Introduction

In this lab we revisit the Denny’s and La Quinta Inn and Suites data we visualized in the previous lab.

Getting started

• Go to the course organization on GitHub: https://github.com/Sta199-S18.

• Find the repo starting with lab-04 and that has your team name at the end (this should be the only lab-04 repo available to you).

• In the repo, click on the green Clone or download button, select Use HTTPS (this might already be selected by default, and if it is, you’ll see the text Clone with HTTPS as in the image below). Click on the clipboard icon to copy the repo URL.

• Go to RStudio Cloud and into the course workspace. Create a New Project from Git Repo. You will need to click on the down arrow next to the New Project button to see this option.

• Copy and paste the URL of your assignment repo into the dialog box:

• Hit OK, and you’re good to go!

Packages

In this lab we will work with the tidyverse package. So we need to install and load it:

install.packages("tidyverse")
library(tidyverse) 

Note that this package is also loaded in your R Markdown document.

Housekeeping

git config --global user.email "your email"
git config --global user.name "your name"

git config --global user.email
git config --global user.name

git config --global credential.helper 'cache --timeout 604800'

Warm up

Pick one team member to complete the steps in this section while the others contribute to the discussion but do not actually touch the files on their computer.

Before we introduce the data, let’s warm up with some simple exercises.

The data

The data consist of two csv (comma separated values) files: one for Denny’s locations and the other for La Quinta.

dn <- read_csv("data/dennys.csv")
lq <- read_csv("data/laquinta.csv")

Exercises

1. Filter the Denny’s dataframe for Alaska (AK) and save the result as dn_ak. How many Denny’s locations are there in Alaska?

2. Filter the La Quinta dataframe for Alaska (AK) and save the result as lq_ak. How many La Quinta locations are there in Alaska?

Next we’ll calculate the distance between all Denny’s and all La Quinta locations in Alaska. Let’s take this step by step:

Step 1: There are 3 Denny’s and 2 La Quinta locations in Alaska. (If you answered differently above, you might want to recheck your answers.)

Step 2: Let’s focus on the first Denny’s location. We’ll need to calculate two distances for it: (1) distance between Denny’s 1 and La Quinta 1 and (2) distance between Denny’s 1 and La Quinta (2).

Step 3: Now let’s consider all Denny’s locations.

3. Without running any code, determine the number of pairings of all Denny’s and all La Quinta locations in Alaska, i.e. how many distances do we need to calculate between the locations of these establishments in Alaska?

In order to calculate these distances we need to first restructure our data to pair the Denny’s and La Quinta locations. To do so, we will join the two data frames. We have six join options in R. Each of these join functions take at least three arguments: x, y, and by.

• x and y are data frames to join
• by is the variable(s) to join by

Four of these join functions combine variables from the two data frames:

⊕These are called mutating joins.

• inner_join(): return all rows from x where there are matching values in y, and all columns from x and y.

• left_join(): return all rows from x, and all columns from x and y. Rows in x with no match in y will have NA values in the new columns.

• right_join(): return all rows from y, and all columns from x and y. Rows in y with no match in x will have NA values in the new columns.

• full_join(): return all rows and all columns from both x and y. Where there are not matching values, returns NA for the one missing.

And the other two join functions only keep cases from the left-hand data frame, and are called filtering joins. We’ll learn about these another time but you can find out more about the join functions in the help files for any one of them, e.g. ?full_join.

In practice we mostly use mutating joins. In this case we want to keep all rows and columns from both dn_ak and lq_ak data frames. So we will use a full_join.

Full join of Denny’s and La Quinta locations in AK

Let’s join the data on Denny’s and La Quinta locations in Alaska, and take a look at what it looks like:

dn_lq_ak <- full_join(dn_ak, lq_ak, by = "state")
dn_lq_ak

4. How many observations are in the joined dn_lq_ak data frame? What are the names of the variables in this data frame?

.x in the variable names means the variable comes from the x data frame (the first argument in the full_join call, i.e. dn_ak), and .y means the variable comes from the y data frame. These varibles are renamed to include .x and .y because the two data frames have the same variables and it’s not possible to have two variables in a data frame with the exact same name.

Now that we have the data in the format we wanted, all that is left is to calculate the distances between the pairs.

5. What function from the tidyverse do we use to add a new variable to a data frame while keeping the existing variables?

One way of calculating the distance between any two points on the earth is to use the Haversine distance formula. This formula takes into account the fact that the earth is not flat, but instead spherical.

This function is not available in R, but we can define it as a custom function. Also, it’s already defined in your R Markdown file.

haversine <- function(long1, lat1, long2, lat2, round = 3) {
  # convert to radians
  long1 = long1 * pi / 180
  lat1  = lat1  * pi / 180
  long2 = long2 * pi / 180
  lat2  = lat2  * pi / 180
  
  R = 6371 # Earth mean radius in km
  
  a = sin((lat2 - lat1)/2)^2 + cos(lat1) * cos(lat2) * sin((long2 - long1)/2)^2
  d = R * 2 * asin(sqrt(a))
  
  return( round(d,round) ) # distance in km
}

This function takes five arguments:

• Longitude and latitude of the first location
• Longitude and latitude of the second location
• A parameter by which to round the responses

6. Calculate the distances between all pairs of Denny’s and La Quinta locations and save this variable as distance. Make sure to save this variable in the dn_lq_ak data frame so that you can use it later.

7. Calculate the minimum distance between a Denny’s and La Quinta for each Denny’s location. To do so we group by Denny’s locations and calculate a new variable that stores the information for the minimum distance.

dn_lq_ak_mindist <- dn_lq_ak %>%
  group_by(address.x) %>%
  summarise(closest = min(distance))

7. Describe the distribution of the distances between Denny’s and the nearest La Quinta locations in Alaska. Also include an appropriate visualization and relevant summary statistics.

8. Repeat the same analysis for North Carolina: (i) filter Denny’s and La Quinta Data Frames for NC, (ii) join these data frames to get a complete list of all possible pairings, (iii) calculate the distances between all possible pairings of Denny’s and La Quinta in NC, (iv) find the minimum distance between each Denny’s and La Quinta location, (v) visualize and describe the distribution of these shortest distances using appropriate summary statistics.

9. Repeat the same analysis for Texas.

10. Repeat the same analysis for a state of your choosing, different than the ones we covered so far.

11. Among the states you examined, where is Mitch Hedberg’s joke most likely to hold true? Explain your reasoning.