Learning goals

• Working with spatial data
• Writing and using a custom function

Getting started

Go to the course website and accept the lab assignment, clone it in RStudio and open the R Markdown document. Knit the document to make sure it compiles without errors.

library(tidyverse) 
library(dsbox) 

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

Exercises

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

dn_ak = dennys %>%
  filter(state == "AK")
nrow(dn_ak)

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

lq_ak = laquinta %>%
  filter(state == "AK")
nrow(lq_ak)

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. How many pairings are there between 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. 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 variables 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.

🧶 ✅ ⬆️ Knit, commit, and push your changes to GitHub with an appropriate commit message. Make sure to commit and push all changed files so that your Git pane is cleared up afterwards.

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 have it saved in a file called haversine.R that we can load and then use. (We do this for you by sourceing the file in the provided code-chunk.)

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
  
  earth_r = 6371 # Earth mean radius in km
  
  a = sin((lat2 - lat1) / 2) ^ 2 + 
    cos(lat1) * cos(lat2) * sin((long2 - long1) / 2) ^ 2
  d = earth_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

5. Still considering the state of Alaska, calculate the distances between all pairs of Denny’s and La Quinta locations and save this variable as distance. Save this variable in dn_lq_ak data frame so that you can use it later.

6. Calculate the minimum distance between a Denny’s and La Quinta for each Denny’s location (recall there are three). 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 nearest La Quinta location for each Denny’s in Alaska. Include an appropriate visualization.

🧶 ✅ ⬆️ Knit, commit, and push your changes to GitHub with an appropriate commit message. Make sure to commit and push all changed files so that your Git pane is cleared up afterwards.

8. Repeat the same analysis for New York: (i) filter Denny’s and La Quinta Data Frames for NY, (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 NY, (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 a state of your choosing, different than the ones we covered so far. Note that there’s a way you could execute steps 8 and 9 simultaneously and generate a faceted visualization. If you understand how to do this, feel free to do so.

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

🧶 ✅ ⬆️ Knit, commit, and push your changes to GitHub with an appropriate commit message. Make sure to commit and push all changed files so that your Git pane is cleared up afterwards and review the md document on GitHub to make sure you’re happy with the final state of your work.