RStudio

Go to jupyter.utoronto.ca/hub/login, select RStudio and Log in with UToronto credentials.

When you open RStudio, you should see something like this:


There should be 3 different windows along with a number of tabs.

Left

This is the R console, where you key in commands to be run in an interactive fashion. Type in your command and hit the Enter key. Once you hit the Enter key, R executes your command and prints the result, if any.

Top-right

  • Environment: List of objects that we have created or have access to. We can also see the list of objects using the command ls().

Bottom-right

  • Plots: Any graphical output you make will be displayed here.
  • Help: Documentation for functionName appears here when you type ?functionName in the console.

R as a calculator

You can use R has a high-powered calculator. For example, type the following command in R console and hit Enter key

1 + 2
## [1] 3

Now try

456 * 7
## [1] 3192
5 / 2
## [1] 2.5

There are several math functions which come with R. For example, to evaluate \(log (e^{25} - 2^{\sin(\pi)})\), we would type

log(exp(25) - 2^(sin(pi)))
## [1] 25

Variable assignment

Often, we want to store the result of a computation so that we can use it later. R allows us to do this by variable assignment. Variable names must start with a letter and can only contain letters, numbers, _ and ..

The following code assigns the value 2 to the variable x:

x = 2

Notice that no output was printed. This is because the act of variable assignment doesn’t produce any output. If we want to see what x contains, simply key its name into the console:

x
## [1] 2

We can use x in computations:

x^2 + 3*x
## [1] 10

We can also reassign x to a different value:

x = x^2
x
## [1] 4

What is the value of x and y after I execute the following code?

y = x
x = x^2

Let’s add a third variable:

z = 3

Note that we now have 3 entries in our Environment tab. Environment shows you all the “saved” object you have. To remove an object/variable, use the rm() function:

rm(x)

To remove more than one object, separate them by commas:

rm(y, z)

Let’s add the 3 variables back again:

x = 1 
y = 2 
z = 3

To remove all objects at once, use the following code:

rm(list = ls())

(Alternatively, press the “Broom” icon in the Environment)

Vectors

For data analysis, we often have to work with multiple values at the same time. There are a number of different R objects which allow us to do this.

The vector is a 1-dimensional array whose entries are the same type. For example, the following code produces a vector containing the numbers 1,2 and 3. Type and run the following lines in R console:

vec = c(1, 2, 3)
vec
## [1] 1 2 3

Typing out all the elements can be tedious. Sometimes there are shortcuts we can use. The following code assigns a vector of the numbers 1 to 100 to vec:

vec = 1:10
vec
##  [1]  1  2  3  4  5  6  7  8  9 10

What if I only want even numbers from 1 to 100 (inclusive)? (Type ?seq and run it to read the documentation for the seq function and figure out what it returns.)

even = seq(from = 2, to = 100, by = 2)
even
##  [1]   2   4   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34  36  38
## [20]  40  42  44  46  48  50  52  54  56  58  60  62  64  66  68  70  72  74  76
## [39]  78  80  82  84  86  88  90  92  94  96  98 100

R allows us to access individual elements in a vector. Unlike many other programming languages, indexing begins at 1, not 0. For example, to return the first even number, I would use the following code:

even[1]
## [1] 2

We can get multiple elements of a vector as well. The following code extracts the 3rd to 7th even number (inclusive), and assigns it to the variable y:

even[3:7]
## [1]  6  8 10 12 14

This extracts just the 3rd and 5th even numbers:

even[c(3,5)]
## [1]  6 10

What if I want all even numbers except the first two? I can use negative indexing to achieve my goal:

even[-c(1,2)]
##  [1]   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34  36  38  40  42
## [20]  44  46  48  50  52  54  56  58  60  62  64  66  68  70  72  74  76  78  80
## [39]  82  84  86  88  90  92  94  96  98 100

Use the length function to figure out how many elements there are in a vector. 

length(even)
## [1] 50

Data frames

R has some user-created datasets. In R, datasets are called data frames.

To check the datasets available in R run:

data()

The following line will open the detailed description of the iris dataset in the help window.

?iris

Let’s view the data with the View() function (note the capital V). A new tab pops up in the top-left pane displaying the data. Clicking on the column names allows us to sort the data.

View(iris)

Seeing parts of the data

50 observations is a lot of observations to look through. Instead of looking through all of it, we can use various functions to give us a feel for the data.

