<p>Learn the fundamentals of R programming language and how to start using it for finance.​</p>



<p>In this course you will learn the fundamentals of R programming language and how to start using it for finance.</p>



<p>R is one of the leading programming languages used in the financial industry where professionals have applied and used R in various areas such as analyzing financial data, building and evaluate statistical models, constructing optimized portfolios, credit risk modelling and more. R has become a tool of choice for financial professionals in their everyday data analysis needs. As the importance of analytics and data science continues to grow in the financial sector, every finance professional will boost their career by having R programming skills in their arsenal.</p>



<p>In this course, we will start with the basics of R programming starting with how to setup the tools to work with r programming. Then we will learn the basic concepts in R programming, starting from variables and basic operations, and then moving on to handling data structures such as vectors, matrices, data frames and lists.</p>

<p>R is one of the leading programming languages used in the financial industry where professionals have applied and used R in various areas such as analyzing financial data, building and evaluate statistical models, constructing optimized portfolios, credit risk modelling and more. R has become a tool of choice for financial professionals in their everyday data analysis needs. As the importance of analytics and data science continues to grow in the financial sector, every finance professional will boost their career by having R programming skills in their arsenal.</p>



<p>In this course, we will start with the basics of R programming starting with how to setup the tools to work with r programming. Then we will learn the basic concepts in R programming, starting from variables and basic operations, and then moving on to handling data structures such as vectors, matrices, data frames and lists.</p>



<h3>Installing R</h3>



<p>You can install R on any computer whether it is running Windows, Mac or Linux.</p>



<h2>Step 1: Download Software</h2>



<p>Download the R software by visiting the Comprehensive R Archive Network (CRAN) at this URL:</p>



<p><a href="https://cran.r-project.org/" target="_blank" aria-label="undefined (opens in a new tab)" rel="noreferrer noopener nofollow">https://cran.r-project.org/</a></p>



<p>Make sure that you download the file relevant for your operating system:</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img src="https://financetrain.com/wp-content/uploads/r-download-page.png" alt="" class="wp-image-27412"/><figcaption>R Download Page</figcaption></figure></div>



<h3>Download R for Windows</h3>



<ol><li>Under “<strong>Download and Install R</strong>”, click on the “Windows” link.</li><li>Under “<strong>Subdirectories</strong>”, click on the “<strong>base</strong>” link.</li><li>On the next page, you should see a link saying something like “<strong>Download R 3.3.2 for Windows</strong>”<em>&nbsp;(or R X.X.X, where X.X.X gives the version of R, eg. R 3.3.2)</em>. Click on this link.</li><li>You may be asked if you want to save or run a file “<strong>R-3.3.2-win.exe</strong>”. Choose “<strong>Save</strong>” and save the file on the Desktop.</li></ol>



<h3>Download R for Mac</h3>



<ol><li>Under “<strong>Download and Install R</strong>”, click on the “<strong>Mac</strong>” link.</li><li>On the next page, under filesyou should see a link saying something like “<strong>R-3.3.2.pkg</strong>”&nbsp;<em>(or R X.X.X, where X.X.X gives the version of R, eg. R 3.3.2)</em>. Click on this link.</li><li>You may be asked if you want to save or run a file “<strong>R-3.3.2.pkg</strong>”. Choose “<strong>Save</strong>” and save the file on the Desktop.</li></ol>



<h2>Step 2: Install the Software</h2>



<p>Installation of R is quite simple. Below instructions will guide you on how to install R on Windows and Mac operating system.</p>



<h3>Install R on Windows</h3>



<ol><li>Double-click on the icon for the downloaded file (R-X.X.X-win.exe) to run it.</li><li>When the window opens, select a language (e.g., English) and click ‘OK’.</li><li>The R Setup Wizard will appear in a window. Click “Next” at the bottom of the R Setup wizard window.</li><li>Click Next to continue.</li><li>On the next screen you will be asked to select a destination location. By defauly a location such as ‘C:\Program Files\R\R-3.3.2’, will already be filled. Leave the location as is and click next to continue.</li><li>On the next screen you will be asked to select Components. Keep all compnonents selected, and click Next.</li><li>The next page says “Startup options” at the top. Keep the default option of ‘No’. Click “Next” again.</li><li>The next page says “Select start menu folder” at the top. Click “Next” again.</li><li>The next page says “Select additional tasks” at the top. Click “Next” again.</li><li>R will now start installing. This will take about a minute. When R has finished, you will see “Completing the R for Windows Setup Wizard” appear. Click “Finish”.</li></ol>



<h3>Install R on Mac</h3>



<ol><li>Double-click on the icon for the downloaded file (R-X.X.X.pkg) to run it.</li><li>When the window opens, select a language (e.g., English) and click ‘OK’.</li></ol>



<h2>Start R</h2>



<p>You can now start R by double clicking on the R icon your desktop. The R console (a rectangle) should pop up:</p>



<figure class="wp-block-image size-large"><img src="https://financetrain.com/wp-content/uploads/r-console-window.png" alt="R Console" class="wp-image-27413"/><figcaption>R Console</figcaption></figure>



<p><em>Note that R works exactly the same on both Mac and Windows. There are some minor UI differences, however, the functionality is exactly the same.</em></p>

Installing R Software on Your Computer

<p>Now that you have R running on your system and you can see the R console, let’s start by having r do some basic arithmetic for us. We can perform all arithmetic operations in R as you would do on a regular calculator.</p>



<p>Let’s begin by clearing the console screen. To do so press CTRL+L. This will clear everything from console.</p>



<p>Consider the following arithmetic operators:</p>



<ul><li>Addition:&nbsp;<code>+</code></li><li>Subtraction:&nbsp;<code>-</code></li><li>Multiplication:&nbsp;<code>*</code></li><li>Division:&nbsp;<code>/</code></li><li>Exponentiation:&nbsp;<code>^</code></li><li>Modulo:&nbsp;<code>%%</code></li></ul>



<p>To calculate the sum of 3 and 5, simply type 3 + 5 in the console and hit Enter. R will compile what you<br>typed, calculate the result and print that result as a numerical value.</p>



<p>Similarly, you can type a string (which is entered in quotes) and hit enter and R will output the result as a string. R understands your input and distinguishes between character string and numerical value.</p>



<p>The other arithmetic operators work in the same way. Try the following in your R console.</p>



