The Basics of Data Visualization: A Guide on GGplot2

I would like this post to be a demonstration on Data Visualization with the ggplot package. As you will discover, the package is adept at creating plots that are attractive and appealing. 

There won't be too much explanation on how to interpret these plots. I list a worthy resource for that at the conclusion of this post. Please look into it if this post inspires you.

I would like this post to go into the basics of ggplot2, which is a package that is meant to specialize in the visualization of data. I am using a book called “ggplot2: Elegant Graphics for Data Analysis,” by Hadley Wickham, as well as lecture material I have learned in class. 

I will use one of my favorite data sets called bikes, and the mpg data set later on, but I will not go into great details for this post. I want this post to show you how you can plot two numerical variables on the x and y-axis, and add appropriate labels to make this plot more interpretable.

As always, if you wish to follow along, please type the text that is highlighted in BLUE in your R Studio environment.

library(tidyverse)

## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --

## v ggplot2 3.3.5     v purrr   0.3.4
## v tibble  3.1.4     v dplyr   1.0.7
## v tidyr   1.1.3     v stringr 1.4.0
## v readr   2.0.1     v forcats 0.5.1

## Warning: package 'stringr' was built under R version 4.1.2

## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

setwd("C:/Users/firstnamelastinitial/OneDrive/Documents/Fund of Bus Anal")
bikes <- read.csv("bikes.csv", header = TRUE)
str(bikes)

## 'data.frame':    731 obs. of  10 variables:
##  $ date       : chr  "2011-01-01" "2011-01-02" "2011-01-03" "2011-01-04" ...
##  $ season     : int  1 1 1 1 1 1 1 1 1 1 ...
##  $ holiday    : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ weekday    : int  6 0 1 2 3 4 5 6 0 1 ...
##  $ weather    : int  2 2 1 1 1 1 2 2 1 1 ...
##  $ temperature: num  46.7 48.4 34.2 34.5 36.8 ...
##  $ realfeel   : num  46.4 45.2 25.7 28.4 30.4 ...
##  $ humidity   : num  0.806 0.696 0.437 0.59 0.437 ...
##  $ windspeed  : num  6.68 10.35 10.34 6.67 7.78 ...
##  $ rentals    : int  985 801 1349 1562 1600 1606 1510 959 822 1321 ...

So, I have loaded tidyverse, which contains ggplot2, and my data set. Now I would like to use ggplot to visualize variables within the bikes data frame. 

But first, allow me to summarize the basic format, or grammar, of the ggplot() function.

1.         You need a data frame.

2.         the second argument for this function requires a mapping aesthetic, or aes, which will have the variables you wish to see in graphical form.

3.         After you have satisfied these two arguments for the ggplot() function, you will need include a geom function, which follows a + sign.

Let me demonstrate what this may look like.

ggplot(bikes, aes(x = temperature, y = rentals))+
  geom_point()

Here is what that plot looks like. Throughout this post, I will use the same plot, but I will make it look more presentable, by making use of various functions and phrases. 

I hope that each iteration of this plot will give you an idea, and basic understanding of how ggplot is used, and its effectiveness in presenting your findings to your managers at your place of work.

Let’s change the color of the plot to blue.

ggplot(bikes, aes(x = temperature, y = rentals))+
  geom_point(colour = "blue")

I would like to note that color and shape work well for categorical variables (non-numerical), and for continuous variables (numerical), size might be a better argument.

Now, it might be difficult to determine what type of relationship exists between the variables in our visualization. To me, it looks like there is a moderate (?) positive LINEAR (?) relationship between temperature and rentals. 

So, let’s test my hypothesis by superimposing a regression line over the data. We can do this with the geom_smooth() function, and inserting “lm” into “method” for our argument.

ggplot(bikes, aes(x = temperature, y = rentals))+
  geom_point()+
  geom_smooth(method = "lm")

## `geom_smooth()` using formula 'y ~ x'

My assumption that the variables in question have a linear relationship appears to have only some merit. Although, at this point, I don’t know how strong the correlation is. And now that I think about it, a linear model might NOT fit this data appropriately, as this line does not fit the outer extremities of our data too well. That is the subject of another post. Let’s continue.