Use the head and tail functions to display the first few or last few rows of the dataset. To control the number of lines shown (default is 6), use the optional n argument.

head(iris)
##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa
tail(iris, n = 2)
##     Sepal.Length Sepal.Width Petal.Length Petal.Width   Species
## 149          6.2         3.4          5.4         2.3 virginica
## 150          5.9         3.0          5.1         1.8 virginica

We can get the data frame’s column names (data variables) using names():

names(iris)
## [1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width"  "Species"

To access the elements in a particular column, we can use the [["..."]] or $... notation:

iris$Sepal.Length
##   [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4 5.1
##  [19] 5.7 5.1 5.4 5.1 4.6 5.1 4.8 5.0 5.0 5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.0
##  [37] 5.5 4.9 4.4 5.1 5.0 4.5 4.4 5.0 5.1 4.8 5.1 4.6 5.3 5.0 7.0 6.4 6.9 5.5
##  [55] 6.5 5.7 6.3 4.9 6.6 5.2 5.0 5.9 6.0 6.1 5.6 6.7 5.6 5.8 6.2 5.6 5.9 6.1
##  [73] 6.3 6.1 6.4 6.6 6.8 6.7 6.0 5.7 5.5 5.5 5.8 6.0 5.4 6.0 6.7 6.3 5.6 5.5
##  [91] 5.5 6.1 5.8 5.0 5.6 5.7 5.7 6.2 5.1 5.7 6.3 5.8 7.1 6.3 6.5 7.6 4.9 7.3
## [109] 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7 7.7 6.0 6.9 5.6 7.7 6.3 6.7 7.2
## [127] 6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7 6.3 6.4 6.0 6.9 6.7 6.9 5.8 6.8
## [145] 6.7 6.7 6.3 6.5 6.2 5.9
iris[["Sepal.Length"]]
##   [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4 5.1
##  [19] 5.7 5.1 5.4 5.1 4.6 5.1 4.8 5.0 5.0 5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.0
##  [37] 5.5 4.9 4.4 5.1 5.0 4.5 4.4 5.0 5.1 4.8 5.1 4.6 5.3 5.0 7.0 6.4 6.9 5.5
##  [55] 6.5 5.7 6.3 4.9 6.6 5.2 5.0 5.9 6.0 6.1 5.6 6.7 5.6 5.8 6.2 5.6 5.9 6.1
##  [73] 6.3 6.1 6.4 6.6 6.8 6.7 6.0 5.7 5.5 5.5 5.8 6.0 5.4 6.0 6.7 6.3 5.6 5.5
##  [91] 5.5 6.1 5.8 5.0 5.6 5.7 5.7 6.2 5.1 5.7 6.3 5.8 7.1 6.3 6.5 7.6 4.9 7.3
## [109] 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7 7.7 6.0 6.9 5.6 7.7 6.3 6.7 7.2
## [127] 6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7 6.3 6.4 6.0 6.9 6.7 6.9 5.8 6.8
## [145] 6.7 6.7 6.3 6.5 6.2 5.9

We can use the ncol() and nrow() functions to get the number of columns and rows of the data frame:

ncol(iris)
## [1] 5
nrow(iris)
## [1] 150

Alternatively, we can use dim() to figure out the number of rows and columns in the data frame:

dim(iris)
## [1] 150   5

To access the 30th row (observation), we can type

iris[30, ]
##    Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 30          4.7         3.2          1.6         0.2  setosa

Getting an overview of the data

For an overview of the entire data set, the str function we introduced last session is very handy. For each column, str tells us what type of variable it is (num = quantitative, Factor = categorical), as well as the first couple of values for the column.

str(iris)
## 'data.frame':    150 obs. of  5 variables:
##  $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
##  $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
##  $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
##  $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
##  $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

The summary function gives us some useful statistics for each variable:

summary(iris)
##   Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   
##  Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100  
##  1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300  
##  Median :5.800   Median :3.000   Median :4.350   Median :1.300  
##  Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199  
##  3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800  
##  Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500  
##        Species  
##  setosa    :50  
##  versicolor:50  
##  virginica :50  
##                 
##                 
##

We can also do summaries on just one column:

summary(iris$Sepal.Length)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   4.300   5.100   5.800   5.843   6.400   7.900

For just the mean or median, use the mean and median functions on the column of interest:

mean(iris$Sepal.Length)
## [1] 5.843333
median(iris$Sepal.Length)
## [1] 5.8

To get the first and third quartiles use:

quantile(iris$Sepal.Length, probs = 0.25)
## 25% 
## 5.1
quantile(iris$Sepal.Length, probs = 0.75)
## 75% 
## 6.4

The sd() and var() functions compute the standard deviation and variance of a vector for us:

sd(iris$Sepal.Length)
## [1] 0.8280661
var(iris$Sepal.Length)
## [1] 0.6856935

The cor() and cov() functions compute the correlation and covariance between two variables:

cor(iris$Sepal.Length, iris$Sepal.Width)
## [1] -0.1175698
cov(iris$Sepal.Length, iris$Sepal.Width)
## [1] -0.042434

Graphics

For this part, we’ll use the built-in mtcars datset as a running example.