<ul><li>Type&nbsp;<code>5-3</code>&nbsp;in the R console to calculate the difference between 5 and 3.</li><li>Type&nbsp;<code>5*3</code>&nbsp;in the R console to calculate the product of 5 and 3.</li><li>Type&nbsp;<code>5/3</code>&nbsp;in the R console to divide 5 by 3</li><li>Type&nbsp;<code>3^5</code>&nbsp;in the editor to calculate 3 to the power 5.</li><li>Type&nbsp;<code>26 %% 3</code>&nbsp;to calculate 26 modulo 3.</li></ul>



<p>The last one, the&nbsp;<em>modulo</em>&nbsp;operation, finds the remainder after division of one number by another. The above expression 26 modulo 3 would evaluate to 2 because 26 divided by 3 leaves a quotient of 8 and a remainder of 2.</p>



<h3>Adding comments</h3>



<p>While writing programs, it is important to add comments in various places so that when you are reviewing a program in future, the comments can help you understand your program.</p>



<p>To add a comment, add the symbol # before the text that you want to show as comment.</p>



<p>For example:</p>



<p><code># This is a comment</code></p>

Performing Basic Math Operations in R

<p>When beginning to work with R code, the first thing that you need to do is setup a working directory. A working directory is a location on on your computer from which R will read and write files to. You can choose any location/folder on your computer where you want to save your code and set that as the working directory.</p>



<p>The following example shows how to set the working directory in R to the folder <code>"C:\r-programming\data"</code> on the C drive in Windows.</p>



<pre class="wp-block-code"><code># Set the working directory
setwd("C:/r-programming/data")</code></pre>



<p><strong>Note: </strong>You need to first create a directory called r-programming and then another directory within it called 'data'. Check that you are able to access this directory "C:/r-programming/data" from Windows Explorer. Once the directory exists, you will be able to use the setwd() command to set that as the working directory.</p>



<p>An example for Mac:</p>



<pre class="wp-block-code"><code>setwd("/Users/User Name/Documents/FOLDER")</code></pre>



<p>Note that you must use the forward slash / or double backslash \\ in R! The Windows format of single backslash will not work.</p>



<p>You can check that your working directory has been correctly set by using the function&nbsp;<code>getwd()</code>&nbsp;as shown below:</p>



<pre class="wp-block-code"><code>> getwd()
&#91;1] "C:/r-programming/data"
></code></pre>



<p>Once you've set a working directory, you can then further navigate to a subfolder by using the same command. In this example, I have a sub-folder called 'arithmetic' where I some r code.</p>



<pre class="wp-block-code"><code>> getwd()
&#91;1] "C:/r-programming/data"
> setwd("arithmetic")
> getwd()
&#91;1] "C:/r-programming/data/arithmetic"</code></pre>



<p>If you want to move back to the parent directory, you can do it as follows:</p>



<pre class="wp-block-code"><code>> setwd("../")
> getwd()
&#91;1] "C:/r-programming/data"</code></pre>



<p class="tip-box"><code>..</code>&nbsp;means the parent directory, so it goes one level up there</p>



<p>Once we are in a particular folder you read and write files in that folder from R.</p>



<p>We can type the command&nbsp;<code>dir()</code>&nbsp;to get a list of files in that folder.</p>



<pre class="wp-block-code"><code>> getwd()
&#91;1] "C:/r-programming/data"
> setwd("arithmetic")
> getwd()
&#91;1] "C:/r-programming/data/arithmetic"
> dir()
&#91;1] "arithmetic-examples.r"
></code></pre>



<p>As you can see we have a file called&nbsp;<code>arithmetic-examples.r</code>&nbsp;in the&nbsp;<code>'data/arithmetic'</code>&nbsp;folder.</p>

Setting Up a Working Directory in R

<p>While R comes with a neat console that you can use for all your R programming needs, you can compliment it with RStudio which is a Gui built on top of R and makes it very easy to manage your programming requirements.</p>



<h3>Installing RStudio</h3>



<p>You can download RStudio from the following link:</p>



<p><a href="https://www.rstudio.com/products/rstudio/download/" target="_blank" label="undefined (opens in a new tab)" rel="noreferrer noopener nofollow">https://www.rstudio.com/products/rstudio/download/</a></p>



<p>On the page you will come across multiple choices for downloading the software.</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img src="https://financetrain.com/wp-content/uploads/rstudio-download.png" alt="" class="wp-image-27422"/></figure></div>



<ul><li>From a licensing perspective, there is a personal license (which is free) and then there is a commercial license. For our purpose, you need the personal license.</li><li>Also, there are two versions for the software: 1) RStudio Desktop and 2) RStudio Server. For now, you just need to download RStudio Desktop.</li></ul>



<p>So, among all the choices available, you will need to download RStudio Desktop with Personal License.</p>



<p>When you click the download button, it will present you with a choice of download files. You must download the file suitable for your operating system.</p>



<p><em>It is preferred to download Installers rather than Zip/Tarballs or Source Code.</em></p>



<p>Click the relevant file and the download will begin.</p>



<p>Once the installer is downloaded, click on it and install it. Follow the onscreen instructions to complete the installation. Once installed, open the application and now you’re running RStudio.</p>



<p>You can quickly try some arithmetic to get the idea of how to use the interface.</p>



<p>For example:</p>



<ul><li><code>CTRL+L</code>&nbsp;to clear the console</li><li><code>3+5</code>&nbsp;to calculate the sum of 3 and 5</li><li><code>26%%3</code>&nbsp;to calculate the 26 modulo 3.</li></ul>



<p>Your RStudio screen should now look something like this:</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img src="https://financetrain.com/wp-content/uploads/RStudio_GUI.png" alt="" class="wp-image-27423"/></figure></div>



<h3>RStudio Orientation</h3>



<p>RStudio being a Gui makes working with R very user-friendly and allows you to execute basic commans without writing commands manually. This includes things like opening a script, import/export .csv files, manage R packages, get help, etc. In general, it accelerates and simplifies these general tasks.</p>



<p>Let’s take a look at the RStudio screen and how it is organized.</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img src="https://financetrain.com/wp-content/uploads/RStudio_Orientation_Annotated.png" alt="R Studio Interface" class="wp-image-27424"/><figcaption>R Studio Interface</figcaption></figure></div>



<ol><li>The upper left window is the script section where you write all your code.</li><li>The upper right window is the environment. This is the place where all the objects you create in your current R session al listed. For example, all datasets you have loaded will appear here, along with any other objects you have created (special text formats, vectors, etc). If you click on the History tab, you will see the complete history of code you have typed, over all sessions</li><li>The lower left window is the R console. This is the same as the R console we have already seen. This is the place where the actual calculations take place. The script section sends the code to the console when you click the ‘Run’ button in the script section. Just like you did in R Console, you can also write the code directly in R Console, but that’s not effective as you cannot manipulate it.</li><li>The lower right window contains five tabs.</li></ol>