In order to keep this post shorter, I want to touch quickly on how you can simply add labels to your graph. Please examine the following code, and note it’s output:

ggplot(bikes, aes(x = temperature, y = rentals))+
  geom_point(colour = "red")+
  geom_smooth(method = "lm")+
  labs(title = "Relationship Between Rentals and Temperature") +
  ylab("Rentals") +
  xlab("Temperature")

## `geom_smooth()` using formula 'y ~ x'

In our final input, we specified that the color of our observations will be red in the geom_point() function. We kept our Regression Line to give management an idea how a linear model might or might not be appropriate for our data set. This was specified in our geom_smooth() function. 

Lastly, we created a title for our graph called, “Relationship Between Rentals and Temperature.” We labeled our y-axis “Rentals” and this is our dependent variable. We labeled our x-axis “Temperature” and this will be our independent variable.

Let me do a comparison of both graphs so we can see how far we have come in our interpretation of the two variables in question.

ggplot(bikes, aes(x = temperature, y = rentals))+
  geom_point()

ggplot(bikes, aes(x = temperature, y = rentals))+
  geom_point(colour = "red")+
  geom_smooth(method = "lm")+
  labs(title = "Relationship Between Rentals and Temperature") +
  ylab("Rentals") +
  xlab("Temperature")

## `geom_smooth()` using formula 'y ~ x'

There are other ways that you can graph variables in ggplot, this goes without saying. Here are some other plots you can experiment with. To demonstrate these variations, I will use the mpg data set.

ggplot(mpg, aes(drv, hwy))+
  geom_jitter()

ggplot(mpg, aes(drv, hwy))+
  geom_boxplot()

ggplot(mpg, aes(drv, hwy))+

  geom_violin()

You can find more information about the advantages and disadvantages of these plots in the book by Hadly Wickham, “ggplot2: Elegant Graphics for Data Analysis,” and I will not go into these elements for this post. I just wish to show you the potential of this powerful and useful package. Here is another plot that you can make:

ggplot(mpg, aes(displ, colour = drv))+
  geom_freqpoly(binwidth = 0.5)

You can explore this further in your own time.

To begin, pick two variables from your data set, try numerical values at first. Alter the default graphs color, add some sort of line to fit the data, and lastly, change the labels of the graph. 

THANK YOU!

I hope that this post gives you a quick solution for visualizing two variables on a plot, and also inspires you to go out and buy Hadley Wickham’s book, “ggplot2: Elegant Graphics for Data Analysis.”

Thank you so much for looking at this post. I hope it was helpful to you in your journey of becoming a data analyst, machine learning leader, or data entrepreneur.

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Data Visualization Basics: 3 Plots and Graphs That Will Make Your Regression Analysis Project Easier

Thank you so much for your continued support and visiting my website. I hope that my content can be useful to all Porn Stars—or anyone and everyone in the Sex Industry—and it is certainly my honor creating a space for you all to access such a relevant and worthy field.

 

At this point, I expect that you read my previous post, “6 Basic Terms That You Should Know For Data Science and Analytics.” I will link that here. This post will go deeper into data science and analytics in that I will introduce to you some basic, yet necessary, graphs and charts that will be vital for your development as data analysts and data entrepreneurs.

I will be discussing the following content:

 

HISTOGRAMS, SKEWNESS and NORMAL DISTRIBUTION

BOX PLOTS

SCATTERPLOTS and CORRELATION COEFFICIENTS

 

Before, I discuss the content for this blog post. I would like to put the above terms in context with Regression Analysis.

 

MACHINE LEARNING AND REGRESSION ANALYSIS

 

Regression Analysis is a form of “supervised machine learning,” in that a machine will ultimately “learn” to make predictions based on input, or code, that humans program into the machine. It is very different from “unsupervised machine learning” in that humans are a necessary component for machine to “grow smarter.”

 

In “unsupervised machine learning” algorithms—we will learn about one of them called Clustering, later—machines are able to detect patterns in the data on their own. The only caveat is that machines need a tremendous amount of data.

 

Back to Regression Analysis.

 

Today’s blog post leans on data visualization as a tool for creating a prediction equation, or more formally known as a Regression algorithm. There are certain assumptions and checks that a data analyst or machine learning expert needs to conduct so that their Regression model (an equation with one or many variables) is appropriate to make predictions—the real magic of machine learning.

