Math 141 – The Grammar of Graphics

Intro to ggplot2

Grayson White

Math 141
Week 2 | Fall 2025

Goals for Today

Recall our motivation for good graphics
Learn the general structure of ggplot2.
Learn a few standard graphs for numerical/quantitative data:
- Histogram: one numerical variable
- Side-by-side boxplot: one numerical variable and one categorical variable
- Side-by-side violin plot: one numerical variable and one categorical variable
- Scatterplot: two numerical variables
- Linegraph: two numerical variables

Load Necessary Packages

ggplot2 is part of this collection of data science packages.

# Load necessary packages
library(tidyverse)

Data Setting: Portland Bikeshare Data

Import the Data

biketown <- read_csv("data/biketown.csv")

# Inspect the data
glimpse(biketown)

Rows: 9,999
Columns: 19
$ RouteID          <dbl> 4074085, 3719219, 3789757, 3576798, 3459987, 3947695,…
$ PaymentPlan      <chr> "Subscriber", "Casual", "Casual", "Subscriber", "Casu…
$ StartHub         <chr> "SE Elliott at Division", "SW Yamhill at Director Par…
$ StartLatitude    <dbl> 45.50513, 45.51898, 45.52990, 45.52389, 45.53028, 45.…
$ StartLongitude   <dbl> -122.6534, -122.6813, -122.6628, -122.6722, -122.6547…
$ StartDate        <chr> "8/17/2017", "7/22/2017", "7/27/2017", "7/12/2017", "…
$ StartTime        <time> 10:44:00, 14:49:00, 14:13:00, 13:23:00, 19:30:00, 10…
$ EndHub           <chr> "Blues Fest - SW Waterfront at Clay - Disabled", "SW …
$ EndLatitude      <dbl> 45.51287, 45.52142, 45.55902, 45.53409, 45.52990, 45.…
$ EndLongitude     <dbl> -122.6749, -122.6726, -122.6355, -122.6949, -122.6628…
$ EndDate          <chr> "8/17/2017", "7/22/2017", "7/27/2017", "7/12/2017", "…
$ EndTime          <time> 10:56:00, 15:00:00, 14:42:00, 13:38:00, 20:30:00, 10…
$ TripType         <lgl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ BikeID           <dbl> 6163, 6843, 6409, 7375, 6354, 6088, 6089, 5988, 6857,…
$ BikeName         <chr> "0488 BIKETOWN", "0759 BIKETOWN", "0614 BIKETOWN", "0…
$ Distance_Miles   <dbl> 1.91, 0.72, 3.42, 1.81, 4.51, 5.54, 1.59, 1.03, 0.70,…
$ Duration         <dbl> 11.500, 11.383, 28.317, 14.917, 60.517, 53.783, 23.86…
$ RentalAccessPath <chr> "keypad", "keypad", "keypad", "keypad", "keypad", "ke…
$ MultipleRental   <lgl> FALSE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE, FALSE…

Inspect the Data

# Look at first few rows
head(biketown)

# A tibble: 6 × 19
  RouteID PaymentPlan StartHub  StartLatitude StartLongitude StartDate StartTime
    <dbl> <chr>       <chr>             <dbl>          <dbl> <chr>     <time>   
1 4074085 Subscriber  SE Ellio…          45.5          -123. 8/17/2017 10:44    
2 3719219 Casual      SW Yamhi…          45.5          -123. 7/22/2017 14:49    
3 3789757 Casual      NE Holla…          45.5          -123. 7/27/2017 14:13    
4 3576798 Subscriber  NW Couch…          45.5          -123. 7/12/2017 13:23    
5 3459987 Casual      NE 11th …          45.5          -123. 7/3/2017  19:30    
6 3947695 Casual      SW Moody…          45.5          -123. 8/8/2017  10:01    
# ℹ 12 more variables: EndHub <chr>, EndLatitude <dbl>, EndLongitude <dbl>,
#   EndDate <chr>, EndTime <time>, TripType <lgl>, BikeID <dbl>,
#   BikeName <chr>, Distance_Miles <dbl>, Duration <dbl>,
#   RentalAccessPath <chr>, MultipleRental <lgl>

What does a row represent here?

