B | Appendix B: Review of R Studio for Data Science

Basic Data Analysis Using R

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:

    > 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.

mean()

median()

min()

max()

weighted.mean()

sum()

summary()

sd()

var()

IQR()

barplot()

boxplot()

hist()

plot()

freq()

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:

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.

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

R Analysis for Probability Distributions

As mentioned earlier, a quick statistical summary can be generated using the summary() command in R, where the usage is summary(data_vector).

R has extensive built-in libraries for calculating confidence intervals, hypothesis testing, and working with various probability distributions such as binomial, Poisson, normal, chi-square, and other probability distributions.

As discussed in Measures of Center, data scientists are often interested in various probability distributions such as the normal distribution, binomial distribution, and Poisson distribution. Excel provides built-in functions to analyze many probability distributions.

R uses the pnorm command to find the area under the normal curve to the left of a specified value:

Usage: pnorm(x_value, mean, standard_deviation)

where pnorm returns the probability that a random variable having a given mean and standard deviation is less than x_value.

pnorm(4000, 3400, 500)

[1] 0.8849303

pnorm(3000, 3400, 500, lower.tail=FALSE)

[1] 0.7881446

Usage: pbinom(k, n, p)

pbinom(13, 20, 0.65)

[1] 0.5833746

Usage: dbinom(k, n, p)

dbinom(13, 20, 0.65)

[1] 0.1844012

Usage: dpois(k, mu)

dpois(5, 3)

[1] 0.1008188

Basic Correlation and Regression Analysis Using R

Recall in Inferential Statistics and Regression Analysis the discussion on correlation and regression analysis. A first step in correlation analysis is to calculate the correlation coefficient (r) for (x, y) data. R provides a built-in function cor() to calculate the correlation coefficient for bivariate data.

As an example, consider the dataset in Table B5 that tracks the return on the S&P 500 versus return on Coca-Cola stock for a seven-month time period.

To calculate the correlation coefficient for this dataset, first create two vectors in R, one vector for the S&P 500 returns and a second vector for Coca-Cola returns:

    > SP500 <- c(8,1,0,2,-3,7,4)
    
    > CocaCola <- c(6,0,-2,1,-1,8,2)

The R command called cor returns the correlation coefficient for the x-data vector and y-data vector:

    > cor(SP500, CocaCola)
    
    [1] 0.9123872

Thus the correlation coefficient for this dataset is approximately 0.912.

lm(dependent_variable_vector ~ independent_variable_vector)

    > lm(CocaCola ~ SP500)
    
    Call:
    
    lm(formula = CocaCola ~ SP500)
    
    Coefficients:
    
    (Intercept)    SP500
    
       -0.3453   0.8641

    > model <- lm(CocaCola ~ SP500)
    
    > summary(model)
    
    Call:
    
    lm(formula = CocaCola ~ SP500)
    
    Residuals:
    
          1    2    3    4    5    6    7
    
    -0.5672 -0.5188 -1.6547 -0.3828 1.9375 2.2969 -1.1109
    
    Coefficients:
    
            Estimate Std. Error t value Pr(>|t|)
    
    (Intercept) -0.3453   0.7836 -0.441 0.67783
    
    SP500     0.8641   0.1734  4.984 0.00416 **
    ---
    Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    
    Residual standard error: 1.658 on 5 degrees of freedom
    
    Multiple R-squared: 0.8325,  Adjusted R-squared: 0.7989
    
    F-statistic: 24.84 on 1 and 5 DF, p-value: 0.004161

    > a <- data.frame(SP500=6)
    
    > predict(model, a)
    
         1
    
    4.839062

    > predict(model, a, interval="predict")
    
      fit    lwr   upr
    
    1 4.839062 0.05417466 9.62395

> model <- lm(y ~ x)

> model <- lm(y ~ x1 + x2 + x3)

    > price <- c(466000, 355000, 405900, 415000, 206000, 462000, 290000)
    > square_footage <- c(4668, 3196, 3998, 4022, 1834, 4668, 2650)
    > bedrooms <- c(6, 5, 5, 5, 2, 6, 3)

    > model <- lm(price ~ square_footage + bedrooms)
    > summary(model)
    
    Call:
    lm(formula = price ~ square_footage + bedrooms)
    
    Residuals:
           1       2       3       4       5       6       7
    -1704.6  1438.4  -606.9  6908.7 -6747.4 -5704.6  6416.5
    
    Coefficients:
                           Estimate Std. Error t value Pr(>|t|)
    (Intercept)    57739.887   9529.693   6.059  0.00375 **
    square_footage    66.017      8.924   7.398  0.00178 **
    bedrooms       16966.536   6283.183   2.700  0.05408 .
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    
    Residual standard error: 6563 on 4 degrees of freedom
    Multiple R-squared:  0.9968,    Adjusted R-squared:  0.9953
    F-statistic: 630.6 on 2 and 4 DF,  p-value: 9.996e-06