 

Charts and plots are an industry standard for checking these assumptions (more on this in a later post). For example, we will eventually be checking to see if there are ANY correlations (or relationships) between the response variable, the variable we are interested in making a prediction, and the explanatory variables, the independent variables that will impact the response variable.

 

In other words, though this post will be basic, there will be relevant information for you so that you can run a Regression algorithm AND create your own projects that you can show to potential employers. Regression is a common, yet POWERFUL, machine learning application that is used in the pretty much any industry where you need to make a prediction about ANYTHING!

 

So, graphs and plots are important tools! Let’s begin with Histograms.

 

HISTOGRAMS

 

A HISTOGRAM is a graph that depicts the distribution of numerical data. A histogram commonly comes in three variations, a symmetrical distribution, a right-skewed distribution, and a left-skewed distribution. Here is a symmetrical distribution, otherwise known as a normal distribution:

We can see from the graph that it is perfectly symmetrical. This means that the mode, mean, and median are ALL equal, and are positioned in the center of the distribution—where most of the data is observed. This graph is also known to have a bell-curve.

 

To put this in context with Regression Analysis, our first task would be to determine if the distribution of the “response variable,” or the variable in which we wish to predict, is normally distributed. Ideally, we want our histogram of the response variable to look like this! More on this in another blog post.

 

So, if a histogram doesn’t have a normal shape, then what else can it took like?

In the above graphic, we have both a Left and Right-Skewed distribution.

 

Left-Skewed distributions are known to have a “negative skewness,” and Right-Skewed distributions are known to have a “positive skewness.”

 

As you can see, the Left-Skewed graph has most of its data positioned on the right side of the graph. Think of a Left-Skewed distribution as a skier gliding down a mountainside (or slope) to the left. The opposite can be said of Right-Skewed distributions.

 

If you can recall, Normal or symmetric distributions have the mode, mean, and median, ALL equaling each other. Now, there is a useful relationship between these three descriptive statistics in that:

 

For Left-Skewed Distributions: The mode (or the peak of the data) is larger than the median, and the median is larger than the mean.

 

For Right-Skewed Distributions: The mode is smaller than the median, and the median is smaller than the mean.

But why is noting this useful?

 

Let’s say that you were analyzing employment report data for Harvard Business School MBA graduates. We might observe that the Median salary for post-graduates is $165,000, and that the Mean salary is $158,937. (These are hypothetical numbers).

 

Since the Median is larger than the Mean, we can conclude that the data is Left-Skewed—assuming it is unimodal. This might be an important deduction for deciding whether or not to pursue a Harvard MBA, as this information tells us that more students lean closer to the Mode post-graduate salary, which we know is greater than $165,000. From this, we can assume that there are many students make more than $165,000.

 

Knowing this, we can make an inference, as to the salary that we might make after graduating from Harvard’s MBA program, given that we have other factors that are common to most of the incoming cohort—like number of work years prior to entry, GMAT testing scores, Undergraduate GPA score, and industry relevant experience.

 

Just knowing the shape of the distribution can help us be CONFIDENT about these assumptions given other factors of note. We can never be certain though, and this is a downside to statistics and any form of science, in general.

 

Let’s discuss Boxplots.

 

BOXPLOTS

 

The Boxplot is also known as a “whisker” plot, and it is a graphical representation of the Five-Number Summary (using quartiles). 

There is a lot to unpack here, so please be patient with me. Let’s break this plot down beginning with the middle.

The yellow line in this plot is known as the median. Sometimes, depending on which software  you are using, there will also be a small diamond-shaped object near this line, and that shape represents the mean of the data.

 

The Red Box is enclosed by Q1 and Q3, which if you remember from the previous post, is known as the Interquartile Range (IQR).

 

The two purple lines are drawn outward to two more lines that come to an intersection. The intersection on the left (sometimes at the bottom) is called the “Minimum” value, and the intersection on the right (sometimes at the top) is called the “Maximum” value. These are the whiskers of the boxplot.

 

The Green dots on either end of the whiskers are called Outliers. These data points are special instances in which their values don’t represent the commonality of the data points in the data set. 

Let’s think about the average salary in the US, roughly $56,310 in 2020, according to the Bureau of Labor Statistics. An outlier would be someone like a corporate executive who made, perhaps, a whopping $2,500,000 that year.

 

This person is not typical! There are more who made closer to the average salary, than there are who brought in a seven figure salary.

