Description

Directions: Create an R Markdown document to complete the tasks below. Include all necessary lines of code and explain your work using complete sentences. Both the code you write and the outputs from R should be included in the compiled/knitted HTML document. Submit both the .Rmd and .html files to CCLE. Name the files #########-lab03.Rmd and #########-lab03.html where the ######### are replaced by your Bruin ID.
1 Tidy Data
1.1 Lord of the Rings
The Lord of the Rings is a movie (and book) fantasy trilogy about a hobbit’s journey to Mordor in hopes of destroying the ring of power. Having re-read the books recently, I highly recommend checking them out when you’re not working on your Stats 20 assignments. The movies are good too, but make sure you find copies of the extended editions if you watch them, ya know … when you’re not working on your Stats 20 assignments. You’ve been given three data files containing the number of words spoken by different races and sexes in each of the three Lord of the Rings films. They are The_Fellowship_Of_The_Ring.csv, The_Two_Towers.csv and The_Return_Of_The_King.csv.
1. Read the individual data files into R using the readr package.
2. Find a function in dplyr that combines the data together by rows and create a single data file with 9 observations and 4 varibles.
3. Use the gather() function from tidyr to create a variable called Sex which combines the Male and Female variables. The Sex variable should contain the values Female and Male. The number of words spoken in each Film, for each Race and each Sex should be contained in a variable called Words. This data should end up containing 18 observations and 4 variables.
4. Use this tidy dataset to answer the following questions:
• What are the means, standard deviations and total number of number words spoken by each race in the films? Create a 3 row by 4 column table displaying this information.
• For each film, describe the distribution of words spoken by each race. That is, which races spoke more, less or about the same number of words in each film. Include a plot to reference as evidence for your answer.
1.2 Comic books
1. Read in the superheroes.csv and the publishers.csv data sets. These data files contain information about comic book superheroes, whether they are good (heroes) or bad (villains), the character’s sex, the publisher of the comic books and the year the comic book publishers were founded.
2. Join these two data files together to include only the characters whose publishers are contained in both datasets. Which character is dropped?
3. Join these two data files together to include only the publishers that are NOT contained in superheroes data.
4. Join these two data files together to create a data frame that keeps all of the publishers and has the superheroes’ information appended to each publisher. What are the dimensions of this new data frame?
5. Join these two data files together too create a data frame containing all of the observations from both datasets. What are the dimensions of this new data frame?
2 Simulations using loops
Simulations are incredibly useful in statistics. Statisticians/data scientists use simulations to answer questions that are too complex to solve mathematically or recreate real-world phenomenon (climate change for example).
2.1 Central limit theorem
According to Wikipedia, the central limit theorem states that the mean of a sufficiently large number of independent random sameples will be approximately normally distributed, regardless of the underlying distribution. I.e. if we take many samples independently from one another, even if the distribution those samples come from is skewed, the distribution of the sampled means will be normally distributed. In this problem, we’ll use a for loop and if/else to demonstrate the central limit theorem.
1. Use the rbinom() function to simulate, one time, the number of “successes” from flipping a coin 10 times where the probability of success is 0.2.
3. Create a histogram of the 100,000 draws. Make sure to specify the binwidth so that you can get a good idea of the shape of the distribution. Based on your plot, describe the center, shape and spread of the number of successes. Pay particular attention to the shape of the distribution.
4. Use the matrix function to turn your 100,000 draws into a matrix with 40 rows and 2,500 columns
(filling the matrix by column … i.e byrow = FALSE).
5. Use a for loop to calculate the column means of your matrix.
• Start by using the vector() function to create a vector of length 2,500 called means.
• Then use a for loop to replace each element in the vector means with the column mean of your matrix.
6. Create a histogram of the means and describe the center, shape and spread. Use the mean() and sd() functions to describe the center and spread of means and then interpret these values. Describe how the center, shape and spread is different than the distribution of the draws from the binomial distribution.
2.2 Random walk
Random walks are used to describe all sorts of real-life phenomenon (such as the stock market or an intoxicated person walking down the sidewalk). In this problem, we’ll simulate a random walk and see how long it takes for us to return to our starting point.
NOTE: In this problem, we’ll use a while() loop which, if not coded properly, can run for an infinitely long time. SAVE YOUR WORK BEFORE AND WHILE WORKING ON THIS PROBLEM. If your code seems to be taking a VERY long time, hit the stop sign symbol in the upper right hand corner of your console to stop your loop. THIS CAN POTENTIALLY CRASH YOUR R SESSION … SAVE YOUR WORK
1. Create the following objects in R.
place <- 0 zeros <- 0 path <- c() iteration <- c()
• place describes our current position. We’ll randomly add +1 or -1 to place during each iteration of the loop.
• zeros describes how many times we’re returned to our starting position, i.e. place = 0.
• path is an empty vector we’ll use to describe what position we were at for each iteration.
• iteration is an empty vector we’ll use to keep track of the set of iterations.
2. Next, fill in the blanks below using the comments as a guide. In your assignment, feel free to remove the comments and replace them with your own.
# We want to loop through the code in the curly braces until we return to our # starting point.Place a condition on the zeros object that will be TRUE until # we return to our starting point. while (____) {
# Overwrite the iteration vector by (1) keeping all of the values currently
# in our iteration vector and (2) adds the current length of the iteration
# object to our iteration vector
____ <- c(____, ____(____))
# Overwrite the path vector by (1) keeping all of the values currently stored # in our path vector and (2) adding our current place to the vector.
____ <- c(____, ____)
# Use the runif() function to draw a single number, uniformally, between the # values 0 and 1. draw <- runif(____)
# Write an if/else statement that does the following:
# If draw >= 0.5, add +1 to our current place.
# else, add -1 to our current place.
if (____) {
place <- ____ + 1 } else {
____ <- ____ – 1
}
# Write an if statement so that once we reach our starting place # (i.e. place == 0):
# (1) We include our current iteration to the iteration vector (just like you
# did before)
# (2) We include our current place to the path vector (just like you did
# before)
# (3) overwrite the zeros object to be zeros + 1
#
# Your while loop should stop once you’re place object is 0.
}
3. Create a line plot that shows that path of our random walk as the number of iterations increased.
Be sure to give your plot a descriptive title.
4. How long did it take for our random walk to return to our starting place?