Chapter 5 Creating Some Basic Plots

Reference: R graphics cookbook (https://r-graphics.org/)

• The base R contains many basic methods for producing graphics. We will learn some of them in this chapter. These plotting functions are good for very quick exploration of data.

• For more elegant plots, we will use the package ggplot2 (next chapter).

• We will use some simple datasets in base R and flights from nycflights13 to illustrate how to create some basic plots in this chapter.

library(tidyverse)
library(nycflights13)

5.1 Scatter Plot

A scatter plot is used to visualize the relationship between two numerical variables. Each point represents one observation, with its horizontal position determined by the \(x\)-variable and its vertical position determined by the \(y\)-variable.

Scatter plots are especially useful for:

• Detecting associations (positive, negative, or none)

• Identifying nonlinear patterns

• Spotting outliers

• Checking whether a linear model might be reasonable

The mtcars dataset comes with base R and contains information on fuel consumption and car characteristics.

head(mtcars) # this is a data frame
##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

str(mtcars) # display the structure of the data frame
## 'data.frame':    32 obs. of  11 variables:
##  $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
##  $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
##  $ disp: num  160 160 108 258 360 ...
##  $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
##  $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
##  $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
##  $ qsec: num  16.5 17 18.6 19.4 17 ...
##  $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
##  $ am  : num  1 1 1 0 0 0 0 0 0 0 ...
##  $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
##  $ carb: num  4 4 1 1 2 1 4 2 2 4 ...

Key variables: mpg: miles/gallon wt: weight (1000lbs)

Scatter plot with base graphics

# x-axis: mtcars$wt
# y-axis: mtcars$mpg
# "x =", "y =" are optional
plot(
  x = mtcars$wt,
  y = mtcars$mpg,
  xlab = "Weight (1000 lbs)",
  ylab = "Miles per Gallon (mpg)",
  main = "Fuel Efficiency vs Vehicle Weight"
) 

Interpretation:

• Heavier cars tend to have lower fuel efficiency

• The relationship appears roughly linear and negative

• A few points may stand out as unusually heavy or fuel-efficient

You can produce the same plot with plot(mtcars$wt, mtcars$mpg)

Scatter plot when you only have x and y (no dataset)

Scatter plots do not require a data frame. As long as you have two numeric vectors of the same length, you can plot them directly.

set.seed(1)
x <- rnorm(100, 0, 1)
y <- 2 * x + rnorm(100, 0, 1)

plot(x, y)

Interpretation:

• There is a clear positive linear relationship

• The randomness around the line reflects noise

• This is a typical pattern generated by a linear model

Nonlinear relationship

Scatter plots are also useful for revealing nonlinear patterns that summary statistics (e.g. covariance, correlation) may miss.

set.seed(1)
x <- runif(200, -3, 3)
y <- x^2 + rnorm(200, 0, 0.5)

plot(x, y)

Interpretation:

• The relationship is clearly nonlinear

• A linear model would be inappropriate here

• The scatter plot immediately reveals the underlying structure

Scatter plot: distance vs arrival delay on a single day

Because the full flights dataset contains many observations, plotting all points at once can lead to severe overplotting. A simple solution is to focus on one specific day.

one_day <- flights %>% 
  filter(month == 1 & day == 1)

plot(
  x = one_day$distance,
  y = one_day$arr_delay,
  xlab = "Flight Distance (miles)",
  ylab = "Arrival Delay (minutes)",
  main = "Arrival Delay vs Distance (Jan 1)"
)
abline(h = 0) # add a reference line for no delay

Interpretation:

• The number of points is much smaller, making the plot easier to read

• Most flights arrive close to on time, regardless of distance

• Large delays still appear as outliers

• There is no strong linear relationship between arrival delay and flight distance

5.2 Line Graph

A line graph is used to show how a numerical variable changes as another variable changes, especially when the \(x\)-axis has a natural order (for example, time, temperature, or distance). Compared to a scatter plot, a line graph emphasizes the trend by connecting points in order.

In base R, the main difference is the use of type = "l" (l = line).

