that are functions of existing variables. Therefore, the `df %>% mutate()` means add a new column into the current dataframe `df`; the `New_region_label` in the `mutate()` function indicates the name of this new column is `New_region_label`. The right side of the `New_region_label =` indicates the value we want to assign to the `New_region_label` in each row.
 
 The right side of `New_region_label` is
 
-`if_else(!Region_label %in% c("London","Wales","Scotland","Northern Ireland"), "Other regions in England",Region_label))`
+`fct_other(Region_label, keep=c("London","Wales","Scotland","Northern Ireland"), other_level="Other regions in England")`
 
-By using the code, the `if_else()` function checks whether each value in the `Region_label` column is **not** (`!`)one of the specified regions: "London", "Wales", "Scotland", or "Northern Ireland". If the region is not in this list, the value is replaced with the label "Other regions in England". If the region is one of these four, the original value in `Region_label` is retained. This process categorizes regions that are outside of the four specified ones into a new group labeled "Other regions in England", while preserving the original labels for the specified regions.
+By using the code, the `fct_other()` function checks whether each value in the `Region_label` column is one of the **keep** regions: "London", "Wales", "Scotland", or "Northern Ireland". If the region is not in this list, the value is replaced with the label "Other regions in England". If the region is one of these four, the original value in `Region_label` is kept. This process categorizes regions that are outside of the four specified ones into a new group labeled "Other regions in England", while preserving the original labels for the specified regions.
 
 Now we use the same way to examine our new column `New_region_label`:
 
@@ -410,6 +446,12 @@ Now you will have a new qualitative variable named `New_region_label` in which t
 
 \(1\) R need to deal with the categorical variables in regression model in the factor type;
 
+```{r}
+class(df$New_region_label)
+```
+
+The `class()` returns the type of the variable. The `New_region_label` is already a factor variable. If not, we need to convert it by the `as.factor()`, as we used above.
+
 ```{r}
 df$New_region_label = as.factor(df$New_region_label)
 ```
@@ -417,7 +459,7 @@ df$New_region_label = as.factor(df$New_region_label)
 2\) Let R know which region you want to use as the baseline category. Here I will use London again, but of course you can choose other regions.
 
 ```{r}
-df$New_region_label <- relevel(df$New_region_label, ref = "London")
+df$New_region_label <- fct_relevel(df$New_region_label, "London")
 ```
 
 The linear regression window is set up below. This time we include `New_region_label` rather than `Region_label` as the region variable: