Basic Commands

R uses functions to perform operations. To run a function called funcname, we type funcname(input1, input2), where the inputs(or arguments) input1 argument and input2 tell R how to run the function. A function can have any number of inputs. For example, to create a vector of numbers, we use the function c() (for concatenate). Any numbers inside the parentheses are joined together. The following command instructs R to join together the numbers, \(1, 3, 2\), and \(5\), and to save them as a vector named x. When we type x, it gives back the vector.

x <- c(1,3,2,5)
x
## [1] 1 3 2 5

Note that the < is not part of the command; rather, it is printed by R to indicate that it is ready for another command to be entered. We can also save things using = rather than <-:

Note that the < is not part of the command; rather, it is printed by R to indicate that it is ready for another command to be entered. We can also save things using = rather than <-:

x = c(1, 6, 2)
x
## [1] 1 6 2
y = c(1, 4, 3)
y
## [1] 1 4 3

Hitting the up arrow multiple times will display the previous commands, which can then be edited. This is useful since one often wishes to repeat a similar command. In addition, typing ?funcname will always cause R to open a new help file window with additional information about the function funcname.

We can tell R to add two sets of numbers together. It will then add the first number from x to the first number from y and so on. However, x and y should be the same length. We can check their length using the length() function.

length(x)
## [1] 3
length(y)
## [1] 3
x+y
## [1]  2 10  5

The ls() function allows us to look at a list of all of the objects, such as data and functions, that we have saved so far. The rm() function can be used to delete any that we don’t want.

ls()
## [1] "x" "y"
rm(x,y)
ls()
## character(0)

It’s also possible to remove all objects at once:

rm(list = ls())

The matrix() function can be used to create a matrix of numbers. Before we use the matrix() function, we can learn more about it:

?matrix

The help file reveals that the matrix() function takes a number of inputs, but for now we focus on the first three: the data (the entries in the matrix), the number of rows, and the number of columns. First, we create a simple matrix.

x <- matrix(data = c(1, 2, 3, 4), nrow= 2, ncol= 2)
x
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4

Note that we could just omit typing data = , nrow =, and ncol = in the matrix() command above: that is, we could just type

x <- matrix(c(1, 2, 3, 4), 2, 2)

and this would have the same effect. However, it can sometimes be useful to specify the names of the arguments passed in, since otherwise R will assume that the function arguments are passed into the function in the same order that is given in the function’s help file. As this example illustrates, by default R creates matrices by successively filling in columns. Alternatively, the byrow = TRUE option can be used to populate the matrix in order of the rows.

x<- matrix(c(1, 2, 3, 4), 2, 2, byrow = TRUE)
x
##      [,1] [,2]
## [1,]    1    2
## [2,]    3    4

Notice that in the above command we did not assign the matrix to a value such as x. In this case the matrix is printed to the screen but is not saved for future calculations. The sqrt() function returns the square root of each element of a vector or matrix. The command x^2 raises each element of x to the power 2; any powers are possible, including fractional or negative powers.

sqrt(x)
##          [,1]     [,2]
## [1,] 1.000000 1.414214
## [2,] 1.732051 2.000000
x^2
##      [,1] [,2]
## [1,]    1    4
## [2,]    9   16

The rnorm function generates a vector of random normal variables, with first argument n the sample size. Each time we call this function, we will get a different answer. Here we create two correlated sets of numbers, x and y, and use the cor() function to compute the correlation between them.

x = rnorm(50)
y = rnorm(50, mean = 50, sd = 0.1)
cor(x,y)
## [1] 0.1393825

By default, rnorm creates standard normal random variables with a mean of 0 and a standard deviation of 1. However, the mean and standard deviation can be altered using the mean and sd arguments, as illustrated above. Sometimes we want our code to reproduce the exact same set of random numbers; we can use the set.seed() function to do this. The set.seed() function takes an (arbitrary) integer argument.

set.seed(1303)
rnorm(50)
##  [1] -1.1439763145  1.3421293656  2.1853904757  0.5363925179  0.0631929665
##  [6]  0.5022344825 -0.0004167247  0.5658198405 -0.5725226890 -1.1102250073
## [11] -0.0486871234 -0.6956562176  0.8289174803  0.2066528551 -0.2356745091
## [16] -0.5563104914 -0.3647543571  0.8623550343 -0.6307715354  0.3136021252
## [21] -0.9314953177  0.8238676185  0.5233707021  0.7069214120  0.4202043256
## [26] -0.2690521547 -1.5103172999 -0.6902124766 -0.1434719524 -1.0135274099
## [31]  1.5732737361  0.0127465055  0.8726470499  0.4220661905 -0.0188157917
## [36]  2.6157489689 -0.6931401748 -0.2663217810 -0.7206364412  1.3677342065
## [41]  0.2640073322  0.6321868074 -1.3306509858  0.0268888182  1.0406363208
## [46]  1.3120237985 -0.0300020767 -0.2500257125  0.0234144857  1.6598706557

We use set.seed() throughout the labs whenever we perform calculations involving random quantities. In general this should allow the user to reproduce our results. However, it should be noted that as new versions of R become available it is possible that some small discrepancies may form between the book and the output from R.