Example: the pressure dataset (base R)

The dataset pressure contains the relationship between:

• temperature: temperature in degrees Celsius

• pressure: vapour pressure of mercury (mm of mercury)

head(pressure)
##   temperature pressure
## 1           0   0.0002
## 2          20   0.0012
## 3          40   0.0060
## 4          60   0.0300
## 5          80   0.0900
## 6         100   0.2700

Line graph with base graphics

plot(
  pressure$temperature,
  pressure$pressure,
  type = "l",
  xlab = "Temperature (°C)",
  ylab = "Vapour Pressure (mm of mercury)",
  main = "Vapour Pressure vs Temperature"
)

Line graph with base graphics with points

A common style is to show both the line (trend) and the points (observations).

plot(
  pressure$temperature,
  pressure$pressure,
  type = "l",
  xlab = "Temperature (°C)",
  ylab = "Vapour Pressure (mm of mercury)",
  main = "Vapour Pressure vs Temperature"
)

points(pressure$temperature, pressure$pressure, pch = 16)

pch = 16 makes filled points, which are easier to see on a line.

Adding another line (illustration)

If you want to compare two curves on the same plot, add the first plot, then use lines() for additional curves.

plot(
  pressure$temperature,
  pressure$pressure,
  type = "l",
  xlab = "Temperature (°C)",
  ylab = "Vapour Pressure (mm of mercury)",
  main = "Vapour Pressure vs Temperature"
)

lines(pressure$temperature, pressure$pressure / 2, col = "red")
points(pressure$temperature, pressure$pressure / 2, col = "red", pch = 16)
legend(
  "topleft",
  legend = c("Original", "Half (illustration)"),
  col = c("black", "red"),
  lty = 1,
  bty = "n"
)

Note: the second curve above is only for demonstrating how to add lines and a legend.

Colors in base R

• In base R, the col argument can be specified in several ways:

• By name: "red", "cornflowerblue"

• By number: 1 (black), 2 (red), 3 (green), 4 (blue), …

• By hex code: "#8B2813"

• By rgb(): rgb(0.1, 0.2, 0.5, 1)

plot(
  pressure$temperature,
  pressure$pressure,
  type = "l",
  xlab = "Temperature (°C)",
  ylab = "Vapour Pressure (mm of mercury)",
  main = "Vapour Pressure vs Temperature",
  col = rgb(0.1, 0.2, 0.5, 1)
)

lines(pressure$temperature, pressure$pressure / 2, col = 2)
lines(pressure$temperature, pressure$pressure * 2, col = "#8B2813")
lines(pressure$temperature, pressure$pressure * 3, col = "cornflowerblue")

Common color names

Color name	Example
black	col = "black"
white	col = "white"
gray	col = "gray"
red	col = "red"
blue	col = "blue"
green	col = "green"
yellow	col = "yellow"
orange	col = "orange"
purple	col = "purple"
brown	col = "brown"
pink	col = "pink"
cyan	col = "cyan"

Example with flights: average daily departure delay over time

A line graph is a natural choice when the \(x\)-axis is time.

Below we compute the average departure delay for each date, then plot it across the year.

# prepare the data
plot_data <- flights %>% 
  group_by(year, month, day) %>% 
  summarize(avg_day_dep_delay = mean(dep_delay, na.rm = TRUE)) %>% 
  ungroup() %>% 
  mutate(date = as.Date(sprintf("%d-%02d-%02d", year, month, day)))

plot(
  plot_data$date,
  plot_data$avg_day_dep_delay,
  type = "l",
  xlab = "Date",
  ylab = "Average departure delay (minutes)",
  main = "Average Daily Departure Delay in 2013"
)

abline(h = 0, lty = 2)  # reference line at 0 minutes

sprintf and Date

year  <- c(2013, 2013)
month <- c(1, 12)
day   <- c(5, 3)

as.Date(sprintf("%d-%02d-%02d", year, month, day))
## [1] "2013-01-05" "2013-12-03"

A character string may look like a date, but R treats it as plain text.

A Date object is a special data type that represents calendar dates correctly. as.Date(): convert strings to Date objects

Using Date objects allows R to:

• order dates chronologically

• compute differences in days

• plot time on a continuous axis

Character dates are sorted and plotted as labels, not as time.

If a variable represents dates, always convert it to a Date object before analysis or plotting.

5.3 Bar Chart

A bar chart is used when the \(x\)-axis is discrete (categories). There are two common types:

1. Bar chart of values. x-axis: categorical variable, y-axis: numeric data (for example, mean, median)
2. Bar chart of count. x-axis: categorical variable, y-axis: count (how many observations fall in each category)

Remark (bar chart vs histogram):

• Bar chart: \(x\) is discrete categories

• Histogram: \(x\) is a continuous variable, and we count observations within intervals (bins)

Bar chart of values with base graphics

# names.arg = a vector of names to be plotted below each bar or group of bars.
plot_data <- flights %>% 
  group_by(year, month) %>% 
  summarize(avg_mon_dep_delay = mean(dep_delay, na.rm = TRUE)) %>% 
  ungroup()
## `summarise()` has grouped output by 'year'. You can override using the
## `.groups` argument.

barplot(
  plot_data$avg_mon_dep_delay,
  names.arg = 1:12,
  main = "Average Monthly Departure Delay",
  xlab = "Month",
  ylab = "Average departure delay (minutes)"
)

Each bar is a mean computed from many flights in that month.

Bar chart of counts with base graphics

In mtcars, cyl is the number of cylinders (possible values are 4, 6, and 8). We first compute the counts:

table(mtcars$cyl)
## 
##  4  6  8 
## 11  7 14

To plot the bar chart, we use

barplot(
  table(mtcars$cyl),
  main = "Distribution of Number of Cylinders",
  xlab = "Number of cylinders",
  ylab = "Count"
)

Another count example using flights (number of flights by month):

count <- table(flights$month)

barplot(
  count,
  names.arg = 1:12,
  main = "Number of Flights by Month",
  xlab = "Month",
  ylab = "Count"
)

Optional improvement: add the counts on top of the bars.

bp <- barplot(
  count,
  names.arg = 1:12,
  main = "Number of Flights by Month",
  xlab = "Month",
  ylab = "Count",
  ylim = c(0, max(count) * 1.1)  # add ~10% headroom
)

text(bp, count, labels = count, pos = 3, cex = 0.7)

5.4 Histogram

A histogram visualizes the distribution of a continuous variable by dividing its range into bins and counting how many observations fall into each bin.

Example: mpg in mtcars is a continuous variable (miles per gallon).

Histogram with base graphics

hist(
  mtcars$mpg,
  xlab = "Miles per Gallon (mpg)",
  main = "Histogram of Fuel Efficiency"
)

Histogram with base graphics

You can control the binning using breaks.

# Specify approximate number of bins with "breaks"
hist(
  mtcars$mpg,
  breaks = 10,
  xlab = "Miles per Gallon (mpg)",
  main = "Histogram of Fuel Efficiency"
)

Remark: different choices of breaks change the appearance.

• Too few breaks oversmooth the data and may hide important structure.

• Too many breaks produce noisy, spiky histograms that are hard to interpret.

Histogram for departure delays in flights

Departure delays contain missing values. (They are removed automatically by hist().)

sum(is.na(flights$dep_delay)) # 8255 missing values!
## [1] 8255

hist(
  flights$dep_delay,
  breaks = 100,
  main = "Distribution of Departure Delays",
  xlab = "Departure delay (minutes)",
  ylab = "Frequency"
)

If you want the histogram to show relative frequency (so the total area is 1), use freq = FALSE:

hist(
  flights$dep_delay,
  breaks = 100,
  main = "Distribution of Departure Delays",
  xlab = "Departure delay (minutes)",
  ylab = "Frequency",
  freq = FALSE
)

Because delays can have extreme outliers, it is often helpful to zoom in.

hist(
  flights$dep_delay,
  breaks = 100,
  xlim = c(-20, 200),
  main = "Departure Delays (Zoomed In)",
  xlab = "Departure delay (minutes)"
)

