# 1 Introduction to R and `tidyverse`

## 1.1 Introduction to R Markdown

When we write code, we often want to be able to make changes and re-use it. To facilitate this process, R allows us to create files that store our code. R Markdown files allow us to insert *chunks* of R code.

To create an R Markdown file, click on

`File`

\(\rightarrow\)`New File`

\(\rightarrow\)`R Markdown...`

. Click`OK`

and then save this markdown file in your`Rmd`

directory. us_r

In your R Markdown file, open a chunk by typing three left quotes, followed by the letter `r`

inside curly brackets (````{r}`

); Close the chunk by typing three left quotes `````

. Anything inside an R chunk is interpreted as R code.

`Cmd`

+ `Option`

+ `I`

(Mac) or
`Ctrl`

+ `Alt`

+ `I`

(Windows)
### 1.1.1 Running chunks

To run an R chunk click on the green button at the end of the first line inside the chunk:

Or click:

`Cmd`+`Shift`+`Enter`(Mac)`Control`+`Shift`+`Enter`(Windows)

To execute the code of a `single line`

inside an R chunk you can click:

`Cmd`+`Enter`(Mac)`Control`+`Enter`(Windows)

The results of the R chunk are also printed out in the console.

### 1.1.2 A basic example

Insert a new R chunk, and then type the following:

```
5+5
4+10
4-9
```

```
## [1] 10
## [1] 14
## [1] -5
```

Run the chunk to see the results.

## 1.2 Variables in R

In programming, variables are essentially nicknames that we use to store values or other language objects. For example, let us say that we want to store a person’s age in a variable. We can create a new variable and name it “age.” Then, we can store the appropriate age value to this variable.

In R, we store values to variables by using the symbol `=`

(or `<-`

, `->`

).

The name of a variable can be any sequence of characters given that it starts with a letter.

Variable names are case sensitive.

```
=36 # A hashtag inside an R chunk creates a comment.
age# R knows to ignore comments (comments are explanations for humans)
<-36 # age is a variable that stores the number 36 age
```

Other variable names that can store the number 36:

```
<- 36 # x is a variable that also stores the number 36
x <- 36 #age36 is a variable that stores the number 36
age36 <- 36 # z1 is a variable that stores the number 36 z1
```

Choose variable names that best represent the stored values.

## 1.3 Vectors

In R, lowercase `c`

followed by a parenthesis is a special keyword that identifies a **vector**. A vector is a sequence of data elements. Below, the variable `quiz_results`

is a vector that stores the scores of a hypothetical quiz.

```
= c(9,8,4,10)
quiz_results quiz_results
```

`## [1] 9 8 4 10`

Note that by just typing the name of a variable (in our example

`quiz_results`

) inside an R chunk and running it R prints out the value(s) of that variable.

Elements in a vector can be accessed by their position. For example, in our vector `quiz_results`

:

- 9 \(\rightarrow\) \(1^{st}\) position
- 8 \(\rightarrow\) \(2^{nd}\) position
- 4 \(\rightarrow\) \(3^{rd}\) position
- 10 \(\rightarrow\) \(4^{th}\) position

Hence, we can access the element in the \(2^{nd}\) position as follows:

`2] quiz_results[`

`## [1] 8`

And we can assign it to a new variable:

```
= quiz_results[2]
second_element second_element
```

`## [1] 8`

## 1.4 Data types

In programming (and in R) each variable has a **data type**, which describes what kind of information the variable stores. For instance, in our previous example, variable age is a `numeric`

variable, because it stores a numeric value.

R allows us to define variables that are not numeric. For example, we can create a variable that is a sequence of characters. Consider a variable that stores the word “data.” We can name this variable `data_var`

and assign to it the characters `data.`

```
<- 'data'
data_var data_var
```

`## [1] "data"`

Any sequence of characters in single (`'`

) or double (`"`

) quotes is considered a string. For instance, the following line of code that uses double quotes has the same result:

```
<- "data"
data_var data_var
```

`## [1] "data"`

Variables that store strings are of data type

`character.`

R allows for other types of variables, such as `date`

variables and `factors.`

We will introduce these types of variables later in the class.