<h3>Files</h3>



<p>This tab shows you all the files you have saved in your RStudio account. The buttons across the top of the tab allow you to upload additional files, delete files, rename files, and many more functions.</p>



<h3>Plots</h3>



<p>When you run code in the Console that creates a plot, the Plots tab will be automatically selected. Any time you want to view plots, you can select this tab manually, but it will be selected when you run plot code. Notice the arrow buttons at the top left of the pane; these allow you to scroll through all the plots you have created in a session.</p>



<h3>Packages</h3>



<p>This tab allows you to see the list of all the packages (add-ons to the R code) you have access to, and which are loaded in already.</p>



<h3>Help</h3>



<p>This tab will be automatically selected whenever you run help code in the Console, but you can access it at any time by clicking on the tab.</p>



<pre class="wp-block-code"><code>help(plot)</code></pre>



<h3>Viewer</h3>



<p>RStudio includes a Viewer pane that can be used to view local web content. We will not be using this till much later in the course.</p>



<p>As we go along in the course, you will get more familiar with RStudio and various features it offers.</p>



<p>When you first start RStudio, you may not see the script window. You can create a new script window, by just clicking the ‘New Script’ button, as shown below:</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img src="https://financetrain.com/wp-content/uploads/r-script-button.png" alt="" class="wp-image-27425"/></figure></div>



<p></p>

Installing and Using RStudio with R

<p>In R programming, we will be using variables all the time, so it is important to understand what a variable is and how it works in R.</p>



<p>A variable refers to a named storage that allows us to store data which our R programs can refer to and manipulate. A variable in R can store a value or an object (more on objects later). For example, we can store value ’50’ in a variable called ‘x’. This is called variable assignment, that is, the variable ‘x’ is assigned value ’50’.</p>



<p>The variables can be assigned values using leftward, rightward and equal to operator, however, the most common way is to use the leftward operator ( &lt;- )</p>



<p>Once we have assigned a value to a variable, we can print it by just calling the variable name or by using the&nbsp;<code>print()</code>&nbsp;or the&nbsp;<code>cat()</code>&nbsp;function.</p>



<pre class="wp-block-code"><code># Assignment using equal operator.
x = 50

# Assignment using leftward operator.
y &lt;- "table"

# Assignment using rightward operator.
100 -> z

x

print (x)
cat ("x is ", x ,"\n")
cat ("y is ", y ,"\n")
cat ("z is ", z ,"\n")</code></pre>



<p>When executed, this will produce the following result:</p>



<pre class="wp-block-code"><code>&#91;1] 50
x is 50
y is table
z is 100</code></pre>



<p>In RStudio, there are various ways you can execute the R script.</p>



<ul><li>Select a code line and Click the ‘Run’ button in the script window. This will execute that line in the code. Select multiple lines of code and click the ‘Run’ button in the script window. This will execute all the selected lines in the code.</li><li>To execute the entire script (using the Source command), press CTRL+SHIFT+ENTER. This will execute the entire script with each source command printed in the console. This is called Source with Echo.</li><li>You can also press CTRL+SHIFT+S to run the Source command, but without Echo. This means that only the output will be printed to console, not the source commands.</li></ul>



<h3>Arithmetic Operations Using Variables</h3>



<p>Once you have assigned variables, you can use these variables to perform arithmetic operations. Let’s say you have 5 Google stocks in your stock portfolio and 7 Microsoft stocks.</p>



<p>In R, you will create variables for these stocks and assign values to them. After that you can calculate the total stocks in portfolio by performing arithmetic operations on these variables and assign the total value to a new variable.</p>



<pre class="wp-block-code"><code>#Assign a value to GOOG and MSFT
GOOG &lt;- 5
MSFT &lt;- 7

#Add the two variables to get the total stocks in the portfolio
GOOG + MSFT

#Assign the total to a new variable
TOTALSTOCKS = GOOG + MSFT
print (TOTALSTOCKS)</code></pre>



<p>Try running this script in RStudio. Also try to run it using different commands described above and notice the difference in the output:</p>



<ul><li>Select all lines of code and press CTRL + ENTER (Or press the R button) to execute all lines of the code.</li><li>Press CTRL + SHIFT + ENTER to execute the script using the Source command with each source command printed in the console (Source with Echo).</li><li>Press CTRL + SHIFT + S to execute the script using the Source command with each source command without echoing the commands in the console.</li></ul>



<h3>Change in Environment</h3>



<p>As you assign the variables, you will also notice one more important change. As we learned earlier, all the objects you create in your current R session will be added to the environment. In this case, you will see three variables in the environment as shown below:</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img src="https://financetrain.com/wp-content/uploads/27256-environment-variables.png" alt="" class="wp-image-27429"/><figcaption>RStudio Environment Variables</figcaption></figure></div>



<h3>Variable types</h3>



<p>r is smart enough to understand the type of data you’re assigning to the variables. In the above examples, the values assigned were numeric and R could interpret them as numeric therefore allowed us to add the values in the two variables. But what will happen if one variable has a numeric value and the other has a character value and you try adding the two? In such a situation, r will throw an error and will ask you to provide numeric data type for the binary operation.</p>



<p>To test this, try running the following code in RStudio:</p>



<pre class="wp-block-code"><code>#Assign a value to GOOG and MSFT
GOOG &lt;- 5
MSFT &lt;- 'stock'

#Add the two variables to get the total stocks in the portfolio
GOOG + MSFT</code></pre>



<p></p>

Using Variables in R

<p>In R programming, there are five basic data types. Also, everything in R is an object, so we will refer to these data types as classes of objects. So, these five types of objects are:</p>



<ul><li>Numeric</li><li>Integer</li><li>Complex</li><li>Logical</li><li>Character</li></ul>



<p>Let's briefly look at each of these.</p>



<h3>Numeric</h3>



<p>In R, decimal values such as&nbsp;<code>8.5</code>&nbsp;are numeric. You can assign a numeric value to a variable and then that variable will be of numeric data type.</p>



<p>For any variable or object, you can check it's data type by using the&nbsp;<code>class</code>&nbsp;command.</p>



<pre class="wp-block-code"><code>> # Assign a decimal value to x
>
> x &lt;- 8.5
>
> # Print the value of x
> x
&#91;1] 8.5
>
> # Print the class name of x
>
> class(x)
&#91;1] "numeric"
></code></pre>