One data-driven method for choosing the histogram bin width: breaks = "FD" (the Freedman–Diaconis rule is designed to approximately minimize the integral of the squared difference between the histogram (i.e., relative frequency density) and the density of the theoretical probability distribution.)

hist(
  flights$dep_delay,
  breaks = "FD",
  xlim = c(-20, 200),
  main = "Departure Delays (Zoomed In)",
  xlab = "Departure delay (minutes)"
)

5.5 Box Plot

A boxplot provides a compact summary of a numerical variable by displaying its distribution through quantiles. It is especially useful for comparing distributions across groups and for detecting outliers.

What a boxplot shows

• Median: the line inside the box (50% quantile)

• First quartile (Q1) and third quartile (Q3): the lower and upper edges of the box

• Interquartile range (IQR): \(Q_3 - Q_1\), representing the middle 50% of the data

• Whiskers: extend to the most extreme observations within \(1.5 \times \mathrm{IQR}\) from the quartiles

• Outliers: points beyond the whiskers

Boxplots are robust summaries because they rely on quantiles rather than means and standard deviations.

Example: flight arrival delays

We use the flights dataset, where arr_delay records arrival delay in minutes.

A single boxplot

boxplot(
  flights$arr_delay,
  xlab = "Arrival Delay (minutes)",
  main = "Boxplot of Flight Arrival Delays"
)

Rotate a boxplot by making it horizontal:

boxplot(
  flights$arr_delay,
  horizontal = TRUE,
  ylab = "Arrival Delay (minutes)",
  main = "Boxplot of Flight Arrival Delays"
)

Interpretation:

• The median delay is near zero.

• The distribution is highly right-skewed.

• Large positive delays appear as outliers.

Boxplots by group

Boxplots are particularly useful for group comparisons.

Arrival delay by carrier

boxplot(
  arr_delay ~ carrier,
  data = flights,
  xlab = "Carrier",
  ylab = "Arrival Delay (minutes)",
  main = "Arrival Delay by Airline Carrier",
  las = 2   # rotate labels
)

Interpretation:

• Differences in medians show typical performance across carriers.

• Box height reflects variability.

• Outliers highlight extreme delays for some airlines.

Arrival delay by month

boxplot(
  arr_delay ~ month,
  data = flights,
  xlab = "Month",
  ylab = "Arrival Delay (minutes)",
  main = "Arrival Delay by Month"
)

Interpretation:

• Seasonal patterns become visible.

• Some months show larger variability and more extreme delays.

5.5.1 Transformation of data

For variables like flight delays:

• The distribution is highly right-skewed

• A few very large delays dominate the scale

• Boxplots on the original scale compress most of the data near zero

Taking a log transform:

• Spreads out the bulk of the data

• Reduces the influence of extreme delays

• Makes differences in medians and IQRs easier to see across groups

Practical issue: zeros and negative values

Arrival delays can be:

• Zero (on time)

• Negative (early arrivals)

So you cannot directly take log(arr_delay).

Possible solutions:

1. shift then log: add the minimum arr_delay and then take log
2. focus on late flights only

late <- flights %>% 
  filter(arr_delay > 0)

Log arrival delay by carrier (Late Flights Only)

boxplot(
  log(arr_delay) ~ month,
  data = late,
  xlab = "Month",
  ylab = "log(Arrival Delay)",
  main = "Log Arrival Delay (Late Flights Only)"
)

Log arrival delay by month (Late Flights Only)

boxplot(
  log(arr_delay) ~ carrier,
  data = late,
  xlab = "Carrier",
  ylab = "log(Arrival Delay)",
  main = "Log Arrival Delay (Late Flights Only)",
  las = 2   # rotate labels
)

5.5.2 When to use boxplots

• To summarize a distribution quickly

• To compare distributions across multiple groups

• To identify skewness and outliers

• When robustness is preferred over mean-based summaries

Boxplots complement histograms: histograms show overall shape, while boxplots emphasize location, spread, and outliers.