If our variables are of data type `numeric`

, we can add, subtract, divide, and multiply them as follows:

```
= 7
x = 13
y + y
x - y
x / y
x * y x
```

```
## [1] 20
## [1] -6
## [1] 0.5384615
## [1] 91
```

## 1.5 Functions in R

A function is a stored, pre-defined block of code that operates on some *input* value to return an *output*.
R has multiple built-in functions that we can apply to our variables.

For instance, the function `log()`

will estimate the logarithm of its input:

`log(age)`

`## [1] 3.583519`

In the above, `age`

is the input of the function `log`

, and the output of the function is the logarithm of variable `age.`

Of course we can also apply the function log to a number:

`log(36)`

`## [1] 3.583519`

Similarly, the function `sqrt()`

estimates the square root of a numeric variable (or a number):

```
sqrt(x)
sqrt(10)
```

```
## [1] 2.645751
## [1] 3.162278
```

The input of a function does not need to be a scalar (one-element) variable; functions can also operate on vectors (and other structures that we will learn in the future).

Since we have a vector of quiz results, it would be nice to know what was the average quiz performance. We can call the function `mean()`

on the vector `quiz_results`

:

```
= mean(quiz_results)
meanQuiz meanQuiz
```

`## [1] 7.75`

Similarly, we can estimate the standard deviation of the quiz results with the function `sd`

:

```
= sd(quiz_results)
sdQuiz sdQuiz
```

`## [1] 2.629956`

Since we have already estimated the mean and the standard deviation of the vector `quiz_results`

,
we can also standardize it by subtracting the mean and dividing with the standard deviation.

```
<- (quiz_results - meanQuiz)/sdQuiz
standardQuiz
quiz_results standardQuiz
```

```
## [1] 9 8 4 10
## [1] 0.47529319 0.09505864 -1.42587956 0.85552774
```

By standardizing the quiz results we created a new vector `standardQuiz`

which has a zero mean and standard deviation of 1.

```
mean(standardQuiz)
sd(standardQuiz)
```

```
## [1] 1.734723e-17
## [1] 1
```

We can plot and compare the histograms of the two vectors with the function `hist`

:

`hist(quiz_results,main = "") # the option main = "" removes the title from the figure`

`hist(standardQuiz, main = "")`

When calling the function

`hist()`

in the previous two examples we used two inputs: the first input was the vector name (`quiz_results`

or`standardQuiz`

); the second input was the empty string`""`

, which told function`hist()`

to not print a title for the figure. In general, a function can take as input multiple variables.

You can experiment with the above code by changing the empty quote to a string, for instance, `main="what a great histogram".`

**arguments**. (e.g.,

`standardQuiz`

in `hist(standardQuiz, main = "")`

is an argument.)

**parameters**. (e.g.,

`main`

in `hist(standardQuiz, main = "")`

is a parameter.)
## 1.6 Logic

Besides `numeric`

and `character`

variables we can also have **logical** variables.
A logical variable can either be `TRUE`

or `FALSE.`

(`TRUE`

and `FALSE`

are special keywords in R).

We can also use the letters

`T`

and`F`

to indicate`TRUE`

and`FALSE`

respectively.

```
= F #FALSE, assign the logical value FALSE to variable x
x = T #TRUE, assign the logical value True to variable x
y x
```

`## [1] FALSE`

` y`

`## [1] TRUE`

### 1.6.1 Logical operators

With logical variables we can use logical operators. A logical operator is a way to make a test in R. R supports the following logical operators:

Operator | Description |
---|---|

< | Less than |

<= | Less than or equal to |

> | Greater than |

>= | Greater than or equal to |

== | Exactly equal to |

! | Not (negation) |

& | Logical AND |

| | Logical OR |

A logical

ANDcompares two statements. If both statements are`TRUE`

then the result of the comparison is also`TRUE`

; Otherwise the result of the comparison is`FALSE`

Here is the truth table of logical **AND**:

X | Y | X AND Y |
---|---|---|

TRUE | TRUE | TRUE |

TRUE | FALSE | FALSE |

FALSE | TRUE | FALSE |

FALSE | FALSE | FALSE |

A logical OR compares two statements. If either or both of the statements are

`TRUE`

then the result of the comparison is`TRUE`

; Otherwise, if both statements are`FALSE`

the result of the comparison is`FALSE`

.