Let’s check the data description first and print the top 6 rows of the data:

?mtcars
head(mtcars)

Scatterplot

Let’s say we are interested in the relationship between mpg and wt. We can make a scatterplot using the plot command, defining the x and y arguments of the function. (Recall that data frames are really just lists, so mtcars$wt refers to the wt element of mtcars, i.e. the values in the wt column.)

plot(x = mtcars$wt, y = mtcars$mpg)

To have the points be represented by other shapes (instead of white circles), add the pch argument to plot (full list of shapes here): To change the size of the points, add the cex option to plot (1 is the default value). To change the color of the points, use the col option:

plot(x = mtcars$wt, y = mtcars$mpg, pch = 5, cex = 2, col = "blue")

The code below shows how you can add titles and change the axis labels and the plot title:

plot(x = mtcars$wt, y = mtcars$mpg,
     main = "Miles per gallon vs. Weight", xlab = "Weight", ylab = "mpg")

Histograms

A histogram shows the frequency count of one variable. To plot a histogram, use the hist command:

hist(mtcars$mpg)

The number of bins is determined by an algorithm that R runs. If you want to specify the number of bins, you can use the breaks option and give it a number:

hist(mtcars$mpg, breaks = 10, col = "red")

Because of R’s algorithm for determining the number of bins, sometimes the number of bins you get doesn’t correspond exactly to the number you gave to breaks. To have exact control over this, instead of giving breaks an integer, you could give it a vector of “breakpoints” instead. For example, the code below bins the values into (10, 12], (12, 14], …, (32, 34].

hist(mtcars$mpg, breaks = seq(10, 34, by = 2), 
     main = "Miles per gallon: histogram", xlab = "mpg", ylab = "Count")

Boxplots

Boxplot is one of the ways to represent the data summary:

summary(mtcars$mpg)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   10.40   15.43   19.20   20.09   22.80   33.90

To make a boxplot, use the boxplot function:

boxplot(mtcars$mpg)

To make a boxplot for each category of cyl run:

boxplot(mtcars$mpg~mtcars$cyl,  
        main = "Miles per gallon vs. Number of cylinders", xlab = "cyl", ylab = "mpg")

Bar plots

As we discussed in class, you can summarize a categorical variable using it’s distribution table.

table(mtcars$cyl)
## 
##  4  6  8 
## 11  7 14

To convert this table to relative frequencies, use prop.table() function.

tab = table(mtcars$cyl) #save the distibution table into tab variable
prop.table(tab) #apply prop.table function to tab
## 
##       4       6       8 
## 0.34375 0.21875 0.43750

If you want a bar plot showing how many rows there are for each value of cyl, I have to use the table function in conjunction with the barplot function.

barplot(table(mtcars$cyl))

Let’s add a bit of color!

barplot(table(mtcars$cyl), col = c("red", "blue", "green"),
         main = "Number of cylinders: barplot", xlab = "cyl", ylab = "Counts")

Another useful plot for categorical variables is a pie chart:

pie(table(mtcars$cyl), col = c("red", "blue", "green"), main = "Number of cylinders: pie chart")

If you want to find the relationship between cyl and am (transmission variable, 0 = automatic, 1 = manual) you can first check the contingency table.

table(mtcars$cyl, mtcars$am)
##    
##      0  1
##   4  3  8
##   6  4  3
##   8 12  2

You can use barplot function to produce the stacked barplot. Note that legend=TRUE creates a legend at the top right corner.

barplot(table(mtcars$cyl, mtcars$am), col = c("red", "blue", "green"), legend = TRUE, 
         xlab = "am", ylab = "Counts")

Use beside=TRUE to specifiy that bars are not stacked.

barplot(table(mtcars$cyl, mtcars$am), beside = TRUE, col = c("red", "blue", "green"), legend = TRUE, 
         xlab = "am", ylab = "Counts")

To find conditional distribution for two variables use prop.table function. Note that we use margin = 1 to condition on cyl and margin = 2 to condition on am.

prop.table(table(mtcars$cyl, mtcars$am), margin  = 1)
##    
##             0         1
##   4 0.2727273 0.7272727
##   6 0.5714286 0.4285714
##   8 0.8571429 0.1428571
prop.table(table(mtcars$cyl, mtcars$am), margin  = 2)
##    
##             0         1
##   4 0.1578947 0.6153846
##   6 0.2105263 0.2307692
##   8 0.6315789 0.1538462

Combining conditional distribution table with the barplot we get:

tab = prop.table(table(mtcars$cyl, mtcars$am), margin  = 2)
barplot(tab, col = c("red", "blue", "green"), legend = TRUE, 
         xlab = "am", ylab = "Counts")

Some other resources if you are interested in learning more about plotting in base R: