### '2018/03/09'에 해당되는 글 3건

1. 2018.03.09 [R] Matrices
2. 2018.03.09 [R] Vectors
3. 2018.03.09 [R] inatallation & Introduction to R
SAS MBA Life/Sejong MBA2018.03.09 16:17

# What's a matrix?

In R, a matrix is a collection of elements of the same data type (numeric, character, or logical) arranged into a fixed number of rows and columns. Since you are only working with rows and columns, a matrix is called two-dimensional.

You can construct a matrix in R with the `matrix()` function. Consider the following example:

``````matrix(1:9, byrow = TRUE, nrow = 3)
``````

In the `matrix()` function:

• The first argument is the collection of elements that R will arrange into the rows and columns of the matrix. Here, we use `1:9` which is a shortcut for `c(1, 2, 3, 4, 5, 6, 7, 8, 9)`.
• The argument `byrow` indicates that the matrix is filled by the rows. If we want the matrix to be filled by the columns, we just place `byrow = FALSE`.
• The third argument `nrow` indicates that the matrix should have three rows.

# Analyzing matrices, you shall

It is now time to get your hands dirty. In the following exercises you will analyze the box office numbers of the Star Wars franchise. May the force be with you!

In the editor, three vectors are defined. Each one represents the box office numbers from the first three Star Wars movies. The first element of each vector indicates the US box office revenue, the second element refers to the Non-US box office (source: Wikipedia).

In this exercise, you'll combine all these figures into a single vector. Next, you'll build a matrix from this vector.

# Naming a matrix

To help you remember what is stored in `star_wars_matrix`, you would like to add the names of the movies for the rows. Not only does this help you to read the data, but it is also useful to select certain elements from the matrix.

Similar to vectors, you can add names for the rows and the columns of a matrix

``````rownames(my_matrix) <- row_names_vector
colnames(my_matrix) <- col_names_vector
``````

We went ahead and prepared two vectors for you: `region`, and `titles`. You will need these vectors to name the columns and rows of `star_wars_matrix`, respectively.

Script

# Calculating the worldwide box office

The single most important thing for a movie in order to become an instant legend in Tinseltown is its worldwide box office figures.

To calculate the total box office revenue for the three Star Wars movies, you have to take the sum of the US revenue column and the non-US revenue column.

In R, the function `rowSums()` conveniently calculates the totals for each row of a matrix. This function creates a new vector:

``rowSums(my_matrix)``

# Adding a column for the Worldwide box office

In the previous exercise you calculated the vector that contained the worldwide box office receipt for each of the three Star Wars movies. However, this vector is not yet part of `star_wars_matrix`.

You can add a column or multiple columns to a matrix with the `cbind()` function, which merges matrices and/or vectors together by column. For example:

``big_matrix <- cbind(matrix1, matrix2, vector1 ...)``

Just like every action has a reaction, every `cbind()` has an `rbind()`. (We admit, we are pretty bad with metaphors.)

Your R workspace, where all variables you defined 'live' (check out what a workspace is), has already been initialized and contains two matrices:

• `star_wars_matrix` that we have used all along, with data on the first trilogy,
• `star_wars_matrix2`, with similar data for the second trilogy.

Type the name of these matrices in the console and hit Enter if you want to have a closer look. If you want to check out the contents of the workspace, you can type `ls()` in the console.

# The total box office revenue for the entire saga

Just like every `cbind()` has a `rbind()`, every `colSums()` has a `rowSums()`. Your R workspace already contains the `all_wars_matrix` that you constructed in the previous exercise; type `all_wars_matrix` to have another look. Let's now calculate the total box office revenue for the entire saga.

# Selection of matrix elements

Similar to vectors, you can use the square brackets `[ ]` to select one or multiple elements from a matrix. Whereas vectors have one dimension, matrices have two dimensions. You should therefore use a comma to separate that what to select from the rows from that what you want to select from the columns. For example:

• `my_matrix[1,2]` selects the element at the first row and second column.
• `my_matrix[1:3,2:4]` results in a matrix with the data on the rows 1, 2, 3 and columns 2, 3, 4.

