Table of Content

• Lecture: Create and Name vectors

  • Exercise 1

  • Lab1

• Lecture: Vector Arithematic

  • Exercise 2

  • Lab 2

• Lecture: Vector Subsetting

  • Exercise 3

  • Lab 3

Create and Name Vectors

Only the miniscules are being covered, the entire of the lecture notes are covered inside the provided handouts.

Miniscules

• Attaching lables to the vector elements:

  • Step1: Create a vector, assign it to some var.
  • Step2: Create another vector, (say) strings.

  • Step3: Using names() function to attach labels.

    Syntax:

  1. names(<vector1>, <name vector>)
  2. c( key = value, ... )
  3. c( "key" = value, ... )

• Under the hood: R vectors have "attributes" associcated with them.

  • i.e. setting the names of the remaining vector, as seeting names attributes of the remains object.

  • To prove this, we can pull up str() function that compactly displays the structure of an R Object.

• Single values are also Vectors! Specifically vectors of "length = 1"

• Vectors are homogeneous( i.e they can hold elements of the same type ).

  • Often called, atomic vectors.
  • If although we forcibly create a heterogenous vector, R performs coercion.
  • Coercion makes sures that you end up with a vector of the same type.

• If we want to store heterogenous data in a vector, R has a different data type for this called list.

Exercise 1

[RQ1]: What function should you use to create a vector?

Ans: The combine function, c().

[RQ2]: Which three of the following actions attach labels to the vector elements?

Ans:

1. Define the labels by using the names() function.

2. Define the labels inside the c() by using the equal sign, putting the names of the labels b/w quotes.

3. Or by putting the names of the labels b/w quotes.

[RQ3]: Which two of the following options are correct?

Ans: Atomic vectors can hold elements only of the same type, whereas lists can hold elements of a different type.

Lab1

Objective:

• Create different types of vectors using the c() function.

• Naming vectors.

• Understanding and Creating Vectors.

Table of Content

1. Create a vector 1

2. Create a vector 2

3. Naming a vector 1

4. Naming a vector 2

5. Different ways to create and name vectors

Create a vector 1

Preface:

Vectors are one dimensional arrays that can hold numeric data, character data, or logical data. You create a vector with the combine function c(). You place the vector elements separated by a comma between the brackets. For example:

numeric_vector <- c(1, 2, 3) character_vector <- c("a", "b", "c") boolean_vector <- c(TRUE, FALSE)

Instructions:

Build a vector, boolean_vector, that contains the three elements: TRUE, FALSE and TRUE (in that order).

Create a vector 2

Preface:

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

Instructions:

Assign the winnings/losses for roulette to the variable roulette_vector.

Naming a vector 1

Part of a job of data analyst is to have a clear view on the data being used.

Preface:

In the previous exercise, we created a vector with our 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 we could show that in the vector itself. Remember the names() function to name the elements of a vector?

some_vector <- c("Johnny", "Poker Player") names(some_vector) <- c("Name", "Profession")

We can do the same thing in our combine function, c():

some_vector <- c(Name = "Johnny", Profession = "Poker Player")

Instructions:

Go ahead and assign the days of the week as names to poker_vector and roulette_vector. In case you are not sure, the days of the week are: Monday, Tuesday, Wednesday, Thursday and Friday.

Naming a vector 2

Preface:

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, there is a more efficient way to do this, namely, to assign the days of the week vector to a variable!

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

Instructions:

• Create a variable days_vector that contains the days of the week, from Monday to Friday.

• Use that variable days_vector to set the names of poker_vector and roulette_vector.

Different ways to create and name vectors

The previous exercises outlined different ways of creating and naming vectors. Have a look at this chunk of code:

poker_vector1 <- c(140, -50, 20, -120, 240)
names(poker_vector1) <- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")

poker_vector2 <- c(Monday = 140, -50, 20, -120, 240)

roulette_vector1 <- c(-24, -50, 100, -350, 10)
days_vector <- names(poker_vector1)
names(roulette_vector1) <- days_vector

roulette_vector2 <- c(-24, -50, 100, -350, 10)
names(roulette_vector2) <- "Monday"

Which of the following statements is true?

Ans: poker_vector1 and roulette_vector1 have the same names, while poker_vector2 and roulette_vector2 show a names mismatch.

Conclusion

We might expect that the names of the vectors roulette_vector1 and roulette_vector2 are named the same; but the different approaches treat missing name information differently. Also, notice here how we can also use names() to get the names of a vector!

Go to top

Vector Arithematic

Nuances:

1. Scalars are single valued vectors! e.g x <- c(3)
2. Arithematic operations on vectors in R are done element wise.
3. This is performed on vectors of same length.

