1  R Basics

1.1 Basic Calculator

R can be used as a calculator. Enter the following in the console.

2 + 2*sin(pi)

[1] 2

1.2 Assign a variable

When we assign a value to a variable, it is better to use the assignment operator “<-” as below.

n <- 20
x <- 3^2

There is a general preference among the R community to use “<-” (instead of “=”) for assignment for compatibility with (very) old versions of S-Plus.

Now you can click on environment (top right panel) to see the variables.

You will make lots of assignments, and <- can be annoying to type. You can save time with RStudio’s keyboard shortcut: Alt & - (the minus sign). Notice that RStudio automatically surrounds <- with spaces, which is a good code formatting practice.

1.3 Basic R workspace functions

command	usage
rm(x)	remove variable x
rm(list = ls())	remove all variables in the current environment
getwd()	list the current working directory
setwd(“/home/username/folder”)	change current working directory
cat(“\014”)	clears console (same as ctrl + l)
help(mean) or ?mean	Getting Help on function mean()
class()	find out data structure
str()	also find out data structure, can be more concise than class()

The # symbol begins a comment. These will be used regularly to notate the action immediately below the comment. If a commented line is run in the R console, nothing will happen.

Keyboard shortcut:

shortcut	function
[Alt] + [-]	generate ” <- ”
[Tab]	auto-fill
[Cmd/ctrl] + [enter]	execute code
[↑]	bring command history
[Cmd/Ctrl] + [↑]	bring command history with the same starting letters typed in console

1.4 Structures in R

There are several types of structures (or variable types) in R.

1.4.1 Vector: a one dimensional array

The following defines a vector in R.

x <- c(3, -1, -3, 5, 2)
x

[1]  3 -1 -3  5  2

You can have a vector of strings.

s <- c("a", "b", "c", "d", "e")

In R, the indexing starts at 1. Retrieve the 4th coordinate of s:

s[4]

[1] "d"

Retrieve the first 3 coordinates of s

s[1:3]

[1] "a" "b" "c"

Retrieve the 1st, 2nd, and 5th coordinates of s

s[c(1, 2, 5)]

[1] "a" "b" "e"

Retrieve all coordinates but the 3rd

s[-3]

[1] "a" "b" "d" "e"

length(s)

[1] 5

The function seq() is very handy in creating equally spaced numbers.

seq(from = 1, to = 10)

 [1]  1  2  3  4  5  6  7  8  9 10

seq(from = 0, to = 1, by = 0.2)

[1] 0.0 0.2 0.4 0.6 0.8 1.0

y <- seq(1, 5)
y

[1] 1 2 3 4 5

And basic arithmetic on vectors is applied to every element of of the vector.

x * y

[1]  3 -2 -9 20 10

1.4.2 Data Frame

To create a df,

my_df <- data.frame(name = c("Amy", "Bob", "Cindy"),
                    Height = c(160, 170, 165))
my_df

   name Height
1   Amy    160
2   Bob    170
3 Cindy    165

1.4.2.1 Subselect

To retrieve the entry at the 3rd row and 2nd column.

my_df[3, 2]

[1] 165

To retrieve the 2nd row of a df.

my_df[2, ]

  name Height
2  Bob    170

Multiple ways to retrieve 1st col: df[,1], df[[1]], df$colname

my_df[, 1]

[1] "Amy"   "Bob"   "Cindy"

my_df[[1]]

[1] "Amy"   "Bob"   "Cindy"

my_df$name

[1] "Amy"   "Bob"   "Cindy"

In all the subselecting commands above, you can always replace the column index by the corresponding column name. For example, my_df[, 1] is the same as my_df[, “name”].

my_df[, 1]

[1] "Amy"   "Bob"   "Cindy"

my_df[, "name"]

[1] "Amy"   "Bob"   "Cindy"

The following is to subselect the first col and keep the data frame structure

my_df[1]

   name
1   Amy
2   Bob
3 Cindy

Recall that we can use class() to find out the data structure of any object.

class(my_df[, 1])

[1] "character"

class(my_df[1])

[1] "data.frame"

The function data() lists all data sets stored in R. “CO2” is a data frame that is stored in R.

Learn more about this data set.

?CO2

The following commands are good for learning the data more.

head(CO2) # show the first 6 rows

  Plant   Type  Treatment conc uptake
1   Qn1 Quebec nonchilled   95   16.0
2   Qn1 Quebec nonchilled  175   30.4
3   Qn1 Quebec nonchilled  250   34.8
4   Qn1 Quebec nonchilled  350   37.2
5   Qn1 Quebec nonchilled  500   35.3
6   Qn1 Quebec nonchilled  675   39.2

colnames(CO2) # get all the column names

[1] "Plant"     "Type"      "Treatment" "conc"      "uptake"   

dim(CO2) # find out the dimension (number of rows and number of columns)

[1] 84  5

nrow(CO2) # find out number of rows

[1] 84

We will be working with data frames a lot throughout this course.