If you want to select all elements of a row or a column, no number is needed before or after the comma, respectively:

• `my_matrix[,1]` selects all elements of the first column.
• `my_matrix[1,]` selects all elements of the first row.

Back to Star Wars with this newly acquired knowledge! As in the previous exercise, `all_wars_matrix` is already available in your workspace.

# A little arithmetic with matrices

Similar to what you have learned with vectors, the standard operators like `+`, `-`, `/`, `*`, etc. work in an element-wise way on matrices in R.

For example, `2 * my_matrix` multiplies each element of `my_matrix` by two.

As a newly-hired data analyst for Lucasfilm, it is your job is to find out how many visitors went to each movie for each geographical area. You already have the total revenue figures in `all_wars_matrix`. Assume that the price of a ticket was 5 dollars. Simply dividing the box office numbers by this ticket price gives you the number of visitors.

# A little arithmetic with matrices (2)

Just like `2 * my_matrix` multiplied every element of `my_matrix`by two, `my_matrix1 * my_matrix2` creates a matrix where each element is the product of the corresponding elements in `my_matrix1` and `my_matrix2`.

After looking at the result of the previous exercise, big boss Lucas points out that the ticket prices went up over time. He asks to redo the analysis based on the prices you can find in `ticket_prices_matrix` (source: imagination).

Those who are familiar with matrices should note that this is not the standard matrix multiplication for which you should use `%*%` in R.

SAS MBA Life/Sejong MBA2018.03.09 13:23

# Create a vector

Feeling lucky? You better, because this chapter takes you on a trip to the City of Sins, also known as Statisticians Paradise!

Thanks to R and your new data-analytical skills, you will learn how to uplift your performance at the tables and fire off your career as a professional gambler. This chapter will show how you can easily keep track of your betting progress and how you can do some simple analyses on past actions. Next stop, Vegas Baby... VEGAS!!

# Create a vector (2)

Let us focus first!

On your way from rags to riches, you will make extensive use of vectors. Vectors are one-dimension arrays that can hold numeric data, character data, or logical data. In other words, a vector is a simple tool to store data. For example, you can store your daily gains and losses in the casinos.

In R, you create a vector with the combine function `c()`. You place the vector elements separated by a comma between the parentheses. For example:

``````numeric_vector <- c(1, 2, 3)
character_vector <- c("a", "b", "c")
``````

Once you have created these vectors in R, you can use them to do calculations.

# Create a vector (3)

After one week in Las Vegas and still zero Ferraris in your garage, you decide that it is time to start using your data analytical superpowers.

Before doing a first analysis, you decide to first collect all the winnings and losses for the last week:

For `poker_vector`:

• On Monday you won \$140
• Tuesday you lost \$50
• Wednesday you won \$20
• Thursday you lost \$120
• Friday you won \$240

For `roulette_vector`:

• On Monday you lost \$24
• Tuesday you lost \$50
• Wednesday you won \$100
• Thursday you lost \$350
• Friday you won \$10

You only played poker and roulette, since there was a delegation of mediums that occupied the craps tables. To be able to use this data in R, you decide to create the variables `poker_vector` and `roulette_vector`.

# Naming a vector

As a data analyst, it is important to have a clear view on the data that you are using. Understanding what each element refers to is therefore essential.

In the previous exercise, we created a vector with your winnings over the week. Each vector element refers to a day of the week but it is hard to tell which element belongs to which day. It would be nice if you could show that in the vector itself.

You can give a name to the elements of a vector with the `names()`function. Have a look at this example:

``````some_vector <- c("John Doe", "poker player")
names(some_vector) <- c("Name", "Profession")
``````

