Creating variables

We can create variables by assigning them values:

firstvariable = 0 
secondvariable = 10
thirdvariable = TRUE
fourthvariable = "hello"

If we want to print a variable, we can type its name. For example:

fourthvariable
## [1] "hello"

We can see the “type” of the variables using the function class:

class(firstvariable)
## [1] "numeric"
class(thirdvariable)
## [1] "logical"
class(fourthvariable)
## [1] "character"

The names of the types of these variables are pretty intuitive but here’s an explanation:

Operations with variables

We can add, subtract, multiply, divide, and exponentiate numeric variables:

firstvariable+secondvariable
## [1] 10
firstvariable-secondvariable
## [1] -10
firstvariable*secondvariable
## [1] 0
firstvariable^secondvariable # exponentiation
## [1] 0

We can combine operations. For example, we can compute the average of firstvariable and secondvariable as

(firstvariable+secondvariable)/2
## [1] 5

R has a built-in mean function, which we’ll see later.

We can’t add, subtract, multiply, divide or exponentiate character variables (try it out: it’ll give you an error), but we can add, subtract, multiply, divide or exponentiate logical variables. If the variable is TRUE it’ll be treated as a 1; if it’s FALSE, it’ll be treated as a 0:

logi1 = TRUE
logi2 = FALSE
logi1+logi2 
## [1] 1
logi1*logi2 
## [1] 0
logi1/logi2 
## [1] Inf
logi1^logi2
## [1] 1

We can combine logical and numeric variables in operations. Again, TRUE will be assigned 1, and FALSE will be assigned 0.

Finally, we can do operations without using variables at all:

6/2*(2+1+TRUE)
## [1] 12

Arithmetic functions

R has built-in functions such as sqrt, exp, log, …

sqrt(4)
## [1] 2
exp(firstvariable)
## [1] 1
log(10, base=2)
## [1] 3.321928

If you’re not sure how a function works, you can ask for help by writing ? before the name of the function.

Vectors

We can define vectors as follows:

x1 = c(1, 2, 3, 4, 5, 6)
y1 = c("a","b","c","d","efg")
z1 = c("a", 2, 3, "e")

And we can create ranges of values with :

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

Operations with vectors

We can add, multiply, divide, etc. all the components of a numeric vector by the same number:

x1+5
## [1]  6  7  8  9 10 11
x1*5
## [1]  5 10 15 20 25 30
x1/5
## [1] 0.2 0.4 0.6 0.8 1.0 1.2

We can add and subtract vectors of the same length:

x2 = c(7, 8, 9, 10, 11, 12)
x1+x2
## [1]  8 10 12 14 16 18
x1-x2
## [1] -6 -6 -6 -6 -6 -6

Similarly, we can do componentwise multiplication and division:

x1*x2
## [1]  7 16 27 40 55 72
x1/x2
## [1] 0.1428571 0.2500000 0.3333333 0.4000000 0.4545455 0.5000000

If two vectors are of different lengths, we have to be careful! R won’t give us a warning message:

x1
## [1] 1 2 3 4 5 6
x3 = c(2,3)
x1+x3
## [1] 3 5 5 7 7 9
x1*x3 
## [1]  2  6  6 12 10 18

We can compute the dot product of 2 numeric vectors of the same length:

t(x1)%*%x2
##      [,1]
## [1,]  217

We can compute means, standard deviations, variances, etc:

mean(x1)
## [1] 3.5
sd(x1)
## [1] 1.870829
var(x1)
## [1] 3.5

length and concatenating

We can find the length of a vector with length:

length(x1)
## [1] 6

And we can add values to an existing vector as follows:

x1
## [1] 1 2 3 4 5 6
c(x1,10) # add at the end
## [1]  1  2  3  4  5  6 10
c(10, x1) # add at the beginning
## [1] 10  1  2  3  4  5  6

We can concatenate vectors, too:

c(x1, x2)
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12

Indexing vectors

We can look at particular entries of a vector using brackets.

x1
## [1] 1 2 3 4 5 6
x1[1] # first entry
## [1] 1
x1[4] # 4th entry
## [1] 4
x1[length(x1)] # last entry
## [1] 6

In R, indices start at 1 (in some other programming languages, indices start at 0).

