Basic Data Analysis Using R

R is a statistical analysis tool that is widely used in the data science field. R provides many tools for data exploration, visualization, and statistical analysis. It is available as a free, open-source program and provides an integrated suite of functions for data analysis, graphing, and statistical programming. R is increasingly being used by data scientists as a data analysis and statistical tool in part because R is an open-source language and additional features are constantly being added by the user community. The tool can be used on many different computing platforms and can be downloaded at the R Project website.

Once you have installed and started R on your computer, at the bottom of the R console, you should see the symbol >, which indicates that R is ready to accept commands.

For a user new to R, typing help.start() at the R prompt provides a menu of Manuals and Reference materials as shown in Figure B1.

Figure B1 R Help Menu Based on 

help.start()

R provides many built-in help resources. When a user types help() at the R prompt, a listing of help resources are provided. For a specific example, typing help(median) will show various documentation on the built-in median function within R.

In addition, if a user types demo() at the R prompt, various demonstration options are shown. For a specific example, typing demo(graphics) will provide some examples of various graphics plots.

R is a command-driven language, meaning that the user enters commands at the prompt, which R then executes one at a time. R can also execute a program containing multiple commands. There are ways to add a graphic user interface (GUI) to R. An example of a GUI tool for R is RStudio.

The R command line can be used to perform any numeric calculation, similar to a handheld calculator. For example, to evaluate the expression 10+3⋅7, enter the following expression at the command line prompt and press return. The numeric result of 31 is then shown:

    > 10+3*7

    [1] 31
    

Most calculations in R are handled via functions. For data science and statistical analysis, there are many pre-established functions in R to calculate mean, median, standard deviation, quartiles, and so on. Variables can be named and assigned values using the assignment operator <-. For example, the following R commands assign the value of 20 to the variable named x and assign the value of 30 to the variable named y:

    > x <- 20
    
    > y <- 30
    

These variable names can be used in any calculation, such as multiplying x by y to produce the result 600:

    > x*y
    
    [1] 600
    

The typical method for using functions in statistical applications is to first create a vector of data values. There are several ways to create vectors in R. For example, the c function is often used to combine values into a vector. The following R command will generate a vector called salaries that contains the data values 40000, 50000, 75000, and 92000:

    > salaries <- c(40000, 50000, 75000, 92000)
    

This vector salaries can then be used in statistical functions such as mean, median, min, max, and so on, as shown:

    > mean(salaries)
    
    [1] 64250
    
    > median(salaries)
    
    [1] 62500
    
    > min(salaries)
    
    [1] 40000
    
    > max(salaries)
    
    [1] 92000
    

Another option for generating a vector in R is to use the seq function, which will automatically generate a sequence of numbers. For example, we can generate a sequence of numbers from 1 to 5, incremented by 0.5, and call this vector example1, as follows:

    > example1 <- seq(1, 5, by=0.5)
    

If we then type the name of the vector and press enter, R will provide a listing of numeric values for that vector name.

    > salaries
    
    [1] 40000 50000 75000 92000
    
    > example1
    
    [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
    

Oftentimes, a data scientist is interested in generating a quick statistical summary of a dataset in the form of its mean, median, quartiles, min, and max. The R command called summary provides these results.

    > summary(salaries)
    
       Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
    
       40000   47500   62500   64250   79250   92000
    

For measures of spread, R includes a command for standard deviation, called sd(), and a command for variance, called var(). The standard deviation and variance are calculated with the assumption that the dataset was collected from a sample.

    > sd(salaries)
    
    [1] 23641.42
    
    > var(salaries)
    
    [1] 558916667
    

To calculate a weighted mean in R, create two vectors, one of which contains the data values and the other of which contains the associated weights. Then enter the R command weighted.mean(values, weights).

The following is an example of a weighted mean calculation in R:

EXAMPLE B.1

Problem

Assume a financial portfolio contains 1,000 shares of XYZ Corporation, purchased on three different dates, as shown in Table B1. Use R to calculate the weighted mean of the purchase price, where the weights are based on the number of shares in the portfolio.

Date Purchased	Purchase Price ($)	Number of Shares Purchased
January 17	78	200
February 10	122	300
March 23	131	500
Total		1000

Table B1 Portfolio of XYZ Shares

Solution

Here is how you would create two vectors in R: the price vector will contain the purchase price, and the shares vector will contain the number of shares. Then execute the R command weighted.mean(price, shares), as follows:

    > price <- c(78, 122, 131)
    
    > shares <- c(200, 300, 500)
    
    > weighted.mean(price, shares)
    
    [1] 117.7

A list of common R statistical commands appears in Table B2.

R Command	Result
mean()	Calculates the arithmetic mean
median()	Calculates the median
min()	Calculates the minimum value
max()	Calculates the maximum value
weighted.mean()	Calculates the weighted mean
sum()	Calculates the sum of values
summary()	Calculates the mean, median, quartiles, min, and max
sd()	Calculates the sample standard deviation
var()	Calculates the sample variance
IQR()	Calculates the interquartile range
barplot()	Plots a bar chart of non-numeric data
boxplot()	Plots a boxplot of numeric data
hist()	Plots a histogram of numeric data
plot()	Plots various graphs, including a scatter plot
freq()	Creates a frequency distribution table

Table B2 List of Common R Statistical Commands

Basic Visualization and Graphing Using R

R provides many built-in functions for data visualization and graphing and allows the data scientist significant flexibility and customization options for graphs and other data visualizations.

There are many statistical applications in R, and many graphical representations are possible, such as bar graphs, histograms, time series plots, scatter plots, and others.

As a simple example of a bar graph, assume a college instructor wants to create a bar graph to show enrollment in various courses such as statistics, history, physics, and chemistry courses.

Table B3 shows the enrollment data:

College Course	Student Enrollment
Statistics	375
History	302
Physics	294
Chemistry	193

Table B3 Enrollment Data

The basic command to create a bar graph in R is the command barchart().

First, create a dataframe called enrollment to hold the data (a dataframe can be considered a table or matrix to store the dataset).

enrollment <- data.frame(course=c("Statistics", "History", "Physics", "Chemistry"),
 enrolled=c(375, 302, 294, 193))
    

Next, use the barplot function to create the bar graph and add labels for x-axis, y-axis, and overall title.

barplot(enrollment$enrolled, names.arg=enrollment$course,
 main="Student Enrollment at the College", xlab="Course Name",
 ylab = "Enrollment")
    

The resulting output is shown below in Figure B2:

Figure B2 Bar Graph of Student Enrollment Data

The basic command to create a scatter plot in R is the plot command, plot(x, y), where x is a vector containing the x-values of the dataset and y is a vector containing the y-values of the dataset.

The general format of the command is as follows:

>plot(x, y, main="text for title of graph",
 xlab="text for x-axis label", ylab="text for y-axis label")

For example, we are interested in creating a scatter plot to examine the correlation between the value of the S&P 500 and Nike stock prices. Assume we have the data shown in Table B4, collected over a one-year time period.

Date	S&P 500	Nike Stock Price ($)
4/1/2020	2912.43	87.18
5/1/2020	3044.31	98.58
6/1/2020	3100.29	98.05
7/1/2020	3271.12	97.61
8/1/2020	3500.31	111.89
9/1/2020	3363.00	125.54
10/1/2020	3269.96	120.08
11/1/2020	3621.63	134.70
12/1/2020	3756.07	141.47
1/1/2021	3714.24	133.59
2/1/2021	3811.15	134.78
3/1/2021	3943.34	140.45
3/12/2021	3943.34	140.45
(source: https://finance.yahoo.com/)

Table B4 Data for S&P 500 and Nike Stock Price over a 12-Month Period

Note that data can be read into R from a text file or Excel file or from the clipboard by using various R commands. Assume the values of the S&P 500 have been loaded into the vector SP500 and the values of Nike stock prices have been loaded into the vector Nike. Then, to generate the scatter plot, we can use the following R command:

>plot(SP500, Nike, main="Scatter Plot of Nike Stock Price vs. S&P 500",
 xlab="S&P 500", ylab="Nike Stock Price")

As a result of these commands, R provides the scatter plot shown in Figure B3.

Figure B3 Scatter Plot Generated by R for Nike Stock Price vs. S&P 500