This code first creates a vector `some_vector` and then gives the two elements a name. The first element is assigned the name `Name`, while the second element is labeled `Profession`. Printing the contents to the console yields following output:

``````          Name     Profession
"John Doe" "poker player" ``````

# Naming a vector (2)

If you want to become a good statistician, you have to become lazy. (If you are already lazy, chances are high you are one of those exceptional, natural-born statistical talents.)

In the previous exercises you probably experienced that it is boring and frustrating to type and retype information such as the days of the week. However, when you look at it from a higher perspective, there is a more efficient way to do this, namely, to assign the days of the week vector to a variable!

Just like you did with your poker and roulette returns, you can also create a variable that contains the days of the week. This way you can use and re-use it.

# Calculating total winnings

Now that you have the poker and roulette winnings nicely as named vectors, you can start doing some data analytical magic.

You want to find out the following type of information:

• How much has been your overall profit or loss per day of the week?
• Have you lost money over the week in total?
• Are you winning/losing money on poker or on roulette?

To get the answers, you have to do arithmetic calculations on vectors.

It is important to know that if you sum two vectors in R, it takes the element-wise sum. For example, the following three statements are completely equivalent:

``````c(1, 2, 3) + c(4, 5, 6)
c(1 + 4, 2 + 5, 3 + 6)
c(5, 7, 9)
``````

You can also do the calculations with variables that represent vectors:

``````a <- c(1, 2, 3)
b <- c(4, 5, 6)
c <- a + b``````

# Calculating total winnings (2)

Now you understand how R does arithmetic with vectors, it is time to get those Ferraris in your garage! First, you need to understand what the overall profit or loss per day of the week was. The total daily profit is the sum of the profit/loss you realized on poker per day, and the profit/loss you realized on roulette per day.

In R, this is just the sum of `roulette_vector` and `poker_vector`.

# Calculating total winnings (3)

Based on the previous analysis, it looks like you had a mix of good and bad days. This is not what your ego expected, and you wonder if there may be a very tiny chance you have lost money over the week in total?

A function that helps you to answer this question is `sum()`. It calculates the sum of all elements of a vector. For example, to calculate the total amount of money you have lost/won with poker you do:

``total_poker <- sum(poker_vector)``

# Comparing total winnings

Oops, it seems like you are losing money. Time to rethink and adapt your strategy! This will require some deeper analysis...

After a short brainstorm in your hotel's jacuzzi, you realize that a possible explanation might be that your skills in roulette are not as well developed as your skills in poker. So maybe your total gains in poker are higher (or `>` ) than in roulette.

# Vector selection: the good times

Your hunch seemed to be right. It appears that the poker game is more your cup of tea than roulette.

Another possible route for investigation is your performance at the beginning of the working week compared to the end of it. You did have a couple of Margarita cocktails at the end of the week...

To answer that question, you only want to focus on a selection of the `total_vector`. In other words, our goal is to select specific elements of the vector. To select elements of a vector (and later matrices, data frames, ...), you can use square brackets. Between the square brackets, you indicate what elements to select. For example, to select the first element of the vector, you type `poker_vector[1]`. To select the second element of the vector, you type `poker_vector[2]`, etc. Notice that the first element in a vector has index 1, not 0 as in many other programming languages.

# Vector selection: the good times (2)

To select multiple elements from a vector, you can add square brackets at the end of it. You can indicate between the brackets what elements should be selected. For example: suppose you want to select the first and the fifth day of the week: use the vector `c(1, 5)`between the square brackets. For example, the code below selects the first and fifth element of `poker_vector`:

``poker_vector[c(1, 5)]``

# Vector selection: the good times (3)

Selecting multiple elements of `poker_vector` with `c(2, 3, 4)` is not very convenient. Many statisticians are lazy people by nature, so they created an easier way to do this: `c(2, 3, 4)` can be abbreviated to`2:4`, which generates a vector with all natural numbers from 2 up to 4.

So, another way to find the mid-week results is `poker_vector[2:4]`. Notice how the vector `2:4` is placed between the square brackets to select element 2 up to 4.

# Vector selection: the good times (4)

Another way to tackle the previous exercise is by using the names of the vector elements (Monday, Tuesday, ...) instead of their numeric positions. For example,

``````poker_vector["Monday"]
``````

will select the first element of `poker_vector` since `"Monday"` is the name of that first element.

Just like you did in the previous exercise with numerics, you can also use the element names to select multiple elements, for example:

``poker_vector[c("Monday","Tuesday")]``

# Selection by comparison - Step 1

By making use of comparison operators, we can approach the previous question in a more proactive way.