This raises a question, what if we have vectors of un-equal lengths?

We will look into it a bit later in the course.

For now, let's see an example:

Exercise 2

RQ1: Complete the following sentence: To calculate the sum of 2 vectors of equal length, __.

Ans: R takes the sum of each element of the vectors and returns a new vector of the same length. correct.

RQ2: How is multiplication and division of vectors performed in R?

Ans: Element wise.

RQ3: Which two of the following statements are correct?

Ans:

1. When multiplying a vector with a scalar (single value) in R, every element in the vector will be multiplyed by this scalar.

2. By using the sum() func., it is possible to add up all the elements in a vector.

Go to top

Lab 2

Objectives:

• Learn about "vector calculus".

• Perform basic "arithematic operations" on both, vectors and scalars.

• Understanding "element wise" arithematic operations.

Lab 2 Content

• Summing and subtracting vectors

• Calculate your earnings

• Calculate total winnings: sum()

• Comparing total winnings

• First steps in rational gambling

Summing and subtracting vectors

Preface:

Now that you have the poker and roulette winnings nicely as a named vector, you can start doing some data science 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?

You'll have to do arithmetic calculations on vectors to solve these problems. Remember that this happens element-wise; 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)

Instructions:

• Take the element-wise sum of the variables A_vector and B_vector and it assign tototal_vector`. The result should be a vector.

• Inspect the result by printing total_vector to the console.

• Do the same thing, but this time subtract B_vector from A_vector and assign the result to diff_vector.

• Finally, print diff_vector to the console as well.

Go to top

Calculate your earnings

Preface:

• First, you need to understand what the overall profit or loss / day of the wek was.

• Total daily profit = sum( profit / loss ) / either poker or roulette day

Instructions:

Assign to the varible total_daily how much you won or lost on each day in total( poker and roulette combined )

Go to top

Calculate total winnings: sum

Preface:

The sum() calculates the sum of all elements of a vector.

Instructions:

• Calculate the total amount of money that you have won/lost with poker and assign it to the variable total_poker.

• Do the same thing for roulette and assign the result to total_roulette.

• Now that you have the totals for roulette and poker, you can easily calculate total_week (which is the sum of all gains and losses of the week).

• Print the variable total_week.

Conclusion: Look's like we are losing money!

Comparing total winnings

Preface:

We rethink our strategy and realize that we might be less skilled in roulette than in poker, we check it by using the > operator.

Instructions:

• Create a new vector containing logicals, poker_better, that tells whether your poker gains exceeded your roulette results on a daily basis.

• Calculate total_poker and total_roulette as in the previous exercise.

• Using total_poker and total_roulette, Check if your total gains in poker are higher than for roulette by using a comparison. Assign the result of this comparison to the variable choose_poker and print it out. What do you conclude, should you focus on roulette or on poker?

Conclusion: Look like we truly are doing much better in "poker".

First steps in rational gambling

Preface:

In the previous exercise, you found out that roulette is not really your forte. However, you have some vague memories from visits in Vegas where you actually excelled at this game. You plan to dig through your receipts of when you withdrew and cashed chips and found out about your actual performance in the previous week you were in Sin City. In that week, you also only played poker and roulette; the information is stored in poker_past and roulette_past. The information for the current week, with which you have been working all along, is in poker_present and roulette_present. All these variables are available in your workspace.

Instructions:

• Use the sum() function twice in combination with the + operator to calculate the total gains for your entire past week in Vegas (this means for both poker and roulette). Assign the result to total_past.

• Calculate difference of past to present poker performance: Using the - operator, subtract poker_past from poker_present, to calculate diff_poker. diff_poker should be a vector with 5 elements.

Vector Subsetting

Exercise 3

[RQ1]: Which kind of brackets should you use in order to subset a vector?

Ans: A pair of square bracket, [].

[RQ2]: When using the minus operator for subsetting a named vector, you can subset by?

Ans: it's index.

[RQ3]: Which two of the following statements are true?

Ans: The following are true:

1. When subsetting multiple numbers from a vector, the order inside the square brackets does matter.
2. way to subset a vector is by using a logical vector. When the length of this logical vector is shorter than the length of the original vector, R will perform recycling.

Lab 3

Objective:

• Subsetting vectors

• Different ways of sbsetting.

  • subsetting by indices.
  • subsetting by names.
  • subsetting using another logical vector.

• Recycling in R.

Lab content

• Selection by index

• Selection by index

• Vector Selection

• Slection by name1

• Selection by name2

• Selection by logicals1

• Selection by logicals2

• Selection by logicals13

• Vectors: Place your bets

Top page

Selection by index1

Preface:

After you figured that roulette is not your forte, you decide to compare 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.