Inspect the Data

# Determine type
# To access one variable: dataset$variable
class(biketown$BikeName)

[1] "character"

class(biketown$Distance_Miles)

[1] "numeric"

class(biketown)

[1] "spec_tbl_df" "tbl_df"      "tbl"         "data.frame"

Grammar of Graphics

data: Data frame that contains the raw data
- Variables used in the graph
geom: Geometric shape that the data are mapped to.
- EX: Point, line, bar, text, …
aesthetic: Visual properties of the geom
- EX: X (horizontal) position, y (vertical) position, color, fill, shape
scale: Controls how data are mapped to the visual values of the aesthetic.
- EX: particular colors, log scale
guide: Legend/key to help user convert visual display back to the data

`ggplot2` example code

Guiding Principle: We will map variables from the data to the aesthetic attributes (e.g. location, size, shape, color) of geometric objects (e.g. points, lines, bars).

ggplot(data = ---, mapping = aes(---)) +
  geom_---(---)

There are other layers, such as scale_---_---() and labs(), but we will wait on those.

Histograms

Binned counts of data.
Great for assessing shape.
Question: are histograms used for quantitative or categorical variables?
Answer: Quantitative.

Data Shapes

Histograms

# Create histogram
ggplot(data = biketown, 
       mapping = aes(x = Distance_Miles)) +
  geom_histogram()

Histograms

# Create histogram
ggplot(data = biketown, 
       mapping = aes(x = Distance_Miles)) +
  geom_histogram(color = "white",
                 fill = "violetred1",
                 bins = 50)

mapping to a variable goes in aes()
setting to a specific value goes in the geom_---()

Boxplots

Five number summary:
- Minimum
- First quartile (Q1)
- Median
- Third quartile (Q3)
- Maximum
Interquartile range (IQR) \(=\) Q3 \(-\) Q1
Outliers: unusual points
- Boxplot defines unusual as being beyond \(1.5*IQR\) from \(Q1\) or \(Q3\).
Whiskers: reach out to the furthest point that is NOT an outlier

Boxplots

# Create boxplot
ggplot(data = biketown, 
       mapping = aes(x = PaymentPlan, 
                     y = Distance_Miles)) +
  geom_boxplot()

Boxplots

ggplot(data = biketown, 
       mapping = aes(x = PaymentPlan, 
                     y = Distance_Miles)) +
  geom_boxplot(fill = "springgreen3")

Is this fill an aesthetic mapping?

Boxplots

ggplot(data = biketown, 
       mapping = aes(x = PaymentPlan, 
                     y = Distance_Miles,
                     fill = PaymentPlan)) +
  geom_boxplot()

Is this fill an aesthetic mapping?
What variable is mapped to fill?

Boxplots

ggplot(data = biketown, 
       mapping = aes(x = PaymentPlan, 
                     y = Distance_Miles,
                     fill = PaymentPlan)) +
  geom_boxplot() +
  guides(fill = "none")

Violin Plots

ggplot(data = biketown, 
       mapping = aes(x = PaymentPlan, 
                     y = Distance_Miles,
                     fill = PaymentPlan)) +
  geom_violin() +
  guides(fill = "none")

Boxplot Versus Violin Plots

New Data Context: `pdxTrees`

The pdxTrees R package contains data on all the trees in the Portland Metro Area.
Today, we’ll look at the Maple, Oak, Pine, Cedar, and Douglas-fir trees in a few parks near Reed.
Let’s load the data

New Data Context: `pdxTrees`

The pdxTrees R package contains data on all the trees in the Portland Metro Area.
Today, we’ll look at the Maple, Oak, Pine, Cedar, and Douglas-fir trees in a few parks near Reed.
Let’s load the data
Don’t worry, we haven’t learned the below code yet.