The mean() and var() functions can be used to compute the mean and variance of a vector of numbers. Applying sqrt() to the output of var() will give the standard deviation. Or we can simply use the sd() function.

set.seed(3)
y <- rnorm(100)
mean(y)
## [1] 0.01103557
var(y)
## [1] 0.7328675
sqrt(var(y))
## [1] 0.8560768
sd(y)
## [1] 0.8560768

Graphics

The plot() function is the primary way to plot data in R. For instance, plot(x,y)produces a scatterplot of the numbers in x versus the numbers in y. There are many additional options that can be passed in to thw plot() function. For example, passing in the argument xlab will result in a label on the x-axis. To find out more information about the plot() function, type ?plot.

x <- rnorm(100)
y <- rnorm(100)
plot(x,y)

plot(x, y, xlab = "this is the x-axis", ylab = "this is the y-axis", main = "Plot of X vs. Y")

We will often want to save the output of an R plot. The command that we use to do this will depend on the file type that we would like to create. For instance, to create a jpeg, we use the jpeg() function, and to create a pdf, we use the pdf() function.

jpeg(file = "filename.jpeg")
plot(x, y, col= "green")
dev.off()
## png 
##   2

The function dev.off() indicates to R that we are done creating the plot. Alternatively, we can simply copy the plot window and paste it into an appropriate file type, such as a Word document.

The function seq() can be used to create a sequence of numbers. For instance, seq(a,b) makes a vector of integers between a and b. There are so many other options: for instance, seq(0, 1, length = 10) makes a sequence of 10 numbers that are equally spaced between 0 and 1. Typing 3:11 is a shorthand for seq(3, 11) for integer arguments.

x <- seq(1, 10)
x
##  [1]  1  2  3  4  5  6  7  8  9 10
x <- seq(-pi, pi, length = 50)

We will now create some more sophisticated plots. The contour() function produces a contour plot in order to represent three-dimensional data; it is like a topographical map. It takes three arguments:

A vector of the x values (the first dimension), A vector of the y values (the second dimension), and A matrix whose elements correspond to the z value (the third dimension) for each pair of (x,y) coordinates. As with the plot() function, here are many other inputs that can be used to fine-tune the output of the contour() function. To learn more about these, take a look at the help file by typing ?contour.

y <- x
f <- outer(x, y, function(x, y){
  cos(y)/(1+x^2)
})
contour(x, y, f)
contour(x, y, f, nlevels = 45, add = TRUE)

fa <- (f -t(f))/2
contour(x, y, fa, nlevels = 15)

The image function works the same way as contour(), except that it produces a color-coded plot whose colors depend on the z value.This is known as a heatmap, and is sometimes used to plot temperature in weather forecasts. Alternatively, persp() can be used to produce a three-dimensional plot. The arguments theta and phi control the angle at which the plot is persp() viewed.

image(x, y, fa)

persp(x, y, fa)

persp(x, y, fa, theta = 30)

persp(x, y, fa, theta = 30, phi = 20)

persp(x, y, fa, theta = 30, phi = 70)

persp(x, y, fa, theta = 30, phi = 40)

##Indexing## We often wish to examine part of a set of data. Suppose that our data is stored in the matrix A.

A <- matrix(1:16, 4, 4)
A
##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14
## [3,]    3    7   11   15
## [4,]    4    8   12   16

Then typing,

A[2, 3]
## [1] 10

will select the element corresponding to the second row and the third column. The first number after the open-bracket symbol [ always refers to the row, and the second number always refers to the column. We can also select multiple rows and columns at a time, by providing vectors as the indices.

A[c(1, 3), c(2, 4)]
##      [,1] [,2]
## [1,]    5   13
## [2,]    7   15
A[1:3, 2:4]
##      [,1] [,2] [,3]
## [1,]    5    9   13
## [2,]    6   10   14
## [3,]    7   11   15
A[1:2,]
##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14
A[, 1:2]
##      [,1] [,2]
## [1,]    1    5
## [2,]    2    6
## [3,]    3    7
## [4,]    4    8

The last two examples include either no index for the columns or no index for the rows. These indicate that R should include all columns or all rows, respectively. R treats a single row or column of a matrix as a vector.