X | Y | X OR Y |
---|---|---|

TRUE | TRUE | TRUE |

TRUE | FALSE | TRUE |

FALSE | TRUE | TRUE |

FALSE | FALSE | FALSE |

Here are some examples that used the logical variables `x`

and `y`

from above:

```
& y
x | y
x !x & y
```

```
## [1] FALSE
## [1] TRUE
## [1] TRUE
```

```
= 5
x = 6
y == y
x != y
x < y
x > y x
```

```
## [1] FALSE
## [1] TRUE
## [1] TRUE
## [1] FALSE
```

We can group conditions together through parentheses:

```
= 10
z != y) & (x < z) #Both parentheses are TRUE and hence the result is TRUE (x
```

`## [1] TRUE`

`!= y) | (x < z) (x `

`## [1] TRUE`

`=`

and a double `==`

: A single `=`

assignes a value to a variable; a double `==`

is a logical test between the left-hand side and the right-hand side.
### 1.6.2 The `ifelse()`

function

A particularly interesting function in R is the `ifelse()`

function, which allows us to apply a transformation only if a condition is `TRUE.`

For instance, we can partially update the quiz scores (in our vector `quiz_results`

) that are less than 9:

```
# return 1 for those scores that are less or equal to 8. Otherwise return 0:
ifelse(quiz_results <= 8,1,0)
```

`## [1] 0 1 1 0`

Of course, we can assign the result of an `ifelse()`

transformation to the original variable (or to a new variable):

```
# update scores lower than 9 with -1:
= ifelse(quiz_results < 9,-1,quiz_results) # assign the transformed result to a new variable
quiz_results_transformed = ifelse(quiz_results < 9,-1,quiz_results) # assign the tranformed results to the original variable
quiz_results quiz_results
```

`## [1] 9 -1 -1 10`

### 1.6.3 More examples of logic and logical operators

Below are some additional examples of logic and logical operators.

```
= 6
A = 7
B = 10
C = T
D ==B # Is A equal to B?
A!(B > C) | (!D) # Not B greater than C OR not D.
# A less or equal than C AND ( not B greater than C OR not D)
<= C) & (!(B > C) | (!D)) (A
```

```
## [1] FALSE
## [1] TRUE
## [1] TRUE
```

## 1.7 R Packages and summarizing a real dataset

Very often we will need to use R functions that are not already built in. In these cases, we will need to install and load **R packages**. These packages include code written by independent developments and teams, and it is free for everyone to use and change.

As an example, let’s install the package `mlbench`

by calling the function `install.packages`

as follows:

`install.packages("mlbench")`

We can also install packages manually from RStudio:

`Packages tab`

\(\rightarrow\)`install.`

**once**. You

**should not**re-install

`mlbench`

from this point on unless there is an updated version of it.
To see the available datasets from the newly installed package `mlbench`

we can call the function data and pass the argument ‘mlbench’ to the parameter `package`

as follows:

`data(package='mlbench')`

To make the functions and datasets of the package `mlbench`

available to us we need to call the function `library()`

:

`library(mlbench)`

`library(package_name)`

Now we can use the datasets and functions of the `mlbench`

package. Let us load the dataset `BreastCancer`

with function `data().`

```
data("BreastCancer")
head(BreastCancer)
```

```
## Id Cl.thickness Cell.size Cell.shape Marg.adhesion Epith.c.size
## 1 1000025 5 1 1 1 2
## 2 1002945 5 4 4 5 7
## 3 1015425 3 1 1 1 2
## 4 1016277 6 8 8 1 3
## 5 1017023 4 1 1 3 2
## 6 1017122 8 10 10 8 7
## Bare.nuclei Bl.cromatin Normal.nucleoli Mitoses Class
## 1 1 3 1 1 benign
## 2 10 3 2 1 benign
## 3 2 3 1 1 benign
## 4 4 3 7 1 benign
## 5 1 3 1 1 benign
## 6 10 9 7 1 malignant
```

The function

`head`

allows us to explore the first six rows of a dataset. Similarly, the function`tail`

allows us to explore the last six rows of a dataset.