library(pdxTrees)
near_Reed <- get_pdxTrees_parks(park = c("Woodstock Park", "Sellwood Riverfront Park", "Kenilworth Park")) %>%
  filter(Genus %in% c("Acer", "Quercus", "Pinus", "Thuja", "Pseudotsuga"))

Inspect the data

glimpse(near_Reed)

Rows: 323
Columns: 34
$ Longitude                  <dbl> -122.6304, -122.6301, -122.6301, -122.6299,…
$ Latitude                   <dbl> 45.49201, 45.49080, 45.49081, 45.49094, 45.…
$ UserID                     <chr> "7670", "7671", "7672", "7902", "7903", "79…
$ Genus                      <chr> "Quercus", "Pseudotsuga", "Pseudotsuga", "Q…
$ Family                     <chr> "Fagaceae", "Pinaceae", "Pinaceae", "Fagace…
$ DBH                        <dbl> 3.3, 43.1, 48.2, 2.4, 11.7, 33.5, 23.5, 37.…
$ Inventory_Date             <dttm> 2018-07-26, 2018-07-26, 2018-07-26, 2018-0…
$ Species                    <chr> "QURU", "PSME", "PSME", "QURU", "PSME", "PS…
$ Common_Name                <chr> "Northern Red Oak", "Douglas-Fir", "Douglas…
$ Condition                  <chr> "Fair", "Fair", "Fair", "Fair", "Good", "Fa…
$ Tree_Height                <dbl> 16, 148, 148, 16, 64, 118, 121, 105, 24, 12…
$ Crown_Width_NS             <dbl> 14, 61, 52, 9, 29, 32, 37, 43, 38, 44, 31, …
$ Crown_Width_EW             <dbl> 10, 43, 48, 14, 32, 50, 31, 44, 35, 36, 33,…
$ Crown_Base_Height          <dbl> 5, 6, 7, 2, 3, 60, 27, 10, 5, 19, 17, 6, 5,…
$ Collected_By               <chr> "Staff", "Staff", "Staff", "Staff", "Staff"…
$ Park                       <chr> "Kenilworth Park", "Kenilworth Park", "Keni…
$ Scientific_Name            <chr> "Quercus rubra", "Pseudotsuga menziesii", "…
$ Functional_Type            <chr> "BD", "CE", "CE", "BD", "CE", "CE", "CE", "…
$ Mature_Size                <fct> L, L, L, L, L, L, L, L, S, L, L, L, L, L, L…
$ Native                     <chr> "No", "Yes", "Yes", "No", "Yes", "Yes", "Ye…
$ Edible                     <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,…
$ Nuisance                   <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,…
$ Structural_Value           <dbl> 288.80, 12462.74, 14395.22, 143.21, 1348.26…
$ Carbon_Storage_lb          <dbl> 25.2, 4221.2, 5206.7, 11.6, 285.3, 2513.2, …
$ Carbon_Storage_value       <dbl> 1.63, 273.80, 337.73, 0.75, 18.51, 163.01, …
$ Carbon_Sequestration_lb    <dbl> 3.7, 43.5, 49.8, 2.4, 9.6, 32.4, 21.4, 37.4…
$ Carbon_Sequestration_value <dbl> 0.24, 2.82, 3.23, 0.15, 0.62, 2.10, 1.39, 2…
$ Stormwater_ft              <dbl> 5.2, 157.1, 145.2, 4.7, 56.8, 73.3, 68.1, 1…
$ Stormwater_value           <dbl> 0.35, 10.50, 9.71, 0.31, 3.80, 4.90, 4.55, …
$ Pollution_Removal_value    <dbl> 0.63, 19.08, 17.64, 0.57, 6.90, 8.90, 8.27,…
$ Pollution_Removal_oz       <dbl> 1.4, 42.3, 39.1, 1.3, 15.3, 19.7, 18.3, 30.…
$ Total_Annual_Services      <dbl> 1.21, 32.40, 30.58, 1.04, 11.31, 15.90, 14.…
$ Origin                     <chr> "North America - eastern Canada and eastern…
$ Species_Factoid            <chr> "Acorns take two years to mature and are an…