We can access subsets of vectors using vectors. For example, if we want to print the third and fifth entries of x1:

x1[c(3,5)]
## [1] 3 5

We can subset using ranges of values with :. For instance, if we want to select the second, third, fourth, and fifth entries of x1:

x1[2:5]
## [1] 2 3 4 5

Matrices

We can create matrices as follows:

A1 = matrix(c(1,2,3,4), nrow=2, ncol=2, byrow=TRUE) # read by row 
A2 = matrix(c(1,3,2,4), nrow=2, ncol=2, byrow=FALSE) # read by column

Doing operations with matrices is straightforward:

A1%*%A2 # matrix product
##      [,1] [,2]
## [1,]    7   10
## [2,]   15   22
A1*A2 # componentwise product
##      [,1] [,2]
## [1,]    1    4
## [2,]    9   16
A1+A2  # componentwise addition
##      [,1] [,2]
## [1,]    2    4
## [2,]    6    8
log(A1) # taking the log of the components
##          [,1]      [,2]
## [1,] 0.000000 0.6931472
## [2,] 1.098612 1.3862944

Indexing matrices is similar to indexing vectors. For example, if we want to access the element in the first row and second column of A1:

A1[1,2] # accessing entries: rows first, then columns
## [1] 2

You can also index by full rows and columns. For example, if you want to select the first row of A1:

A1[1,]
## [1] 1 2

If you want to access the second column:

A1[,2]
## [1] 2 4

Installing libraries

Statisticians use R because there are many libraries that contain useful functions. We can install libraries with install.packages. For example, if we want to install ggplot2, which is a useful library for plotting:

install.packages('ggplot2')

Once the library is installed, we can load it using library(). If we want to load ggplot2, we need to type:

library(ggplot2)

Introduction to data.frames

We’ll use the dataset mpg, which is in the ggplot2 library. First, we load it:

data(mpg)

The class of the dataset is data.frame (and others), which are matrices that have columns that can have different types.

The function str gives us some information about the variables in the dataset:

str(mpg) 
## Classes 'tbl_df', 'tbl' and 'data.frame':    234 obs. of  11 variables:
##  $ manufacturer: chr  "audi" "audi" "audi" "audi" ...
##  $ model       : chr  "a4" "a4" "a4" "a4" ...
##  $ displ       : num  1.8 1.8 2 2 2.8 2.8 3.1 1.8 1.8 2 ...
##  $ year        : int  1999 1999 2008 2008 1999 1999 2008 1999 1999 2008 ...
##  $ cyl         : int  4 4 4 4 6 6 6 4 4 4 ...
##  $ trans       : chr  "auto(l5)" "manual(m5)" "manual(m6)" "auto(av)" ...
##  $ drv         : chr  "f" "f" "f" "f" ...
##  $ cty         : int  18 21 20 21 16 18 18 18 16 20 ...
##  $ hwy         : int  29 29 31 30 26 26 27 26 25 28 ...
##  $ fl          : chr  "p" "p" "p" "p" ...
##  $ class       : chr  "compact" "compact" "compact" "compact" ...

We can print the first and last 5 observations in the dataset using head and tail:

head(mpg)
## # A tibble: 6 x 11
##   manufacturer model displ  year   cyl trans drv     cty   hwy fl    class
##   <chr>        <chr> <dbl> <int> <int> <chr> <chr> <int> <int> <chr> <chr>
## 1 audi         a4      1.8  1999     4 auto… f        18    29 p     comp…
## 2 audi         a4      1.8  1999     4 manu… f        21    29 p     comp…
## 3 audi         a4      2    2008     4 manu… f        20    31 p     comp…
## 4 audi         a4      2    2008     4 auto… f        21    30 p     comp…
## 5 audi         a4      2.8  1999     6 auto… f        16    26 p     comp…
## 6 audi         a4      2.8  1999     6 manu… f        18    26 p     comp…
tail(mpg)
## # A tibble: 6 x 11
##   manufacturer model displ  year   cyl trans drv     cty   hwy fl    class
##   <chr>        <chr> <dbl> <int> <int> <chr> <chr> <int> <int> <chr> <chr>
## 1 volkswagen   pass…   1.8  1999     4 auto… f        18    29 p     mids…
## 2 volkswagen   pass…   2    2008     4 auto… f        19    28 p     mids…
## 3 volkswagen   pass…   2    2008     4 manu… f        21    29 p     mids…
## 4 volkswagen   pass…   2.8  1999     6 auto… f        16    26 p     mids…
## 5 volkswagen   pass…   2.8  1999     6 manu… f        18    26 p     mids…
## 6 volkswagen   pass…   3.6  2008     6 auto… f        17    26 p     mids…