<h3>Integer</h3>



<p>Integers are the natural numbers such as 1, 2, 3, etc. In R, when you assign a number to a variable, it is by default of the numeric class type. In order to create an integer variable, we use a function called&nbsp;<code>as.integer()</code>. This ensures that the variable created is indeed an integer.</p>



<pre class="wp-block-code"><code>> #Assign a value to a variable
> x &lt;- 8
>
> #check the class type of x
> class(x)
&#91;1] "numeric"
>
> # You will notice that it is numeric.
>
> # Use the as.integer() function to create an integer
>
> y &lt;- as.integer(8)
>
> #check the class type of yx
> class(y)
&#91;1] "integer"
>
> > # It is an integer now
></code></pre>



<h3>Complex</h3>



<p>In R, a complex value is defined using a pure imaginary value&nbsp;<code>&lt;em&gt;i&lt;/em&gt;</code>.</p>



<pre class="wp-block-code"><code>> #Assign a complex value to a variable
> x = 1 + 2i
>
> #Print the complex value x
> x
&#91;1] 1+2i
>
> #Print the class of x
> class(x)
&#91;1] "complex"
></code></pre>



<h3>Logical</h3>



<p>Logical values are boolen values (<code>TRUE</code>&nbsp;or&nbsp;<code>FALSE</code>) often created by comparison between variables.</p>



<pre class="wp-block-code"><code>> #Create sample variables
> x &lt;- 5
> y &lt;- 7
>
> #Check if y is less than x
> z &lt;- y &lt; x
>
> # z will have a logical value. Let's print it
>
> z
&#91;1] FALSE
>
> #Print the class of z
> class(z)
&#91;1] "logical"
></code></pre>



<h3>Character</h3>



<p>Character values are string or text values. We can create a character type variable by assigning a string to the variable. Notice the use of double quotes.</p>



<pre class="wp-block-code"><code>> #Create a character variable
>
> x &lt;-"John Doe"
>
> #Print the character string
>
> x
&#91;1] "John Doe"
></code></pre>



<p>If we have an object of some other data type (e.g., numeric), we can convert it into character type using the <code>as.character()</code> function.</p>



<pre class="wp-block-code"><code>> #Create a numeric variable
>
> x &lt;- 8.75
>
> #Print the variable x
>
> x
&#91;1] 8.75
>
> #Print the class of x
>
> class(x)
&#91;1] "numeric"
>
> #convert x into a character value
>
> y &lt;- as.character(x)
>
> #Print the variable y
>
> y
&#91;1] "8.75"
>
> #Print the class of y
>
> class(y)
&#91;1] "character"
></code></pre>



<h3>Standard Logical Operations</h3>



<p>We can perform standard logical operations such as&nbsp;"&amp;"&nbsp;(and),&nbsp;"|"&nbsp;(or), and&nbsp;"!"&nbsp;(negation) on logical values in R.</p>



<pre class="wp-block-code"><code>> x = TRUE; y = FALSE
> x &amp; y # Checks that both x AND y are true
&#91;1] FALSE
> x | y # Checks that either x OR y is true
&#91;1] TRUE
> !x # Returns the negation of x
&#91;1] FALSE
></code></pre>



<h3>Standard String Operations</h3>



<p>We can easily perform basic string operations in R such as concatenation, or creating readable strings.</p>



<pre class="wp-block-code"><code>> #Define sample character variables
> fname &lt;- "John"
> lname &lt;- 'Doe'
>
> # Concatenate strings using paste function
> paste(fname, lname)
&#91;1] "John Doe"
>
> #Create a readable string using sprintf() function
> #Use %s for strings and %d for numeric values
>
> sprintf("His first name is %s and last name is %s",fname,lname)
&#91;1] "His first name is John and last name is Doe"
>
> # Extract a substr from a long string. In the following example, we
> # are extracting stock symbol from text
>
> substr("Google's stock symbol is GOOG", start=26, stop=29)
&#91;1] "GOOG"
>
> #Replace the first occurance of a word in a string by another word.
>
> sub("John","Sam","His first name is John")
&#91;1] "His first name is Sam"
></code></pre>



<p>The sprintf() function allows you to create strings as output using formatted data. For example:</p>



<pre class="wp-block-code"><code>sprintf("I go for a walk at %s:%s%s a.m.", 7, 0, 5)</code></pre>



<p>This will output:</p>



<pre class="wp-block-code"><code>#> &#91;1] "I go for a walk at 7:05 a.m."</code></pre>



<p>See the special syntax <code>%s</code>. Each <code>%</code> is referred to as a slot, which is basically a placeholder for a variable that will be formatted. The values after the comma are the variables or values that will be filled in each slot.</p>



<h3>Getting Help</h3>



<p>We can find many more functions for these data types in the R documentation. For each function, the help also provides details about how to use these functions. For example, you can get help for&nbsp;<code>sprintf()</code>&nbsp;function by using the command&nbsp;<code>help('sprintf')</code>. The documentation will open in the help window (bottom right).</p>

Data Types in R

<p>In R, a vector is a series of data elements of the same data type, for example, a series of numbers, a series of characters, or a series of logical values. In finance, for example, the daily profit/loss from your stock investments could be represented as a vector. A vector is also referred to as a one-dimensional array.</p>



<p>An important point to remember is that within a vector, all the data elements must be of the same type, i.e., you cannot mix different data types in the same vector.</p>



<p>In R, you can create a vector using the&nbsp;<code>combine()</code>&nbsp;function. For example, here is a vector containing three numeric values&nbsp;<code>5</code>,&nbsp;<code>7</code>&nbsp;and&nbsp;<code>8</code>.</p>



<pre class="wp-block-code"><code>> c(5,7,8)
&#91;1] 5 7 8
></code></pre>



<p>Let's say John and Ivan, two colleagues engage in day trading for a week and want to analyze their daily performance. Their daily profit and loss from the trading activity is shown below:</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img src="https://financetrain.com/wp-content/uploads/ID-27277-day-trading.png" alt="" class="wp-image-27435"/></figure></div>



<p>We can use this data in R by creating vectors and assigning them to variables.</p>



<pre class="wp-block-code"><code>#John's earnings in the week
john_earnings &lt;- c(120,-40,25,-130,260)
#Ivan's earnings in the week.
ivan_earnings &lt;- c(-30,-60,80,-250,200)
#Print John's earnings
john_earnings
#Print Ivan's earnings
ivan_earnings</code></pre>



<p>Run this script in RStudio (CTRL+ENTER) and you will see the results in RConsole.</p>



<pre class="wp-block-code"><code>> #John's earnings in the week
    > john_earnings &lt;- c(120,-40,25,-130,260)
    > 
    > #Ivan's earnings in the week.
    > ivan_earnings &lt;- c(-30,-60,80,-250,200)
    > 
    > #Print John's earnings
    > john_earnings
    &#91;1]  120  -40   25 -130  260
    > 
    > #Print Ivan's earnings
    > ivan_earnings
    &#91;1]  120  -40   25 -130  260
    ></code></pre>



<p>Now that we have the data, we can start working with it to measure performance.</p>



<h2>Vector Operations</h2>



<p>We will use this earnings data to understand how to perform some important arithmetic operations on vectors.</p>



<h3>Combined Earnings Per Day</h3>



<p>We can calculate the combined earnings of both John and Ivan by just adding the two vectors. When you add two vectors, the addition is performed member-wise (i.e., each element in the vector is added to the element on the same index in the other vector.</p>



<pre class="wp-block-code"><code>#John's earnings in the week
john_earnings &lt;- c(120,-40,25,-130,260)
#Ivan's earnings in the week.
ivan_earnings &lt;- c(-30,-60,80,-250,200)
#Calculate total earnings
total_earnings_per_day = john_earnings + ivan_earnings
#Print total earnings
total_earnings_per_day</code></pre>



<p>Run this script in your computer and compare the results with the ones below:</p>



<pre class="wp-block-code"><code>> #Print Ivan's earnings
> total_earnings_per_day
&#91;1] 90 -100 105 -380 460</code></pre>



<p>As you can see, earnings for each day are added and assigned to the new variable.</p>



<h3>Total Earnings</h3>



<p>The next thing we want to know is - "What were their total earnings for the whole week?"</p>



<p>We can claculate thus using the&nbsp;<code>Sum()</code>&nbsp;function in R which calculates the sum of all elements of a vector.</p>



<pre class="wp-block-code"><code>#John's earnings in the week
john_earnings &lt;- c(120,-40,25,-130,260)
#Ivan's earnings in the week.
ivan_earnings &lt;- c(-30,-60,80,-250,200)
#Calculate John's total earnings for the week
john_total &lt;- sum(john_earnings)
#Calculate Ivan's total earnings for the week
ivan_total &lt;- sum(ivan_earnings)
# calculate total combined earnings for the week
total_earnings &lt;- john_total + ivan_total
#Print individual totals and combined total
john_total
ivan_total
total_earnings</code></pre>



<p>Run this script in your computer and compare the results with the ones below:</p>



<pre class="wp-block-code"><code>> #Print individual totals and combined total
> john_total
&#91;1] 235
> ivan_total
&#91;1] -60
> total_earnings
&#91;1] 175
></code></pre>



<h3>Compare Performance</h3>



<p>By visually analyzing the above numbers we already know that John has performed much better than Ivan. However, when we deal with large datasets, such visual scans will not be possible. So, we can give the job of comparing performance to R script.</p>



<p>In the following script, we compare performance as a daily level as well as total. To compare the daily performance, we just have to compare the two vectors. For example, we can check "Did John perform better than Ivan each day?". To do so, we can use the logical operator to compare the two vectors. R will automatically compare each element in the vector and return a boolen value.</p>



<pre class="wp-block-code"><code>#John's earnings in the week
john_earnings &lt;- c(120,-40,25,-130,260)
#Ivan's earnings in the week.
ivan_earnings &lt;- c(-30,-60,80,-250,200)
#Check if John performed better than Ivan each day
john_vs_ivan &lt;- john_earnings > ivan_earnings
#Calculate John's total earnings for the week
john_total &lt;- sum(john_earnings)
#Calculate Ivan's total earnings for the week
ivan_total &lt;- sum(ivan_earnings)
#Check if John performed better than Ivan overall
overall_perfromance &lt;- john_total > ivan_total
#Print John's performance vis-a-vis Ivan's each day
john_vs_ivan
#Print overall performance
overall_perfromance</code></pre>



<p>The results should match our visual understanding of the numbers:</p>



<pre class="wp-block-code"><code>> #Print John's performance vis-a-vis Ivan's each day
> john_vs_ivan
&#91;1] TRUE TRUE FALSE TRUE TRUE
>
> #Print overall performance
> overall_perfromance
&#91;1] TRUE
></code></pre>



<h3>Other Arithmetic Operations</h3>



<p>Just like addition we can perform all arithmetic operations on vectors such as subtraction, multiplication, and division. The following example shows the difference between John's and Ivan's earnings each day.</p>



<pre class="wp-block-code"><code>#John's earnings in the week
john_earnings &lt;- c(120,-40,25,-130,260)
#Ivan's earnings in the week.
ivan_earnings &lt;- c(-30,-60,80,-250,200)
#Calculate difference in earnings
difference &lt;- john_earnings - ivan_earnings
#Print the difference
difference</code></pre>



<p>The results will be as follows:</p>



<pre class="wp-block-code"><code>> #Print the difference
> difference
&#91;1] 150 20 -55 120 60
></code></pre>



<h3>Vector Index</h3>



<p>We can retrieve individual values from a vector by referring to its index. For example, you can select the first element in the vector by typing&nbsp;<code>vector_name[1]</code>. Similarly, you can select multiple values from the vector by using the notations demonstrated below:</p>



<pre class="wp-block-code"><code>> #John's earnings in the week
> john_earnings &lt;- c(120,-40,25,-130,260)
>
> #Ivan's earnings in the week.
> ivan_earnings &lt;- c(-30,-60,80,-250,200)
>
> #Select John's earnings on 3rd day
> john_earnings&#91;3]
&#91;1] 25
>
> #Select John's earnings on 2nd and 5th day
> #You can select multiple values by supplying a vector of indexes
>
> john_earnings&#91;c(2,5)]
&#91;1] -40 260
>
> #Select John's earnings from 2nd to 4th day
> #To produce a vector slice between two indexes,
> #you can use the colon operator ":". Helpful for large vectors.
>
> john_earnings&#91;2:4]
&#91;1] -40 25 -130
></code></pre>



<h3>Naming Vector Members</h3>



<p>We learned how to refer to the elements of the vector but it's still difficult to tell which earnings belong to which day. In such situations, we can assign names to the members of the vectors. In our case, we can assign the names of days to the elements. We can do so by using the&nbsp;<code>names()</code>&nbsp;function as shown below:</p>