1.4.2.2 Subselect with a condition

CO2[CO2$uptake > 40, ]

   Plant   Type  Treatment conc uptake
11   Qn2 Quebec nonchilled  350   41.8
12   Qn2 Quebec nonchilled  500   40.6
13   Qn2 Quebec nonchilled  675   41.4
14   Qn2 Quebec nonchilled 1000   44.3
17   Qn3 Quebec nonchilled  250   40.3
18   Qn3 Quebec nonchilled  350   42.1
19   Qn3 Quebec nonchilled  500   42.9
20   Qn3 Quebec nonchilled  675   43.9
21   Qn3 Quebec nonchilled 1000   45.5
35   Qc2 Quebec    chilled 1000   42.4
42   Qc3 Quebec    chilled 1000   41.4

1.4.3 Factors

The 2nd column of “CO2” is a factor. Factors are very useful for categorical variables.

class(CO2[, 2])

[1] "factor"

levels(CO2[, 2])

[1] "Quebec"      "Mississippi"

table(CO2[, 2])

     Quebec Mississippi 
         42          42 

type2 <- factor(CO2[, 2], levels = c("Quebec", "Mississippi", "Others"))
table(type2)

type2
     Quebec Mississippi      Others 
         42          42           0 

1.4.4 Lists

Also see Section 27.3.3 of Hadley

A list can be thought of a vector that store different types of structures.

l <- list(a = 1:3,
          b = "string",
          c = data.frame(c1 = c(1, 2), c2 = c(2, 2)))

[ extracts a sub-list. For example, l[1:2] is still a list.

l[1:2]

$a
[1] 1 2 3

$b
[1] "string"

[[ or $ extracts a single component from a list. For example, l[[1]] is a vector.

l[[1]]

[1] 1 2 3

1.5 Coding Style

• Variable name style: my_variable
• Put spaces on either side of mathematical operators and the assignment operator, except “^”. For “*” or “/”, some coders choose to put spaces around it, and some don’t.
• Put a space after comma.

Good examples:

# x^2
# x * y
# x*y
# x / y
# x/y
# x + y
# x - y
# x[1:3] # no space around colon
# df[1, ]

Read 4.1 and 4.2 of this book for more details.

1.6 Probability related functions

R is great in terms of probability tasks and statistical analysis.

For each kind of probability distribution, R has four accompanying functions. For example, for Gaussian (normal) distribution,

• rnorm(): this randomly generates numbers following the normal distribution with specified mean and standard deviation.
• pnorm(): this gives the cumulative probability function of the specified normal distribution.
• dnorm(): this gives the density function of the specified normal distribution.
• qnorm(): this gives the quantile/percentile of the specified normal distribution. This is inverse function or pnorm().

# generate 3 random numbers following the normal distribution with mean 2 and sd 0.2.
rnorm(n = 3, mean = 2, sd = 0.2)

[1] 1.757635 2.092836 2.035169

If we use set.seed(), then the results are repeatable.

set.seed(10)
rnorm(4) # default is the standard normal distribution: mean = 0, sd = 1

[1]  0.01874617 -0.18425254 -1.37133055 -0.59916772

The density function of \(X \sim N(\mu, \sigma^2)\) is \[f(x) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}.\] This function is dnorm() in R.

mu <- 1.6
sigma <- 1
x <- 1.8
dnorm(x, mu, sigma)

[1] 0.3910427

1/sqrt(2*pi*sigma^2)*exp(- (x - mu)^2/(2*sigma^2))

[1] 0.3910427

The following computes \(P(X<2)\) where \(X\) follows the normal distribution with \(\mu=1.6, \sigma=1\).

pnorm(2, 1.6, 1) 

[1] 0.6554217

The following computes \(q\) such that \(P(X<q) = 0.8\) where \(X\) follows the normal distribution with \(\mu=1.6, \sigma=1\).

qnorm(0.8, 1.6, 1)

[1] 2.441621

pnorm() and qnorm() are inverse functions of each other.

a <- 2
b <- pnorm(a, 1.6, 1) 
qnorm(b, 1.6, 1) # the output has to be a

[1] 2

The other distributions work similarly. For example, runif() generates random numbers coming from the uniform distribution.

1.7 Define functions in R

The syntax for defining a new function in R is

# function_name <- function(parameter){content}

1.8 Loops in R

To be filled

1.9 Read/save files

• read_csv creates a tibble.
• read.csv creates a regular data frame.
• write.csv(df, “specify_path_and_file_name.csv”)

to be continued

1.10 Base R plotting

In the near future, we will be using package “ggplot2” for its great data visualization ability. However, it is still very useful to know how to use base R to plot for its convenience and simplicity.

1.10.1 scatter plot

x <- c(2, 1, 3)
y <- c(100, 200, 300)
plot(x, y)

plot(x, y, type = "l", col = "red",
     main = "Title", xlab = "x label", ylab = "y label")

1.10.2 histogram

hist(CO2$uptake)

hist(CO2$uptake, breaks = seq(5, 50, 2.5))