We can index the rows and columns of mpg using the same syntax we used for indexing matrices:

mpg[3:7,c(1,4:5)]
## # A tibble: 5 x 3
##   manufacturer  year   cyl
##   <chr>        <int> <int>
## 1 audi          2008     4
## 2 audi          2008     4
## 3 audi          1999     6
## 4 audi          1999     6
## 5 audi          2008     6

With data.frames we can extract variables using $. For example, if we want to look at year:

mpg$year
##   [1] 1999 1999 2008 2008 1999 1999 2008 1999 1999 2008 2008 1999 1999 2008
##  [15] 2008 1999 2008 2008 2008 2008 2008 1999 2008 1999 1999 2008 2008 2008
##  [29] 2008 2008 1999 1999 1999 2008 1999 2008 2008 1999 1999 1999 1999 2008
##  [43] 2008 2008 1999 1999 2008 2008 2008 2008 1999 1999 2008 2008 2008 1999
##  [57] 1999 1999 2008 2008 2008 1999 2008 1999 2008 2008 2008 2008 2008 2008
##  [71] 1999 1999 2008 1999 1999 1999 2008 1999 1999 1999 2008 2008 1999 1999
##  [85] 1999 1999 1999 2008 1999 2008 1999 1999 2008 2008 1999 1999 2008 2008
##  [99] 2008 1999 1999 1999 1999 1999 2008 2008 2008 2008 1999 1999 2008 2008
## [113] 1999 1999 2008 1999 1999 2008 2008 2008 2008 2008 2008 2008 1999 1999
## [127] 2008 2008 2008 2008 1999 2008 2008 1999 1999 1999 2008 1999 2008 2008
## [141] 1999 1999 1999 2008 2008 2008 2008 1999 1999 2008 1999 1999 2008 2008
## [155] 1999 1999 1999 2008 2008 1999 1999 2008 2008 2008 2008 1999 1999 1999
## [169] 1999 2008 2008 2008 2008 1999 1999 1999 1999 2008 2008 1999 1999 2008
## [183] 2008 1999 1999 2008 1999 1999 2008 2008 1999 1999 2008 1999 1999 1999
## [197] 2008 2008 1999 2008 1999 1999 2008 1999 1999 2008 2008 1999 1999 2008
## [211] 2008 1999 1999 1999 1999 2008 2008 2008 2008 1999 1999 1999 1999 1999
## [225] 1999 2008 2008 1999 1999 2008 2008 1999 1999 2008

We can also index by logical conditions. For instance, if we want to work with the subset of Toyota cars:

mpg[mpg$manufacturer == "toyota",]
## # A tibble: 34 x 11
##    manufacturer model displ  year   cyl trans drv     cty   hwy fl    cla…
##    <chr>        <chr> <dbl> <int> <int> <chr> <chr> <int> <int> <chr> <ch>
##  1 toyota       4run…   2.7  1999     4 manu… 4        15    20 r     suv 
##  2 toyota       4run…   2.7  1999     4 auto… 4        16    20 r     suv 
##  3 toyota       4run…   3.4  1999     6 auto… 4        15    19 r     suv 
##  4 toyota       4run…   3.4  1999     6 manu… 4        15    17 r     suv 
##  5 toyota       4run…   4    2008     6 auto… 4        16    20 r     suv 
##  6 toyota       4run…   4.7  2008     8 auto… 4        14    17 r     suv 
##  7 toyota       camry   2.2  1999     4 manu… f        21    29 r     mid…
##  8 toyota       camry   2.2  1999     4 auto… f        21    27 r     mid…
##  9 toyota       camry   2.4  2008     4 manu… f        21    31 r     mid…
## 10 toyota       camry   2.4  2008     4 auto… f        21    31 r     mid…
## # ... with 24 more rows

Factors

factor is a variable type in R useful for encoding categorical variables. Defining them is easy:

fac1 = factor(c("dog","cat","cat","dog"))

We can use summary to create a quick table (note that summary didn’t work well with character variables):

summary(fac1)
## cat dog 
##   2   2

The default ordering of the categories in a factor is alphabetical, which isn’t always the best or most intutive. We can see the different categories (in R lingo, levels) of a factor and its ordering using levels:

levels(fac1)
## [1] "cat" "dog"

Let’s use the hsb2 dataset (on the course website) to illustrate this point. The dataset contains a variable called ses, which is socioeconomic status of the student. It can take on the values low, middle, and high. Unfortunately, the default ordering of the factor is alphabetical, that is:

levels(hsb2$ses)
## [1] "high"   "low"    "middle"

The problem with this ordering is that if we create tables, plots, etc. R will use this ordering, which is counterintuitive. For instance, if we create a 2 x 2 table of ses and race, we get

table(hsb2$ses, hsb2$race)
##         
##          african american asian hispanic white
##   high                  3     3        4    48
##   low                  11     3        9    24
##   middle                6     5       11    73

This is not great.