<pre class="wp-block-code"><code>#John's earnings in the week
john_earnings &lt;- c(120,-40,25,-130,260)
#Ivan's earnings in the week.
ivan_earnings &lt;- c(-30,-60,80,-250,200)
#Assign the names of the day to John's Earnings vector
names(john_earnings) &lt;- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")
#If you're applying these names to multiple vectors, you can even
#create a new vector with these names and then assign it.
days_in_week &lt;- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")
#Assign the names of the day to Ivan's Earnings vector
names(ivan_earnings) &lt;- days_in_week
#Print John's and Ivan's earnings
john_earnings
ivan_earnings</code></pre>



<p>Results will now look like below:</p>



<pre class="wp-block-code"><code>> #Print John's and Ivan's earnings
    > john_earnings
    Monday   Tuesday Wednesday  Thursday    Friday 
    120       -40        25      -130       260 
    > ivan_earnings
    Monday   Tuesday Wednesday  Thursday    Friday 
    -30       -60        80      -250       200 
    ></code></pre>



<h3>Select Only Positive Earnings</h3>



<p>Let's learn a few more things about vectors using our earnings example. Let's say we want to create a new variable, which contains only the positive earnings. In this case we will use the combined earnings vector for John and Ivan.</p>



<p><strong>Step 1: Create a logical vector that tells us on which days we have positive earnings</strong></p>



<pre class="wp-block-code"><code>#John's earnings in the week
john_earnings &lt;- c(120,-40,25,-130,260)
#Ivan's earnings in the week.
ivan_earnings &lt;- c(-30,-60,80,-250,200)
#Total Earnings
total_earnings &lt;- john_earnings + ivan_earnings
#Vector for days in week
days_in_week &lt;- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")
#Assign the names of the day to Total Earnings vector
names(total_earnings) &lt;- days_in_week
#On which days did we have positive earnings
#To do so we use comparison operators on vectors. The comparison operator
#will compare each element in the vector if the condition stated by the
#comparison operator is TRUE or FALSE
positive_vector &lt;- total_earnings > 0
#Print the positive_vector
positive_vector</code></pre>



<p>The positive vector should look like this:</p>



<pre class="wp-block-code"><code></code></pre>



<p><strong>Step 2 is to use the positive selection vector to slice the positive earnings from <code>total_earnings</code> vector.</strong></p>



<pre class="wp-block-code"><code>> #Select the positive earing days from the total_earnings vector

> positive_earning_days &lt;- total_earnings&#91;positive_vector]

> 

> #Print the positive earnings days

> positive_earning_days

Monday Wednesday    Friday 

90       105       460 

></code></pre>



<p>In the second step, we used the logical index vector to slice our earnings factor. If the logical value is TRUE, the member is included in the resulting slice, otherwise not.</p>

Creating and Using Vectors in R

<p>A matrix is a table of numbers. In math text, it is conventional to denote matrices with bold letters. For example, consider a matrix&nbsp;<strong>D</strong>&nbsp;of the prices of the securities on first three days of the week.</p>



<pre class="wp-block-code"><code>D = 
     64    31 
     65    28 
     66    35</code></pre>



<p>This matrix is {3*2} matrix (pronounced "3 by 2") . The number of rows is given first, followed by the number of columns. The Matrix&nbsp;<strong>D</strong>&nbsp;shows that on the first day, the bond was worth $64 and the stock was worth $31. On the second day the bond was worth $65 and the stock $28. On the third day the bond was worth $66 and the stock $35.</p>



<p>With this data in place, we can answer many analytics questions considering someone was holding these assets in their portfolio. Let's learn how to use matrices in R and then how to perform statistical analysis on them.</p>



<h3>Defining a Matrix in R</h3>



<p>Let's say we have the above data in the form of a vector:</p>



<pre class="wp-block-code"><code>> price_data &lt;- c(64,31,65,28,66,35)</code></pre>



<p>We know that this data represents three rows with each row containing the bond price and the stock price. In R, we can use this vector to create a matrix using the&nbsp;<code>matrix()</code>&nbsp;function as shown below:</p>



<pre class="wp-block-code"><code>#price data each number pair represents the bond an dstock price
price_data &lt;- c(64,31,65,28,66,35)
#Create matrix of prices
price_matrix &lt;- matrix(price_data, nrow=3,byrow=TRUE)
#print the matrix
price_matrix</code></pre>



<p><strong>Matrix function parameters:</strong></p>



<ul><li>The first argument is the data that the matrix function will convert into rows and columns.</li><li>The second argument&nbsp;<code>nrow</code>&nbsp;indicates that the matrix will have three rows. A similar argument&nbsp;<code>ncol</code>&nbsp;could be used to indicate the number of columns.</li><li>The third argument&nbsp;<code>byrow</code>&nbsp;indicates how the data should be processed.&nbsp;<code>byrow=TRUE</code>&nbsp;indicates that it should be processed by row, i.e., as data comes in it will first fill the first row, then second and so on. To process data by columns,&nbsp;<code>byrow</code>&nbsp;should be set to&nbsp;<code>FALSE</code>.</li></ul>



<p>When this matrix is printed, it will look as follows:</p>



<pre class="wp-block-code"><code>> price_matrix
     &#91;,1] &#91;,2]
&#91;1,]   64   31
&#91;2,]   65   28
&#91;3,]   66   35
></code></pre>



<h2>Naming Rows and Columns</h2>



<p>Currently our matrix doesn't have any names for the rows and columns and it's difficult to understand the data. Our first column represents the prices of the bond and the second column represents the prices of stock. The three rows represent three days, namely, Mon, Tue and Wed.</p>



<p>In R, we can assign names to the matrix using the&nbsp;<code>rownames()</code>&nbsp;and&nbsp;<code>colnames()</code>&nbsp;functions as shown below:</p>



<pre class="wp-block-code"><code>#set row names and column names for price_matrix
rownames(price_matrix) &lt;- c("Mon","Tue", "Wed")
colnames(price_matrix) &lt;- c("Bond","Stock")
#print the matrix
price_matrix</code></pre>



<p>We can now print the matrix:</p>



<pre class="wp-block-code"><code>> price_matrix
    Bond Stock
Mon   64    31
Tue   65    28
Wed   66    35
></code></pre>



<p>Another easy way to assign names to a matrix is to use the&nbsp;<code>dimnames()</code>&nbsp;function, as shown below. Note the use of&nbsp;<code>list()</code>&nbsp;function which we will discuss in the upcoming lessons. This list has two objects, the first is the vector for row names and the second is the vector for column names.</p>