The (logical) comparison operators known to R are:

• `<` for less than
• `>` for greater than
• `<=` for less than or equal to
• `>=` for greater than or equal to
• `==` for equal to each other
• `!=` not equal to each other

As seen in the previous chapter, stating `6 > 5` returns `TRUE`. The nice thing about R is that you can use these comparison operators also on vectors. For example:

``````> c(4, 5, 6) > 5
[1] FALSE FALSE TRUE
``````

This command tests for every element of the vector if the condition stated by the comparison operator is `TRUE` or `FALSE`.

# Selection by comparison - Step 2

Working with comparisons will make your data analytical life easier. Instead of selecting a subset of days to investigate yourself (like before), you can simply ask R to return only those days where you realized a positive return for poker.

In the previous exercises you used `selection_vector <- poker_vector > 0` to find the days on which you had a positive poker return. Now, you would like to know not only the days on which you won, but also how much you won on those days.

You can select the desired elements, by putting `selection_vector`between the square brackets that follow `poker_vector`:

``````poker_vector[selection_vector]
``````

R knows what to do when you pass a logical vector in square brackets: it will only select the elements that correspond to `TRUE` in `selection_vector`.

SAS MBA Life/Sejong MBA2018.03.09 11:55

## [R] inatallation & Introduction to R

https://cran.r-project.org/mirrors.html

R Studio

Packages

• install.packages("package_name")
• library(package_name)

• data(dataset_name)
• get()
• setwd()

# How it works

In the editor on the right you should type R code to solve the exercises. When you hit the 'Submit Answer' button, every line of code is interpreted and executed by R and you get a message whether or not your code was correct. The output of your R code is shown in the console in the lower right corner.

R makes use of the `#` sign to add comments, so that you and others can understand what the R code is about. Just like Twitter! Comments are not run as R code, so they will not influence your result. For example, Calculate 3 + 4 in the editor on the right is a comment.

You can also execute R commands straight in the console. This is a good way to experiment with R code, as your submission is not checked for correctness.

# Arithmetic with R

In its most basic form, R can be used as a simple calculator. Consider the following arithmetic operators:

• Addition: `+`
• Subtraction: `-`
• Multiplication: `*`
• Division: `/`
• Exponentiation: `^`
• Modulo: `%%`

The last two might need some explaining:

• The `^` operator raises the number to its left to the power of the number to its right: for example `3^2` is 9.
• The modulo returns the remainder of the division of the number to the left by the number on its right, for example 5 modulo 3 or `5 %% 3` is 2.

With this knowledge, follow the instructions below to complete the exercise.

# Variable assignment

A basic concept in (statistical) programming is called a variable.

A variable allows you to store a value (e.g. 4) or an object (e.g. a function description) in R. You can then later use this variable's name to easily access the value or the object that is stored within this variable.

You can assign a value 4 to a variable `my_var` with the command

``my_var <- 4``

# Variable assignment (2)

Suppose you have a fruit basket with five apples. As a data analyst in training, you want to store the number of apples in a variable with the name `my_apples`.

# Variable assignment (3)

Every tasty fruit basket needs oranges, so you decide to add six oranges. As a data analyst, your reflex is to immediately create the variable `my_oranges` and assign the value 6 to it. Next, you want to calculate how many pieces of fruit you have in total. Since you have given meaningful names to these values, you can now code this in a clear way:

``my_apples + my_oranges``

# Basic data types in R

R works with numerous data types. Some of the most basic types to get started are:

• Decimals values like `4.5` are called numerics.
• Natural numbers like `4` are called integers. Integers are also numerics.
• Boolean values (`TRUE` or `FALSE`) are called logical.
• Text (or string) values are called characters.

Note how the quotation marks on the right indicate that "some text" is a character.

# What's that data type?

Do you remember that when you added `5 + "six"`, you got an error due to a mismatch in data types? You can avoid such embarrassing situations by checking the data type of a variable beforehand. You can do this with the `class()` function, as the code on the right shows.