Now, we can get the summary statistics of this dataset with the function `summary().`

`summary(BreastCancer)`

```
## Id Cl.thickness Cell.size Cell.shape Marg.adhesion
## Length:699 1 :145 1 :384 1 :353 1 :407
## Class :character 5 :130 10 : 67 2 : 59 2 : 58
## Mode :character 3 :108 3 : 52 10 : 58 3 : 58
## 4 : 80 2 : 45 3 : 56 10 : 55
## 10 : 69 4 : 40 4 : 44 4 : 33
## 2 : 50 5 : 30 5 : 34 8 : 25
## (Other):117 (Other): 81 (Other): 95 (Other): 63
## Epith.c.size Bare.nuclei Bl.cromatin Normal.nucleoli Mitoses
## 2 :386 1 :402 2 :166 1 :443 1 :579
## 3 : 72 10 :132 3 :165 10 : 61 2 : 35
## 4 : 48 2 : 30 1 :152 3 : 44 3 : 33
## 1 : 47 5 : 30 7 : 73 2 : 36 10 : 14
## 6 : 41 3 : 28 4 : 40 8 : 24 4 : 12
## 5 : 39 (Other): 61 5 : 34 6 : 22 7 : 9
## (Other): 66 NA's : 16 (Other): 69 (Other): 69 (Other): 17
## Class
## benign :458
## malignant:241
##
##
##
##
##
```

We will use the functions

`head`

,`tail`

, and`summary()`

repeatedly throughout this book to get a first look at each new dataset.

## 1.8 `tidyverse`

`tidyverse`

is a collection of R packages designed for data science. All packages share an underlying design philosophy, grammar, and data structures.
Install the `tidyverse`

package as follows:

`install.packages("tidyverse")`

**once**. You

**should not**re-install

`tidyverse`

from this point on unless there is an updated version of it.

`tidyverse`

here: https://www.tidyverse.org

Once installed, load the package into your environment:

`library(tidyverse)`

### 1.8.1 `tibble`

The basic data structure that works with tidyverse is called `tibble.`

You can think of a `tibble`

as a spreadsheet in excel, or as a table in a relational database system, or as a dataframe in R or python. If you are familiar with dataframes in R or Python, `tibbles`

are data frames but they tweak some behaviors to make coding a little bit easier.

In this book (and in real life) I will use the terms

`tibble`

and`dataframe`

interchangeably.

We can create a new `tibble`

from vectors by calling the function `tibble().`

Each vector will become a new column in the new `tibble`

:

```
= tibble(
t x = c(0,2,4,6), # vector x will become column x in the new tibble.
y = c('a','b','d', 'amazing'), #vector y will become column y in the new tibble.
z = x^2) #vector z, which is vector x squared, will become column z in the new tibble.
t
```

```
## # A tibble: 4 × 3
## x y z
## <dbl> <chr> <dbl>
## 1 0 a 0
## 2 2 b 4
## 3 4 d 16
## 4 6 amazing 36
```

R comes with many pre-loaded datasets. To explore these datasets run `data().`

Next, we will use the dataset `population`

:

`head(population) # The function head() prints out only the first six rows of the tibble. `

```
## # A tibble: 6 × 3
## country year population
## <chr> <int> <int>
## 1 Afghanistan 1995 17586073
## 2 Afghanistan 1996 18415307
## 3 Afghanistan 1997 19021226
## 4 Afghanistan 1998 19496836
## 5 Afghanistan 1999 19987071
## 6 Afghanistan 2000 20595360
```

### 1.8.2 `dplyr`

and `filter`

Now, we can apply some logic on the population dataset. Assume that we are interested in selecting only population data from Brazil. How can we do this?

We can use the function `filter()`

from package `dplyr.`

`dplyr`

is a grammar of data manipulation that provides a set of functions to solve some of the most common data manipulation challenges.