<pre class="wp-block-code"><code>#Use the dimnames function to assign names to matrix elements
dimnames(price_matrix) &lt;-list(c("Mon","Tue", "Wed"),c("Bond","Stock"))
#print the matrix
price_matrix</code></pre>



<h2>Selecting the Matrix Elements</h2>



<p>We can select specific elements of a matrix by using the expression&nbsp;<code>D[m, n]</code>, i.e., mth row and nth column of matrix D.</p>



<p>Below R script shows some different ways of selecting the matrix elements:</p>



<pre class="wp-block-code"><code>> #print the matrix
> price_matrix
    Bond Stock
Mon   64    31
Tue   65    28
Wed   66    35
> 
> #What is the bond price on 3rd day? (3rd row and 1st column)
> price_matrix&#91;3,1]
&#91;1] 66
> 
> #Get me just the stock prices for all days
> #In this case we want to access all rows, so we will just omit supplying the row
> #stock prices are in 2nd column
> price_matrix&#91;,2]
Mon Tue Wed 
 31  28  35 
> 
> #Get stock and bond price on Tuesday
> #Tuesday is the 2nd row
> price_matrix&#91;2,]
 Bond Stock 
   65    28 
> 
> #Get all prices for Monday and Wednesday
> #Monday and Wednesday data is in row 1 and 3
> price_matrix&#91;c(1,3),]
    Bond Stock
Mon   64    31
Wed   66    35
> 
> #Get stock prices for Tuesday and Wednesday
> #We can use colon for continuing elements
> price_matrix&#91;2:3,2]
Tue Wed 
 28  35 
></code></pre>



<h2>Arithmetic Operations on Matrices</h2>



<p>Just like vectors, we can use standard operators&nbsp;<code>+</code>,&nbsp;<code>-</code>,&nbsp;<code>/</code>,&nbsp;<code>*</code>&nbsp;with matrices. Let's take a few examples to understand the matrix arithmetic and also understand a few other matrix operations along the way.</p>



<ol><li>Let's say that you hold 5 quantity each of this bond and stock. We can multiple the&nbsp;<code>price_matrix</code>&nbsp;to get the dollar holding value of your assets. We store this in the matrix&nbsp;<code>portfolio_value</code>.</li><li>Now that we have the portfolio values, we can calculate the total portfolio value on each day by adding the value of stocks and bonds. This can be done using the&nbsp;<code>rowSums()</code>&nbsp;function. We store the results in a vector called&nbsp;<code>days_total</code>.</li><li>We now have a new vector which contains daily portfolio value totals. But it is not a part of the&nbsp;<code>portfolio_value</code>&nbsp;matrix. We can add the&nbsp;<code>days_total</code>&nbsp;vector to the main matrix using&nbsp;<code>cbind()</code>&nbsp;function.</li><li>Since we have the portfolio values over a three day period, we can calculate the average portfolio value during this period. The values are in columns so we can use&nbsp;<code>colMeans()</code>&nbsp;function to calculate the column means. We store these values in a vector called&nbsp;<code>days_average</code>.</li><li>Finaly we can add the&nbsp;<code>days_average</code>&nbsp;vector as a new row to our main matrix. Since we are adding a row, we will use&nbsp;<code>rbind()</code>&nbsp;function.</li><li>The resulting matrix contains portfolio values along with totals and average over a period of three days.</li></ol>



<pre class="wp-block-code"><code>> #print the matrix
> price_matrix
    Bond Stock
Mon   64    31
Tue   65    28
Wed   66    35
> 
> #You hold 5 quantity ech of bond and stock. What is the value?
> portfolio_value &lt;- price_matrix * 5
> 
> #What is the total portfolio value on each day
> days_total &lt;- rowSums(portfolio_value)
> 
> #print days total
> days_total
Mon Tue Wed 
475 465 505 
> 
> #We can added the days_total vector to the main matrix using cbind()
> portfolio_value_totals &lt;- cbind(portfolio_value,days_total)
> 
> #Calculate average value per day
> days_average &lt;- colMeans(portfolio_value_totals)
> 
> #Add the averages row to the portfolio_value_totals matrix
> final_matrix &lt;-rbind(portfolio_value_totals,days_average)
> 
> #print final_matrix
> final_matrix
             Bond    Stock days_total
Mon           320 155.0000   475.0000
Tue           325 140.0000   465.0000
Wed           330 175.0000   505.0000
days_average  325 156.6667   481.6667
></code></pre>



<h3>Multiplying Matrix with a Vector</h3>



<p>In the above example, we assumed the same quantity&nbsp;<code>5</code>&nbsp;for both stock and bond and simply multiplied it with the matrix. R took care of multiplying each matrix element with 5 to get us the values. However, what if we have different quantities of stock and bond. In such a case we can store the quantities in a new vector and then do standard matrix multiplication to achieve our results. Note that what we did earlier (multiply by&nbsp;<code>*</code>) is not the standard matrix multiplication for which you should use&nbsp;<code>%*%</code>&nbsp;in R. The calculation and nuances are demonstrated below:</p>



<pre class="wp-block-code"><code>#print the matrix
price_matrix
# Assign quantities - 5 bonds and 3 stocks
quantities &lt;-c(5,3)
# Multiply prices with quantities to get the values.
portfolio_value &lt;- price_matrix %*% diag(quantities)</code></pre>



<ul><li><code>%*%</code>&nbsp;represents standard matrix multiplication.</li><li><code>diag()</code>&nbsp;create a diagnal matrix from the vector so that we can then multiply the two matrices.</li><li>Multiplying the price matrix with the quantity vector will look as follows:</li><li><em>Note: If you did not understand this calculation, don't worry about it at this stage. We will learn a lot more about matrix multiplication in future courses. The objective of bringing this up here was to just familiarize you with the possibilities of the advance calculations that can be done.</em></li></ul>



<p>The resulting matrix will look as follows:</p>



<pre class="wp-block-code"><code>> portfolio_value
    &#91;,1] &#91;,2]
Mon  320   93
Tue  325   84
Wed  330  105
></code></pre>



<h3>Workspace</h3>



<p>When you create a new vector, matrix or any other R object, it gets saved into the workspace and is available for you to use in your calculations. These variables can be seen in the Global Environment, i.e., the top-right window in RStudio. You can also access all objects available in the workspace using the&nbsp;<code>ls()</code>&nbsp;command in R console.</p>



<div class="wp-block-image"><figure class="aligncenter size-large"><img src="https://financetrain.com/wp-content/uploads/ID-27281-workspace.png" alt="" class="wp-image-27532"/></figure></div>



