Recap of session 1: R as calculator

3 + 4

## [1] 7

exp(1)

## [1] 2.718282

log(exp(1))

## [1] 1

pi

## [1] 3.141593

5.2 / 0

## [1] Inf

Recap of session 1: Variables

• Types of variables in R
  • Numeric (e.g. 1, -3.5, 200)
  • Character/string (“abc”, “R”, “94305”)
  • Boolean/logical (TRUE or FALSE)
  • NAs
• Variable assignment

Reminder!

• Install R, RStudio and the relevant R packages!
• Instructions on the course website under Session 1
• Make sure you are using the latest versions!

Agenda for today

• Basic R objects
  • Vectors
  • Matrices/arrays
  • Lists
  • Data frames

Vectors

• One-dimensional array whose entries are the same type
• Can be created using the c() function, or using the : shortcut

vec <- c("a", "b", "c")
vec

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

Vectors

• One-dimensional array whose entries are the same type
• Can be created using the c() function, or using the : shortcut

vec <- 1:100
vec

##   [1]   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17
##  [18]  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34
##  [35]  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51
##  [52]  52  53  54  55  56  57  58  59  60  61  62  63  64  65  66  67  68
##  [69]  69  70  71  72  73  74  75  76  77  78  79  80  81  82  83  84  85
##  [86]  86  87  88  89  90  91  92  93  94  95  96  97  98  99 100

Vectors

• We can manipulate vectors using arithmetic operations (just like numbers).
• Arithmetic operations happen element-wise.

even <- 1:50 * 2
even

##  [1]   2   4   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34
## [18]  36  38  40  42  44  46  48  50  52  54  56  58  60  62  64  66  68
## [35]  70  72  74  76  78  80  82  84  86  88  90  92  94  96  98 100

Vectors

• We can manipulate vectors using arithmetic operations (just like numbers).
• Arithmetic operations happen element-wise.

even <- 1:50 * 2
even

##  [1]   2   4   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34
## [18]  36  38  40  42  44  46  48  50  52  54  56  58  60  62  64  66  68
## [35]  70  72  74  76  78  80  82  84  86  88  90  92  94  96  98 100

How can we get the odd numbers from 1 to 100 from even?

Vectors

• We can manipulate vectors using arithmetic operations (just like numbers).
• Arithmetic operations happen element-wise.

How can we get the odd numbers from 1 to 100 from even?

odd <- even - 1
odd

##  [1]  1  3  5  7  9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45
## [24] 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91
## [47] 93 95 97 99

Vectors

We can use the c() function to concatenate vectors.

z <- 1:5
z <- c(z, 3, z)
z

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

Vectors: Indexing

To extract a subset of elements by their indices, put a vector of indices in square brackets

even

##  [1]   2   4   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34
## [18]  36  38  40  42  44  46  48  50  52  54  56  58  60  62  64  66  68
## [35]  70  72  74  76  78  80  82  84  86  88  90  92  94  96  98 100

even[1]

## [1] 2

Vectors: Indexing

To extract a subset of elements by their indices, put a vector of indices in square brackets

even

##  [1]   2   4   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34
## [18]  36  38  40  42  44  46  48  50  52  54  56  58  60  62  64  66  68
## [35]  70  72  74  76  78  80  82  84  86  88  90  92  94  96  98 100

even[3:7]

## [1]  6  8 10 12 14

Vectors: Indexing

To extract a subset of elements by their indices, put a vector of indices in square brackets

even

##  [1]   2   4   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34
## [18]  36  38  40  42  44  46  48  50  52  54  56  58  60  62  64  66  68
## [35]  70  72  74  76  78  80  82  84  86  88  90  92  94  96  98 100

even[c(3,5)]

## [1]  6 10

Note: even[3,5] will not work!

