A Look At ggplot

Note: When you run the first code block to start the session, remember to give it the path to the posts-output folder so you don't need the path when saving the plots.

library("assertthat")
library("ggplot2")
library("knitr")
library("tidyverse")

These are stuff that get re-used in the plotting.

DISPLACEMENT <- "Engine Displacement (Liters)"
EFFICIENCY <-"Gallons Per Mile (Combined)"
DISPLACEMENT_VS_EFFICIENCY = partial(labs, x=DISPLACEMENT, y=EFFICIENCY)

BLUE <- "#4687b7"
RED <- "#ce7b6d"

It's a data frame with 234 rows and 11 variables:

I'll do some column renaming here since I keep forgetting what abbreviations they used.

mpg <- mpg %>%
  rename(
    displacement=displ,
    cylinders=cyl,
    transmission=trans,
    drive_train=drv,
    city_mpg=cty,
    highway_mpg=hwy,
    fuel_type=fl,
    )

str(mpg)

tibble [234 × 11] (S3: tbl_df/tbl/data.frame)
 $ manufacturer: chr [1:234] "audi" "audi" "audi" "audi" ...
 $ model       : chr [1:234] "a4" "a4" "a4" "a4" ...
 $ displacement: num [1:234] 1.8 1.8 2 2 2.8 2.8 3.1 1.8 1.8 2 ...
 $ year        : int [1:234] 1999 1999 2008 2008 1999 1999 2008 1999 1999 2008 ...
 $ cylinders   : int [1:234] 4 4 4 4 6 6 6 4 4 4 ...
 $ transmission: chr [1:234] "auto(l5)" "manual(m5)" "manual(m6)" "auto(av)" ...
 $ drive_train : chr [1:234] "f" "f" "f" "f" ...
 $ city_mpg    : int [1:234] 18 21 20 21 16 18 18 18 16 20 ...
 $ highway_mpg : int [1:234] 29 29 31 30 26 26 27 26 25 28 ...
 $ fuel_type   : chr [1:234] "p" "p" "p" "p" ...
 $ class       : chr [1:234] "compact" "compact" "compact" "compact" ...

kable(head(mpg), caption="MPG Dataset (EPA Automobile Data)")

Table: MPG Dataset (EPA Automobile Data)

The EPA uses a weighted average to create a combined metric that uses both Highway and City mileage.

\[ \textrm{Combined Fuel Economy} = 0.55 \times \textit{city} + 0.45 \times \textit{highway} \]

I've also seen it done as the harmonic mean (on Illustrative Mathematics), but if you round to the nearest whole number it comes out about the same.

mpg$combined_fuel_economy <- 0.55 * mpg$city_mpg + 0.45 * mpg$highway_mpg

plot = ggplot(data=mpg) +
  geom_point(mapping=aes(x=displacement, y=combined_fuel_economy, color=combined_fuel_economy)) +
  labs(x=DISPLACEMENT, y="Combined MPG",
       title="Displacement vs Mileage")

filename = "displacement_vs_combined_mileage.png"
ggsave(filename)

We can plot them together to see how much the combined MPG differs from the highway MPG.

plot = ggplot(data=mpg) +
  geom_smooth(mapping=aes(x=displacement, y=combined_fuel_economy), color="red") +
  geom_smooth(mapping=aes(x=displacement, y=highway_mpg), color="blue") +
  labs(x=DISPLACEMENT, y="MPG",
       title="Displacement vs Mileage (Highway and Combined)")

filename = "highway_vs_combined_mileage.png"
ggsave(filename)

Adding the city mileage drops the mileage somewhat, although the line looks to be about the same shape.

The EPA's explanation of their vehicle labels mentions that the reason why they put a Fuel Consumption Rate is that the Miles Per Gallon metric is actually not a good way to compare mileage - it is subject to a "Miles Per Gallon Illusion" (ReaClearScience has an article about it). Here's how the number of gallons used per 1,000 miles driven changes with miles-per-gallon.

mileage <- seq(1, 100)
miles = 1000
gallons_per_1000_miles <- miles/mileage

improvement <- data.frame(MPG=mileage,
                          gallons=gallons_per_1000_miles)
plot = ggplot(data=improvement) +
  geom_point(mapping=aes(x=mileage, y=gallons), alpha=0.5, color="blue") +
  geom_line(mapping=aes(x=mileage, y=gallons), color="blue") +
  labs(title="Fuel Consumption vs MPG",
       x="Miles Per Gallon",
       y="Gallons Used Per 1,000 Miles")

ggsave("gallons_vs_mpg.png")