 

This example represents a Right-Skewed distribution in which the mode, median, and mean are closer to the peak of the data. The outlier would be far out, residing in the tail of the data. There are less US citizens making salaries outside of where the peak is, where the tails are. Athletes are another example of outlier in salary data—they make more money than the average American citizen.

 

One last observation! The above boxplot has a Normal Distribution, and you can tell because the whiskers are equal in length (just eyeballing it). If the Right whisker is larger than the left, we have a Right-Skewed distribution. If the Left whisker is larger than the right, we have a Left-skewed distribution.

 

Let’s move on to Scatter Plots and Correlation Coefficients.

 

SCATTER PLOTS

 

A Scatter Plot basically depicts how much of one variable impacts another. Scatter Plots are useful in the beginning of a Regression Analysis when you need to determine whether the response variable (y-variable) has a “linear” correlation with any of the explanatory variables (x-variables). Regression analysis relies on these correlations, and they are necessary for the prediction equation to hold merit for the final Regression line.

 

Scatter Plots can have Positive, Negative, or No Correlation. Here is what that looks like:

A Positive Linear Relationship has an increase in the x-axis (horizontal axis) for every unit increase in the y-axis (vertical axis). It has an upward slope, pointing up and to the right.

 

A Negative Linear Relationship has an increase in the x-axis (horizontal axis) for every unit decrease in the y-axis (vertical axis). It has a downward slope, pointing down and to the right.

 

A graph with No Correlation cannot be distinguished between a positive or negative linear relationship. There is no pattern, and the data points appear to be scattered randomly.

 

For a Regression Analysis, you MUST have both Positive and Negative correlations between the response variable, and the explanatory variable.

 

Furthermore, correlations can be Weak, Moderate, Strong, or Perfect. Here is what that looks like:

 

The Stronger the correlation, the MORE data points fit along—or are at least, close to—the Regression line (depicted by the red line). A plot with a Strong Positive Linear Correlation will look like the plot on the upper left. It will have a positive Correlation Coefficient value closer to 1 (more on this soon).

 

Similarly, there can exist a plot with a Strong Negative Linear Correlation, and that plot is represented by the one in the upper right. It will have a Correlation Coefficient closer to negative 1.

 

The Weaker the correlation, the LESS data points fit on or along the Regression line. You can observe a Weak Positive Linear Correlation, on the lower left, and a Weak Negative Linear Correlation, on the lower right. The Weaker the correlation, the closer the Correlation Coefficient is to zero.

 

Now that I have confused you with correlation coefficients, I will discuss them here in greater detail.

 

CORRELATION COEFFICIENTS

 

Correlation Coefficients are commonly denoted as “r” scores, and these scores range from negative one (-1) to positive one (+1).

 

These scores are measured between two variables, a dependent variable (y-variable, or response variable) and an independent variable (x-variable, or explanatory variable).

 

The score represents both the Strength and the Direction of the correlation.

 

There is no unified, or exact range, but here are some sensible metrics for you to begin describing your correlation coefficient. Keep in mind that Positive “r” scores represent a Positive Linear Relationship (recall when the graph is going up and to the right). Conversely, Negative “r” scores represent a Negative Linear Relationship (when the graph is going down and to the right):

 

1 would be Perfect Positive Linear Correlation

.8 would be Strong Positive Linear Correlation

.6 would be Moderate Positive Linear Correlation

.3 would be Weak Positive Linear Correlation

0 No Linear Correlation

-0.3 would be Weak Negative Linear Correlation

-0.6 would be Moderate Negative Linear Correlation

-0.8 would be Strong Negative Linear Correlation

-1 would be Perfect Negative Linear Correlation

 

Keep in mind that when you are comparing your x and y-variables with scatterplots that you want to see “r” scores of Moderate or higher (0.6 or higher, or -0.6 or lower), in any direction for an appropriate use of Regression Analysis. This ensures that there IS a relationship between the variables, and that Regression can be used to make predictions.

 

 

THANK YOU, AGAIN, and ALWAYS!

 

It is my pleasure and honor to continue to post about analytics for you in an accessible way. This is all very boring at the moment, and that’s ok, because the fun part is coming soon! Don’t get discouraged if the material seems ambiguous and complicated. Part of the beauty of the world wide web is that information is abundant and permanent. You can read these posts as many times as you wish for the content to stick. Enjoy them, and have fun with them!

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