Vectors: Negative indexing

To extract all except a few indices, put a negative sign before the vector of indices

even

##  [1]   2   4   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34
## [18]  36  38  40  42  44  46  48  50  52  54  56  58  60  62  64  66  68
## [35]  70  72  74  76  78  80  82  84  86  88  90  92  94  96  98 100

even[-c(1,2)]

##  [1]   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34  36  38
## [18]  40  42  44  46  48  50  52  54  56  58  60  62  64  66  68  70  72
## [35]  74  76  78  80  82  84  86  88  90  92  94  96  98 100

Vectors: Length

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

even

##  [1]   2   4   6   8  10  12  14  16  18  20  22  24  26  28  30  32  34
## [18]  36  38  40  42  44  46  48  50  52  54  56  58  60  62  64  66  68
## [35]  70  72  74  76  78  80  82  84  86  88  90  92  94  96  98 100

length(even)

## [1] 50

Vectors: Things to watch out for

What happens if we try to extract an invalid index?

odd[0]

Vectors: Things to watch out for

What happens if we try to extract an invalid index?

odd[0]

## numeric(0)

No error thrown!!

Vectors: Things to watch out for

What happens if we try to extract an invalid index?

odd[0]

## numeric(0)

No error thrown!!

odd[51]

Vectors: Things to watch out for

What happens if we try to extract an invalid index?

odd[0]

## numeric(0)

No error thrown!!

odd[51]

## [1] NA

No error thrown!!

Vectors: Things to watch out for

If we try to assign a vector with different types, type coercion happens.

c(1, 2, "a")

## [1] "1" "2" "a"

Matrices and arrays

Two-dimensional analogs of vectors

A <- matrix(1:12, nrow = 3)
A

##      [,1] [,2] [,3] [,4]
## [1,]    1    4    7   10
## [2,]    2    5    8   11
## [3,]    3    6    9   12

Indexing: put the rows you want before the comma, columns you want after the comma

A[1, 2]

## [1] 4

Matrices: Indexing example

A

##      [,1] [,2] [,3] [,4]
## [1,]    1    4    7   10
## [2,]    2    5    8   11
## [3,]    3    6    9   12

What does A[c(1,3), c(2,4)] return?

Matrices: Indexing example

A

##      [,1] [,2] [,3] [,4]
## [1,]    1    4    7   10
## [2,]    2    5    8   11
## [3,]    3    6    9   12

What does A[c(1,3), c(2,4)] return?

A[c(1,3), c(2,4)]

##      [,1] [,2]
## [1,]    4   10
## [2,]    6   12

Lists

• A collection of key-value pairs
• Keys are character strings, values can be anything!
• Values do not have to be of the same type for different keys
• Created with the list() function

List example

cars <- list(make = "Honda", 
             models = c("Fit", "CR-V", "Odyssey"), 
             available = c(TRUE, TRUE, TRUE))

Extracting parts of a list

Use [[ or $ notation to refer to a specific key-value pair

cars$make         # no quotation marks

## [1] "Honda"

cars[["models"]]  # remember quotation marks!

## [1] "Fit"     "CR-V"    "Odyssey"

What is a data frame?

• A data frame is R’s data structure for storing datasets
  • First row: variable/covariate/feature names
  • Each subsequent row represents one observation
  • Each column contains the values of that variable across observations
• Tibbles: A data frame with some cosmetic changes

Example of a dataset

Data frame/tibble printed to screen

df

##   votes_dem votes_gop
## 1    486351     91189
## 2       318       211
## 3      5904     10239

tbl

## # A tibble: 3 x 2
##   votes_dem votes_gop
##       <dbl>     <dbl>
## 1    486351     91189
## 2       318       211
## 3      5904     10239

Structure of data frame

str(df)

## 'data.frame':    3 obs. of  2 variables:
##  $ votes_dem: num  486351 318 5904
##  $ votes_gop: num  91189 211 10239

Data frames “under the hood”

• To R, a data frame is simply a special type of list!
  • Keys of the list are the variable/covariate names
  • Values are vectors of the same length

Data frames “under the hood”

is.list(df)

## [1] TRUE

df$votes_dem

## [1] 486351    318   5904

Today’s dataset: Fuel economy

(Source: SuperCars)

fueleconomy: Package information on CRAN

https://cran.r-project.org/web/packages/fueleconomy/index.html

Optional material

Measures of central tendency

• Mean: sum of all values divided by the number of values
  
• Mode: most commonly occuring value
  
• \(x\)th percentile: value such that \(x\)% of the values fall below it
  • Median: 50th percentile
  • 1st quartile: 25th percentile
  • 3rd quartile: 75th percentile

Measures of spread

• Variance: average squared deviation from the mean
• Standard deviation: square root of variance
• Interquartile range: 3rd quartile - 1st quartile