As you can see the improvement in the number of gallons used goes down pretty fast as the miles-per-gallon goes up. Let's see about adding a fuel-efficency column. What happens when you switch to Gallons Per Mile?

gallons_per_mile <- mileage
gallons_per_1000_miles <- miles * gallons_per_mile

improvement <- data.frame(gpm=gallons_per_mile,
                          gallons=gallons_per_1000_miles)
plot = ggplot(data=improvement) +
  geom_point(mapping=aes(x=gpm, y=gallons), alpha=0.5, color="blue") +
  geom_line(mapping=aes(x=gpm, y=gallons), color="blue") +
  labs(title="Fuel Consumption vs Gallons Per Mile",
       x="Gallons Per Mile",
       y="Gallons Used Per 1,000 Miles")

ggsave("gallons_vs_efficiency.png")

I suppose you could just figure that that'd be the case, but this is about plotting.

mpg$gallons_per_mile <- 1/mpg$combined_fuel_economy

plot = ggplot(data=mpg, mapping=aes(x=displacement, y=gallons_per_mile)) +
  geom_point() +
  DISPLACEMENT_VS_EFFICIENCY(title="Displacement vs Fuel Efficiency")

filename = "displacement_vs_fuel_efficiency.png"
ggsave(filename)

Even though this is just the inverse of the MPG plot it seems more intuitive to me. I didn't really notice that big outlier at the top when I plotted it using MPG, so I think I'll stick with this.

plot = ggplot(data=mpg) +
  geom_point(mapping=aes(x=displacement, y=gallons_per_mile, color=class),
             position="jitter") +
  DISPLACEMENT_VS_EFFICIENCY(title="Displacement vs Fuel Efficiency")

filename = "displacement_vs_mileage_with_class.png"
ggsave(filename)

I added a little jitter because it looked like the top outlier was just one point. It looks like 2-seaters and one of the mid-sized cars had unusually good mileage given their engine displacement. What's a two-seater?

kable(filter(mpg, class=="2seater"))

Just Corvettes here.

While the use of color is useful for comparing the classes on the same plot, sometimes it can be easier to interpret plots that have the categorical classes separated into sub-plots (called facets).

By default the faceting functions use aphabetical order, I'm going to use a slightly different ordering to see if it makes it clearer how the classes compare (this is based on the medians that I plotted below).

mpg$class_order <- factor(mpg$class,
                          levels=c("compact", "subcompact", "midsize",
                                   "2seater",
                                   "minivan", "suv", "pickup"))

plot = ggplot(data=mpg) +
  geom_point(mapping=aes(x=displacement, y=gallons_per_mile, color=gallons_per_mile)) +
  facet_grid(. ~ class_order) + 
  DISPLACEMENT_VS_EFFICIENCY(title="Displacement vs Efficiency")

filename = "displacement_vs_mileage_faceted_classes.png"
ggsave(filename)

I'm using facet_grid here, which is actually meant to use two variables (creating row and column separation). By putting the . before the ~ we're telling it to only facet using columns. There's also a facet_wrap function that only does one variable but adds the ability to specify the number of rows you want to use, which might be helpful if you have a lot of classes.

I wouldn't have thought it, but the Corvette falls between the minivan and the sub-compact for fuel efficiency. I guess when you consider that it can only be used to transport two people and not anything relatively large it's still inefficient, just not as much if you're only using it to commute.

Instead of plotting a scatterpoint, you can use geom_smooth to fit a single line representing the trend for the data (using a linear model).

plot = ggplot(data=mpg, mapping=aes(x=displacement, y=gallons_per_mile)) +
  geom_smooth() +
  geom_point() +
  facet_grid(class_order ~ drive_train) +
  DISPLACEMENT_VS_EFFICIENCY(title="Displacement vs Efficiency By Type")

ggsave("displacement_vs_mileage_smooth.png")

One interesting thing here is that the four-wheel-drive compact and sub-compact cars did better than some of the front-wheel drive cars in the same class.

If you look at the front-wheel-drive sub-compact cars you'll see that the curve-fitting can get a little funky if you're not careful.

Note the syntax for the plot. Before we were passing the aes mapping to the geometry object. You can do that here too, but if you pass it to the ggplot call then it will automatically apply it to all the geometries. If you wanted to then change one of them you could pass in the aes mapping to it and override the base mapping you gave to ggplot.