Inspect the data

head(near_Reed)

# A tibble: 6 × 34
  Longitude Latitude UserID Genus       Family   DBH Inventory_Date      Species
      <dbl>    <dbl> <chr>  <chr>       <chr>  <dbl> <dttm>              <chr>  
1     -123.     45.5 7670   Quercus     Fagac…   3.3 2018-07-26 00:00:00 QURU   
2     -123.     45.5 7671   Pseudotsuga Pinac…  43.1 2018-07-26 00:00:00 PSME   
3     -123.     45.5 7672   Pseudotsuga Pinac…  48.2 2018-07-26 00:00:00 PSME   
4     -123.     45.5 7902   Quercus     Fagac…   2.4 2018-07-26 00:00:00 QURU   
5     -123.     45.5 7903   Pseudotsuga Pinac…  11.7 2018-07-26 00:00:00 PSME   
6     -123.     45.5 7905   Pseudotsuga Pinac…  33.5 2018-07-26 00:00:00 PSME   
# ℹ 26 more variables: Common_Name <chr>, Condition <chr>, Tree_Height <dbl>,
#   Crown_Width_NS <dbl>, Crown_Width_EW <dbl>, Crown_Base_Height <dbl>,
#   Collected_By <chr>, Park <chr>, Scientific_Name <chr>,
#   Functional_Type <chr>, Mature_Size <fct>, Native <chr>, Edible <chr>,
#   Nuisance <chr>, Structural_Value <dbl>, Carbon_Storage_lb <dbl>,
#   Carbon_Storage_value <dbl>, Carbon_Sequestration_lb <dbl>,
#   Carbon_Sequestration_value <dbl>, Stormwater_ft <dbl>, …

What does a row represent here?

Scatterplots

Explore relationships between numerical variables.
- We will be especially interested in linear relationships.

ggplot(data = near_Reed,
       mapping = aes(x = DBH,
                     y = Carbon_Storage_lb)) +
  geom_point(size = 2)

Scatterplots

ggplot(data = near_Reed,
       mapping = aes(x = DBH,
                     y = Carbon_Storage_lb)) +
  geom_point(size = 2, alpha = 0.25)

Fix over-plotting
What’s going on in this graph?

Scatterplots

ggplot(data = near_Reed,
       mapping = aes(x = DBH,
                     y = Carbon_Storage_lb,
                     color = Genus)) +
  geom_point(size = 2, alpha = 0.25)

Linegraphs

ggplot(data = near_Reed,
       mapping = aes(x = DBH,
                     y = Carbon_Storage_lb)) +
  geom_line(size = 2)

Linegraphs

ggplot(data = near_Reed,
       mapping = aes(x = DBH,
                     y = Carbon_Storage_lb,
                     color = Genus)) +
  geom_line(size = 2)

Linegraphs vs scatterplots

Which do you prefer?
Does it depend on context?
Which might be better if we put time on the x-axis?

Recap: `ggplot2`

library(tidyverse)
ggplot(data = ---, mapping = aes(---)) +
  geom_---(---)

Next time:

More ggplot2!

Goals for Today

Load Necessary Packages

Data Setting: Portland Bikeshare Data

Import the Data

Inspect the Data

Inspect the Data

Grammar of Graphics

ggplot2 example code

Histograms

Data Shapes

Histograms

Histograms

Boxplots

Boxplots

Boxplots

Boxplots

Boxplots

Violin Plots

Boxplot Versus Violin Plots

New Data Context: pdxTrees

New Data Context: pdxTrees

Inspect the data

Inspect the data

Scatterplots

Scatterplots

Scatterplots

Linegraphs

Linegraphs

Linegraphs vs scatterplots

Recap: ggplot2

Next time:

`ggplot2` example code

New Data Context: `pdxTrees`

New Data Context: `pdxTrees`

Recap: `ggplot2`