<p>Using&nbsp;<code>ls()</code>&nbsp;command:</p>



<pre class="wp-block-code"><code>> ls()
&#91;1] "days_average"           "days_total"             "final_matrix"
&#91;4] "portfolio_value"        "portfolio_value_totals" "price_data"
&#91;7] "price_matrix"          
></code></pre>

Matrices in R Programming

<p>In R programming, factors are variables that take on a limited number of different values. Factors are used to represent categorical data.</p>



<p>Some examples of factors:</p>



<ul><li>A common example of a factor is gender, which can have category values as Male and Female.</li><li>A data field such as marital status may contain only values from single, married, separated, divorced, or widowed.</li><li>For stocks, we can have them categorized as Large-cap, Mid-cap, and Small-cap</li></ul>



<p>In R, the function <code>factor()</code> is used to encode a vector as a factor. In the following example, we first create a vector which for this example categorizes stocks as Large-cap, Mid-cap, and Small-cap. And then we use the <code>factor()</code> function to encode this vector as a factor.</p>



<pre class="wp-block-code"><code>#The following vector classifies 5 stocks
    stock_vector &lt;- c("large-cap","small-cap","large-cap","mid-cap","small-cap")
    # Convert the stock vector to a factor
    stock_factor &lt;- factor(stock_vector)
    #Print the stock_factor
    stock_factor</code></pre>



<p>When you print this vector, the results will look as follows:</p>



<pre class="wp-block-code"><code>> stock_factor
    &#91;1] large-cap small-cap large-cap mid-cap   small-cap
    Levels: large-cap mid-cap small-cap
    ></code></pre>



<h3>Levels and Order</h3>



<p>When you print the factor, you can see that it also prints the Levels. By default, the levels are sorted based on their character value. However, you can change the order in which the levels will be displayed from their default sorted order, the&nbsp;<code>levels=</code>&nbsp;argument can be given a vector of all the possible values of the variable in the order you desire.</p>



<p>Factors can be unordered or ordered. For example, we can consider the gender factor (Male and Female) to be an unordered factor as it is not important which ones come first. However, some other categories may have an order associated with them, for example, in our stock factor we may want to have them ordered as per their market capitalization (Mid-cap being the smallest and large-cap being the largest). If the ordering should also be used when performing comparisons, use the optional&nbsp;<code>ordered=TRUE</code>&nbsp;argument. In this case, the factor is known as an ordered factor.</p>



<p>We can now update our factor to have pre-defined levels and set the order to TRUE.</p>



<pre class="wp-block-code"><code># Convert the stock vector to a factor
    stock_factor &lt;- factor(stock_vector, ordered=TRUE, levels=c("small-cap", "mid-cap", "large-cap"))
    #Print the stock_factor
    stock_factor</code></pre>



<p>Results:</p>



<pre class="wp-block-code"><code>> #Print the stock_factor
    > stock_factor
    &#91;1] large-cap small-cap large-cap mid-cap   small-cap
    Levels: small-cap &lt; mid-cap &lt; large-cap
    ></code></pre>



<h2>Changing Levels</h2>



<p>Sometimes, you may have a factor with values in it and you may want to change the names of those levels for more clarity or for relating it to something else in your model. In R, you can do so using the <code>levels()</code> function. Let's say that our original factor contained letters L, M and S to represent the three types of stocks. We can change the levels to Large-cap, Mid-cap and Small-cap using the <code>levels()</code> function.</p>



<pre class="wp-block-code"><code># The following vector classifies 5 stocks
    stock_vector &lt;- c("L","S","L","M","S")
    # Convert the stock vector to a factor
    stock_factor &lt;- factor(stock_vector, ordered=TRUE, levels=c("S","M","L"))
    levels(stock_factor) &lt;- c("small-cap", "mid-cap", "large-cap")
    #Print the stock_factor
    stock_factor</code></pre>



<p>In the results, you will have new levels applied to the factor.</p>



<pre class="wp-block-code"><code>> #Print the stock_factor
    > stock_factor
    &#91;1] large-cap small-cap large-cap mid-cap   small-cap
    Levels: small-cap &lt; mid-cap &lt; large-cap
    >
&lt;/div>
&lt;h2>Summarize a Factor&lt;/h2>
&lt;p>We can use the &lt;code>summarize()&lt;/code> function to summarize the contents of the factor variable. As you can see, it prints a quick snapshot of how many stocks you have of each type in your portfolio.
&lt;/p>
&lt;pre class="lang-r">> #Summarize stock_factor
> summary(stock_factor)
small-cap   mid-cap large-cap 
        2         1         2 
></code></pre>



<h3>Use of Ordered Factor</h3>



<p>In R the most apparent effect of using ordered vs. unordered factor is in pretty printing of the output. Apart from this, ordering and levels can be important in linear modelling because the first level is used as the baseline level. We will learn about these use cases when we learn linear modelling, however, here we will take a simple example to understand the use of ordering.</p>



<p>Let's say you have five stock traders in your team, and you have their performance evaluated as <code>"Poor"</code>, <code>"Average"</code>, and <code>"Good"</code>. The following R script shows how we can compare the performances of these traders.</p>



<pre class="wp-block-code"><code>> # The following vector classifies 5 stocks
> performance_vector &lt;- c("Good","Average","Poor","Poor","Good")
> 
> # Convert the stock vector to a factor
> performance_factor &lt;- factor(performance_vector, ordered=TRUE, levels=c("Poor","Average","Good"))
> 
> #Print the stock_factor
> performance_factor
&#91;1] Good    Average Poor    Poor    Good   
Levels: Poor &lt; Average &lt; Good
> 
> #Summarize stock_factor
> summary(performance_factor)
   Poor Average    Good 
      2       1       2 
> 
> #Performance value of 2nd and 4th trader
> pv2 &lt;- performance_factor&#91;2]
> pv4 &lt;- performance_factor&#91;4]
> 
> #Is trader 2 better than trader 4?
> pv2 > pv4
&#91;1] TRUE
></code></pre>



<p><em>Note that if the factor was not ordered this comparison would not work. It will give you a warning message that comparison operator <code>'>'</code> is not meaningful. However, once you set the <code>ordered=TRUE</code>, it will recognize the comparison operator.</em></p>



<h3>Statistical Modelling</h3>



<p>One of the most important uses of factors is in statistical modeling. Since categorical variables enter into statistical models differently than continuous variables, storing data as factors insures that the modeling functions will treat such data correctly. (Note: Categorical variables are different from continuous variables in that a categorical variable can take on a limited number of categories while a continuous variable can have an infinite number of values.)</p>

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