Besides passing in different aes mappings, you can also pass in different sub-sets of the data to each geometry (using dplyr's filter to isolate the SUVs here).

plot = ggplot(data=mpg, mapping=aes(x=displacement, y=gallons_per_mile)) +
  geom_smooth(data=filter(mpg, class=="suv")) +
  geom_point(mapping=aes(color=class), position="jitter") +
  DISPLACEMENT_VS_EFFICIENCY(title="Displacement vs Fuel Efficiency")

filename = "displacement_vs_mileage_subsets.png"
ggsave(filename)

Looking at the trend-line for SUVs you can see that it encompasses a surprising swath of the displacements, and it is mostly upwardly linear to begin with but then flattens out.

plot = ggplot(
  data = mpg,
  mapping = aes(x = displacement, y = gallons_per_mile, color = drive_train)
) +
  geom_point() +
  geom_smooth(se = FALSE) +
  DISPLACEMENT_VS_EFFICIENCY(title="Effect of Drive (Four, Front, or Rear) on Mileage")

ggsave("displacement_exercise_2.png")

It kind of looks like an emerging pattern that up to a point gasoline consumption goes up with engine size but then once a certain point is passed consumption flattens out, even as the engines get bigger.

Just out of curiosity, I'd like to see what those small four-wheel drive cars are.

small <- filter(mpg, displacement<3 & drive_train=="Four-Wheel")
plot = ggplot(
  data=small,
  mapping=aes(x=displacement, y=gallons_per_mile, color=model)
) +
  geom_point() +
  facet_grid(class_order ~ manufacturer) +
  DISPLACEMENT_VS_EFFICIENCY(title="4WD Less Than 3 Liters")

ggsave("small_4wd.png")

There are only three companies making these small four-wheel-drive automobiles, with Audi being the one focused on sedans.

The Bar Plot is an example of what the Grammar of Graphics calls a Statistical Transformation (I guess the scatter plots are so called "Identity" transformations, but, whatever). It doesn't display the values in the data (unless you tell it to) but instead shows how often categorical values appear in the data. We can also have it set the color to create a stacked bar plot.

plot = ggplot(data=mpg) +
  geom_bar(
    mapping = aes(x=class_order, fill=drive_train)
  ) +
  labs(title="Count of Cars by Class", x="Class Ordered by Median MPG", y="Count")

ggsave("class_count.png")

So most models of car are SUVs, how disheartening. This is only a sub-set of cars, though, and it doesn't reflect sales, just model counts.

Instead of using counts we can use proportions to show how the sub-category portions compare across categories.

plot = ggplot(data=mpg) +
  geom_bar(
    mapping = aes(x=class_order, fill=drive_train),
    position="fill"
  ) +
  labs(title="Proportion of Drives by Class", x="Class Ordered by Median MPG", y="Proportion")

ggsave("class_count_filled.png")

This shows what proportion if each class of car has what type of drive.

To make it easier to see how sub-categories compare within the class, we can change the positioning so that the bars are put side-by-side.

plot = ggplot(data=mpg) +
  geom_bar(
    mapping = aes(x=class_order, fill=drive_train),
    position="dodge"
  ) +
  labs(title="Count of Model Drives by Class", x="Class Ordered by Median MPG", y="Count")

ggsave("class_count_dodged.png")

Our original bar graph showed the counts, but we can show the same plot using the proportion that each categories' count is of the total count as the y-axis.

plot = ggplot(data=mpg, mapping=aes(color=class)) +
  geom_bar(
    mapping = aes(x=class_order, y=..prop.., group=1)
  ) +
  labs(title="Proportion of Cars by Class", x="Class Ordered by Median MPG", y="Proportion")

ggsave("class_proportion.png")

Two things:

• That funky ..prop.. is really how R specifies that argument
• The group=1 argument tells ggplot that there's only one group for the whole dataset, otherwise each category is taken as a separate group and they are all end up as 100% of their group.
• I couldn't get ggplot to set the colors based on the class

That was a nice clean way to show it, and it's flexible, but maybe a good old-fashioned box-plot is the best, in the end.

plot = ggplot(data=mpg) +
  geom_boxplot(
    mapping = aes(x=class_order, y=gallons_per_mile, color=class_order),
  ) +
  labs(title="Spread of Efficiency by Class", y=EFFICIENCY, x="Class")

ggsave("mpg_class_boxplot.png")