5.6 Plotting a function curve

A function plot shows how \(y=f(x)\) changes as \(x\) varies. In base R, curve() is the most convenient tool for plotting a mathematical function because it automatically chooses a grid of \(x\) values and draws the resulting curve.

curve(x^3 - 5 * x, from = -4, to = 4,
      xlab = "x", ylab = "f(x)",
      main = expression(f(x) == x^3 - 5*x))

curve() is best when you can write the function as an expression in x

Alternatively:

x <- seq(-4, 4, length.out = 1000)
y <- x^3 - 5 * x

plot(x, y, type = "l",
     xlab = "x", ylab = "f(x)",
     main = expression(f(x) == x^3 - 5*x))

This approach is more general

Plotting a built-in function

curve(dnorm(x), from = -4, to = 4)

Plotting a self-defined function

my_function <- function(x) {
  1 / (1 + exp(-x + 10))
}

curve(my_function, from = 0, to = 20,
      xlab = "x", ylab = "f(x)",
      main = "A Logistic-Shaped Curve")

Plotting a function with additional arguments

curve(dnorm(x, mean = 2, sd = 3), from = -4, to = 4)

5.7 More on plots with base R

5.7.1 Multi-frame plot

You can place multiple plots in one figure using par(mfrow = c(r, c)), which creates an \(r \times c\) layout.

set.seed(1)
x <- rnorm(100, 50, 5)
y <- x + rnorm(100, 2, 2)

# create a 2x2 multi-frame plot
par(mfrow=c(2, 2))
hist(x)
hist(y,breaks = 10)
plot(x, y)
boxplot(x, y)

5.7.2 Type of Plot

Option	Type
type = "p"	Points (default)
type = "l"	Lines connecting the data points
type = "b"	Points and non-overlapping lines
type = "h"	Height lines
type = "o"	Points and overlapping lines

par(mfrow = c(3, 2))
x <- -5:5
y <- x^2

plot(x, y, main = 'Default: type = "p"')
plot(x, y, type = "p", main = 'type = "p"')
plot(x, y, type = "l", main = 'type = "l"')
plot(x, y, type = "b", main = 'type = "b"')
plot(x, y, type = "h", main = 'type = "h"')
plot(x, y, type = "o", main = 'type = "o"')

par(mfrow = c(1, 1))

5.7.3 Common plot parameters

Parameter	Meaning
type	See Type of Plot
main	Title
sub	Subtitle
xlab	x-axis label
ylab	y-axis label
xlim	x-axis range
ylim	y-axis range
pch	Symbol of data points
col	Color of data points
lty	Type of the line
cex	Size of points/text
lwd	Line width

To illustrate some of the components:

set.seed(1)
x <- rnorm(100, 50, 15)
y <- x + rnorm(100, 2, 13)

plot(
  x, y,
  pch = 16,
  col = "red",
  main = "A Scatter Plot with Custom Settings",
  sub = "Example: change labels, limits, and point style",
  xlab = "x",
  ylab = "y",
  xlim = c(0, 100),
  ylim = c(0, 100)
)

5.7.4 Elements on plot

These functions add layers after the main plot is created.

Function	What it adds
points(x, y)	add points
lines(x, y)	add lines
abline(a, b)	add line \(y = a + b x\)
abline(h = a)	add horizontal line \(y = a\)
abline(v = b)	add vertical line \(x = b\)
legend()	add a legend

set.seed(1)
x <- rnorm(100, 50, 15)
y <- x + rnorm(100, 2, 13)

plot(x, y, pch = 16, main = "Adding Lines and Reference Lines", xlab = "x", ylab = "y")

# connect three chosen points with a line
lines(x = c(20, 30, 40), y = c(20, 80, 40), col = "red", lwd = 2)

# add reference lines
abline(v = 60, col = "blue", lty = 2)
abline(h = 50, col = "blue", lty = 2)

# Optional: add a legend.
legend(
  "topleft",
  legend = c("Data", "Custom line", "Reference lines"),
  pch = c(16, NA, NA),
  lty = c(NA, 1, 2),
  col = c("black", "red", "blue"),
  bty = "n"
)