Instructions:

• Assign the poker results of Wednesday to the variable poker_wednesday.

• Assign the roulette results of Friday to the variable roulette_friday.

Selection by index2

Preface:

How about analyzing your midweek results? Instead of using a single number to select a single element, you can also select multiple elements by passing a vector inside the square brackets. For example,

poker_vector[c(1,5)] selects the first and the fifth element of poker_vector.

Instructions:

• Assign the poker results of Tuesday, Wednesday and Thursday to the variable poker_midweek.

• Assign the roulette results of Thursday and Friday to the variable roulette_endweek.

Vector selection

Preface:

Now, selecting multiple successive 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. Try it out in the console!

Instructions:

• Assign to roulette_subset the roulette results from Tuesday to Friday inclusive by making use of :.

• Print the resulting variable to the console.

Selection by name1

Preface:

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.

Instructions:

• Select the fourth element, corresponding to Thursday, from roulette_vector. Name it roulette_thursday.

• Select Tuesday's poker gains using subsetting by name. Assign the result to poker_tuesday.

Selection by name2

Preface:

Just like selecting single elements using numerics extends naturally to selecting multiple elements, you can also use a vector of names. As an example, try:

roulette_vector[c("Monday","Wednesday")]

Of course you can't use the colon trick here:

`"Monday":"Wednesday" will generate an error.

Instructions:

• Create a vector containing the poker gains for the first three days of the week; name it poker_start.

• Using the function mean(), calculate the average poker gains during these first three days. Assign the result to a variable avg_poker_start.

Selection by logicals1

Preface:

There are basically three ways to subset vectors: by using the indices, by using the names (if the vectors are named) and by using logical vectors. Filip already told you about the internals in the instructional video. As a refresher, have a look at the following statements to select elements from poker_vector, which are all equivalent:

selection by index

poker_vector[c(1,3)]

selection by name

poker_vector[c("Monday", "Wednesday")]

selection by logicals

poker_vector[c(TRUE, FALSE, TRUE, FALSE, FALSE)]

Instructions:

• Assign the roulette results from the first, third and fifth day to roulette_subset.

• Select the first three days from poker_vector using a vector of logicals. Assign the result to poker_start.

Selection by logicals2

Preface:

By making use of a combination of comparison operators and subsetting using logicals, you can investigate your casino performance in a more pro-active 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

Experiment with these operators in the console. The result will be a logical vector, which you can use to perform subsetting! This means that 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.

Instructions:

• Check if your poker winnings are positive on the different days of the week (i.e. > 0), and assign this to selection_vector.

• Assign the amounts that you won on the profitable days, so a vector, to the variable poker_profits, by using selection_vector.

Selection by logicals3

Preface:

To fully prepare you for the challenge that's coming, you'll do a final analysis of your casino ventures. This time, you'll use your newly acquired skills to perform advanced selection on roulette_vector.

Along the way, you'll need the sum() function. You used it before to calculate the total winnings, so an a numeric vector. However, you can also use sum() on a logical vector; it simply counts the number of vector elements that are TRUE.

Instructions:

• Assign the amounts that you made on the days that you ended positively for roulette to the variable roulette_profits. This vector thus contains the positive winnings of roulette_vector. You can do this with a one-liner!

• Calculate the sum of the amounts on these profitable days; assign the result to roulette_total_profit.

• Find out how many roulette days were profitable, using the sum() function. Store the result in a variable num_profitable_days.

Placing the bets

Preface:

By now, you should have gained some insights on how your casino habits are actually working out for you. In fact, why not decide on changing your game completely? Let's dive into the world of Blackjack for once, and analyze some game outcomes here. In short, blackjack is a game where you have to ask for cards until you arrive at a sum that is as close to 21 as possible. However, if you exceed 21, you've lost. You can be greedy and go for 21, or you can be careful and settle for 16 or so. A player wins when his or her sum, or score, exceeds that of the house.

The sums for the player's last 7 games are stored in player; the house's scores are contained in house. Both are available in the workspace. In both cases, the scores were never higher than 21.

Instructions:

• With square brackets, select the player's score for the third game, using any of the techniques that you've learned about. Store the result in player_third.

• Subset the player vector to only select the scores that exceeded the scores of house, so the scores that had the player win. Use subsetting in combination with the relational operator >. Assign the subset to the variable winning_scores.

• Count the number of times the score inside player was lower than 18. This time, you should use a relational operator in combination with sum(). Save the resulting value in a new variable, n_low_score.