A[1,]
## [1]  1  5  9 13

The use of a negative sign - in the index tells R to keep all rows or columns except those indicated in the index.

A[-c(1,3),]
##      [,1] [,2] [,3] [,4]
## [1,]    2    6   10   14
## [2,]    4    8   12   16

The dim() function outputs the number of rows followed by the number of columns of a given matrix.

dim(A)
## [1] 4 4

Loading Data

For most analyses, the first step involves importing a data set into R. The read.table() function is one of the primary ways to do this. The help file contains details about how to use this function. We can use the function write.table() to export data. Before attempting to load a data set, we must make sure that R knows to search for the data in the proper directory. For example on a Windows system one could select the directory using the Change dir. . . option under the File menu. However, the details of how to do this depend on the operating system (e.g. Windows, Mac, Unix) that is being used, and so we do not give further details here. We begin by loading in the Auto data set. This data is part of the ISLR library (we discuss libraries in Chapter 3) but to illustrate the read.table() function we load it now from a text file. The following command will load the Auto.data file into R and store it as an object called Auto, in a format referred to as a data frame. (The text file can be obtained from this book’s website.)

site <- "http://www-bcf.usc.edu/~gareth/ISL/Auto.data"
Auto <- read.table(file = site)
head(Auto)
##     V1        V2           V3         V4     V5           V6   V7     V8
## 1  mpg cylinders displacement horsepower weight acceleration year origin
## 2 18.0         8        307.0      130.0  3504.         12.0   70      1
## 3 15.0         8        350.0      165.0  3693.         11.5   70      1
## 4 18.0         8        318.0      150.0  3436.         11.0   70      1
## 5 16.0         8        304.0      150.0  3433.         12.0   70      1
## 6 17.0         8        302.0      140.0  3449.         10.5   70      1
##                          V9
## 1                      name
## 2 chevrolet chevelle malibu
## 3         buick skylark 320
## 4        plymouth satellite
## 5             amc rebel sst
## 6               ford torino

Note that Auto.data is simply a text file, which you could alternatively open on your computer using a standard text editor. It is often a good idea to view a data set using a text editor or other software such as Excel before loading it into R. This particular data set has not been loaded correctly, because R has assumed that the variable names are part of the data and so has included them in the first row. The data set also includes a number of missing observations, indicated by a question mark ?. Missing values are a common occurrence in real data sets. Using the option header = TRUE in the read.table() function tells R that the first line of the file contains the variable names, and using the option na.strings tells R that any time it sees a particular character or set of characters (such as a question mark), it should be treated as a missing element of the data matrix.

Auto <- read.table(file = site, header = TRUE, sep = "", na.strings = "?")
head(Auto)
##   mpg cylinders displacement horsepower weight acceleration year origin
## 1  18         8          307        130   3504         12.0   70      1
## 2  15         8          350        165   3693         11.5   70      1
## 3  18         8          318        150   3436         11.0   70      1
## 4  16         8          304        150   3433         12.0   70      1
## 5  17         8          302        140   3449         10.5   70      1
## 6  15         8          429        198   4341         10.0   70      1
##                        name
## 1 chevrolet chevelle malibu
## 2         buick skylark 320
## 3        plymouth satellite
## 4             amc rebel sst
## 5               ford torino
## 6          ford galaxie 500
library(DT)
datatable(Auto)

Excel is a common-format data storage program. An easy way to load such data into R is to save it as a csv (comma separated value) file and then use the read.csv() function to load it in.

site <- "http://www-bcf.usc.edu/~gareth/ISL/Auto.csv"
Auto1 <- read.csv(file = site, na.strings = "?")
dim(Auto1)
## [1] 397   9
datatable(Auto1, rownames = FALSE, class = 'cell-border stripe', colnames = c('cyl' = 'cylinders', 'disp' = 'displacement', 'hp' = 'horsepower', 'accel' = 'acceleration'))

The dim() function tells us that the data has 397 observations, or rows, and 9 variables, or columns. There are various ways to deal with the missing data. In this case, only five of the rows contain missing observations, and so we choose to use the na.omit() function to simply remove these rows.

Auto2 <- na.omit(Auto1)
dim(Auto2)
## [1] 392   9
names(Auto2)
## [1] "mpg"          "cylinders"    "displacement" "horsepower"  
## [5] "weight"       "acceleration" "year"         "origin"      
## [9] "name"