`dplyr`

here: https://dplyr.tidyverse.org
The function `filter()`

allows us to subset a `tibble`

by retaining all rows that satisfy certain conditions. For instance, we can keep only rows for which the country column is equal to Brazil
and the year column is greater or equal than 2000:

`filter(population,country=='Brazil' & year >= 2000) # Recall the logical and operator &`

```
## # A tibble: 14 × 3
## country year population
## <chr> <int> <int>
## 1 Brazil 2000 174504898
## 2 Brazil 2001 176968205
## 3 Brazil 2002 179393768
## 4 Brazil 2003 181752951
## 5 Brazil 2004 184010283
## 6 Brazil 2005 186142403
## 7 Brazil 2006 188134315
## 8 Brazil 2007 189996976
## 9 Brazil 2008 191765567
## 10 Brazil 2009 193490922
## 11 Brazil 2010 195210154
## 12 Brazil 2011 196935134
## 13 Brazil 2012 198656019
## 14 Brazil 2013 200361925
```

Alternatively, we can show the population of every other country except Brazil, for the same years:

```
= filter(population,country!='Brazil' & year >= 2000) # we also are saving the result into a new tibble, tf.
tf head(tf)
```

```
## # A tibble: 6 × 3
## country year population
## <chr> <int> <int>
## 1 Afghanistan 2000 20595360
## 2 Afghanistan 2001 21347782
## 3 Afghanistan 2002 22202806
## 4 Afghanistan 2003 23116142
## 5 Afghanistan 2004 24018682
## 6 Afghanistan 2005 24860855
```

### 1.8.3 Distributions: `ggplot2`

Often, when analyzing data, we need to create basic visualizations. For example, what is the distribution of the population column in our filtered tibble `tf`

?

For such quick visualizations we can use the package `ggplot2`

from `tidyverse`

. The `ggplot2`

package is a powerful library for creating graphics.

The `ggplot()`

function initializes a `ggplot`

object where we can declare the input data. Inside the `ggplot`

function, we also define the
**aesthetic** mappings, with the function `aes()`

. These aesthetics describe how variables in the data are mapped to visual properties of `geoms`

.

A `geom`

tells the plot how we want to display our data.

In our example we want to display the population data through a distribution plot. As a result, we will call the `geom_density()`

geom that will display the distribution of our aesthetics (i.e., population):

```
#we use the tibble tf we created before;
#x=population sets the aesthetics mappings of the graphs;
ggplot(tf, aes(x=population))+geom_density()
```

In a distribution plot, the y-axis shows the density and as a result it is calculated directly from the `

`gf_density()`

function. As a result, we do not need to define \(y\) inside`gf_density().`

The population distribution is highly skewed: most countries have low population numbers, but very few countries have very high population numbers (100s of millions or even more than a billion). This concentrates the plot in te left side and creates a very long tail. These types of distributions are broadly described as power-law distributions. Their means are not informative, as they are being stretched by the very high scores of very few points. Their standard deviation is large, often higher than their means. For instance, in our example we see that the mean population is \(>30M\), even though the vast majority of the countries have lower population numbers (the \(75^{th}\) percentile population number is \(19M\)):

`summary(tf)`

```
## country year population
## Length:2986 Min. :2000 Min. :1.129e+03
## Class :character 1st Qu.:2003 1st Qu.:6.202e+05
## Mode :character Median :2007 Median :5.398e+06
## Mean :2007 Mean :3.012e+07
## 3rd Qu.:2010 3rd Qu.:1.909e+07
## Max. :2013 Max. :1.386e+09
```

The standard deviation, which we can estimate from function `sd()`

is \(124M\), greater than the mean of \(30M\):

`sd(tf$population)`

`## [1] 123915350`

In fact, we can test it as follows:

`sd(tf$population) > mean(tf$population)`

`## [1] TRUE`

`$`

to isolate the `population`

column from the tibble `tf.`

This is one way of accessing a single column from a tibble. As a single column, `population`

is perceived as a vector from functions `sd()`

and `mean().`

In such cases, log-transforming the variable often results in more “normal-like” distributions:

```
#Let's log-transform this power-law looking distribution:
ggplot(tf, aes(x=log(population)))+geom_density()
```

`ggplot2()`

in Section 3.
*For comments, suggestions, errors, and typos, please email me at: kokkodis@bc.edu*