How can we reorder the levels of a factor? The answer is

hsb2$ses = factor(hsb2$ses, ordered = TRUE, levels = c("low", "middle", "high"))

The code above rewrites the ses variable in hsb2 to an ordered factor whose levels are low, middle, and high (in that order).

If you don’t believe me (and you shouldn’t), here’s the code to verify that ses is now ordered:

levels(hsb2$ses)
## [1] "low"    "middle" "high"
table(hsb2$ses, hsb2$race)
##         
##          african american asian hispanic white
##   low                  11     3        9    24
##   middle                6     5       11    73
##   high                  3     3        4    48

Lists

We won’t say much about lists, but they’re useful if we want to keep objects of different types in a single place.

For example, suppose that we have a vector and a matrix:

v = 1:6
m = matrix(c(1,0,0,1),byrow=T,nrow=2)

Then, the following code creates a list whose entries are the vector v and the matrix m:

l = list(v,m)

We can access, say, the second element of the list with

l[[2]]
##      [,1] [,2]
## [1,]    1    0
## [2,]    0    1

And we can do things such as

l[[2]][2,1]
## [1] 0
l[[1]][4]
## [1] 4

We can add a new element to the list indexing by a new element

v2 = 3:4
l[[3]] = v2

We probably won’t see lists again in the course, but it’s good to know that they exist.

Basic data summaries with R

We can get quick summaries of numeric variables with summary

summary(mpg) 
##  manufacturer          model               displ            year     
##  Length:234         Length:234         Min.   :1.600   Min.   :1999  
##  Class :character   Class :character   1st Qu.:2.400   1st Qu.:1999  
##  Mode  :character   Mode  :character   Median :3.300   Median :2004  
##                                        Mean   :3.472   Mean   :2004  
##                                        3rd Qu.:4.600   3rd Qu.:2008  
##                                        Max.   :7.000   Max.   :2008  
##       cyl           trans               drv                 cty       
##  Min.   :4.000   Length:234         Length:234         Min.   : 9.00  
##  1st Qu.:4.000   Class :character   Class :character   1st Qu.:14.00  
##  Median :6.000   Mode  :character   Mode  :character   Median :17.00  
##  Mean   :5.889                                         Mean   :16.86  
##  3rd Qu.:8.000                                         3rd Qu.:19.00  
##  Max.   :8.000                                         Max.   :35.00  
##       hwy             fl               class          
##  Min.   :12.00   Length:234         Length:234        
##  1st Qu.:18.00   Class :character   Class :character  
##  Median :24.00   Mode  :character   Mode  :character  
##  Mean   :23.44                                        
##  3rd Qu.:27.00                                        
##  Max.   :44.00

We can tabulate with table

table(mpg$manufacturer) 
## 
##       audi  chevrolet      dodge       ford      honda    hyundai 
##         18         19         37         25          9         14 
##       jeep land rover    lincoln    mercury     nissan    pontiac 
##          8          4          3          4         13          5 
##     subaru     toyota volkswagen 
##         14         34         27
table(mpg$manufacturer,mpg$year)
##             
##              1999 2008
##   audi          9    9
##   chevrolet     7   12
##   dodge        16   21
##   ford         15   10
##   honda         5    4
##   hyundai       6    8
##   jeep          2    6
##   land rover    2    2
##   lincoln       2    1
##   mercury       2    2
##   nissan        6    7
##   pontiac       3    2
##   subaru        6    8
##   toyota       20   14
##   volkswagen   16   11
table(mpg$year)
## 
## 1999 2008 
##  117  117

We can plot stuff, too. For example, hist does histograms:

hist(mpg$displ, main="Engine displacement (in litres)",
     col=rainbow(20),
     xlim=c(0,10))

You can learn more about how to change the attributes of the plot with ?hist.

We can create individual boxplots and boxplots grouped by values of categorical variables:

boxplot(mpg$displ)

boxplot(mpg$displ~mpg$manufacturer)

These plots are created using the graphics library. There are other libraries that you can use to produce plots. One of them is ggplot2, which we installed earlier. A nice thing about ggplot2 is that it has the function qplot, which produces good-looking plots by default. For example:

qplot(mpg$displ)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

qplot(mpg$manufacturer)

qplot is smart enough to produce different plots depending on the type of the object. We’ll cover ggplot2 in more detail later in the semester.

Sources