Unit 3 — Data Visualization in R

Topics Covered

1. Plotting in R — Overview

R offers three major plotting systems:

• Base R graphics (this unit) — easy, immediate, controllable via parameters.
• lattice — formula-based multi-panel plots.
• ggplot2 — grammar of graphics; most popular modern system.

The generic plot() function dispatches on the class of the first argument:

• Numeric vector → scatter or line.
• Factor → bar chart of counts.
• Data frame → matrix scatter plot.
• Model object (lm) → residual diagnostics.

Common Graphical Parameters

2. Histograms

Use hist() to display the distribution of a continuous variable.

data(mtcars)
hist(mtcars$mpg,
     breaks = 10,
     col    = "skyblue",
     border = "white",
     main   = "Distribution of Fuel Economy",
     xlab   = "Miles per Gallon",
     ylab   = "Frequency")

# With density curve overlay
hist(mtcars$mpg,
     freq = FALSE,            # density instead of counts
     col  = "lightyellow",
     main = "MPG Density")
lines(density(mtcars$mpg), col = "red", lwd = 2)
rug(mtcars$mpg)               # tick marks under axis

Controlling Bins

• breaks = 15 — approximately 15 bins.
• breaks = c(10,15,20,25,30,35) — explicit boundaries.
• breaks = "Sturges" (default), "Scott", "FD" — algorithms.

# Compare two histograms side by side
par(mfrow = c(1, 2))
hist(iris$Sepal.Length, col = "lightblue", main = "Sepal Length")
hist(iris$Petal.Length, col = "lightgreen", main = "Petal Length")
par(mfrow = c(1, 1))           # reset

x <- rnorm(500, mean = 60, sd = 10)
hist(x, freq = FALSE, breaks = 25, col = "lavender",
     main = "Sample vs Theoretical Normal", xlab = "Value")
lines(density(x), lwd = 2)              # sample density (black)
curve(dnorm(x, mean = 60, sd = 10),
      add = TRUE, col = "red", lwd = 2) # theoretical curve (red)
legend("topright", c("Sample density","N(60, 10)"),
       col = c("black","red"), lty = 1, lwd = 2, bty = "n")

3. Boxplots

Display the median, quartiles and outliers. The box spans Q1–Q3; each whisker extends to the most extreme observation still within 1.5 × IQR of the box; anything beyond that is drawn as an individual outlier point.

boxplot(mtcars$mpg,
        col  = "lightgreen",
        main = "Boxplot of MPG",
        ylab = "MPG")

# By group (formula syntax)
boxplot(mpg ~ cyl, data = mtcars,
        col  = c("salmon","skyblue","palegreen"),
        main = "MPG by Number of Cylinders",
        xlab = "Cylinders", ylab = "MPG",
        notch = TRUE)              # adds notches around medians

Interpretation: circles beyond the whiskers are outliers — points below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR (the fences are measured from the quartiles, not the median). Non-overlapping notches suggest the medians differ significantly.

# All four iris numeric variables on one plot
boxplot(iris[, 1:4],
        col  = c("pink","skyblue","lightgreen","plum"),
        main = "Iris Measurements",
        ylab = "cm")

boxplot(Sepal.Length ~ Species, data = iris,
        col = "lightyellow",
        main = "Sepal Length by Species")

4. Scatter Plots

plot(mtcars$wt, mtcars$mpg,
     pch  = 19, col = "navy",
     main = "Fuel Economy vs Weight",
     xlab = "Weight (1000 lbs)",
     ylab = "MPG")

# Add a regression line
fit <- lm(mpg ~ wt, data = mtcars)
abline(fit, col = "red", lwd = 2)

# Add LOESS smooth
lines(lowess(mtcars$wt, mtcars$mpg), col = "blue", lty = 2, lwd = 2)

legend("topright", c("Linear fit","LOESS"),
       col = c("red","blue"), lty = c(1,2), lwd = 2, bty = "n")

Multi-variable Scatter Matrix

pairs(iris[, 1:4], col = iris$Species, pch = 19,
      main = "Iris Scatter Plot Matrix")

Plotting Symbols (pch) Reference

plot(1:25, rep(1, 25), pch = 1:25, cex = 2,
     main = "Plotting characters 1–25", ylab = "", yaxt = "n")
text(1:25, rep(1.2, 25), labels = 1:25)

plot(Petal.Length ~ Petal.Width, data = iris,
     col  = iris$Species, pch = 19,
     main = "Iris: Petal length vs width")
legend("topleft", levels(iris$Species),
       col = 1:3, pch = 19, bty = "n")

data(airquality)
plot(airquality$Day[1:31],
     airquality$Temp[1:31],
     type = "o", col = "darkred",
     main = "May Temperatures (NY)",
     xlab = "Day", ylab = "Temp (°F)")
grid()

5. Bar Charts

counts <- table(mtcars$cyl)
barplot(counts,
        col  = c("salmon","skyblue","palegreen"),
        main = "Number of Cars by Cylinders",
        xlab = "Cylinders", ylab = "Count")

# Horizontal
barplot(counts, horiz = TRUE)

# Stacked / grouped (two-way table)
tbl <- table(mtcars$gear, mtcars$cyl)
barplot(tbl, beside = TRUE,        # set FALSE for stacked
        col = c("lightblue","lightgreen","lightyellow"),
        main = "Cylinders by Gears",
        legend.text = TRUE)

Pie Chart

pie(counts,
    col    = c("salmon","skyblue","palegreen"),
    labels = paste(names(counts), counts),
    main   = "Cars by Cylinders")

Note: Bar charts are usually preferable to pie charts for comparison.

fruits  <- c("Apple","Banana","Cherry","Date")
prices  <- c(80, 40, 200, 150)
barplot(prices, names.arg = fruits,
        col = "lightcoral",
        main = "Fruit Prices (₹/kg)", ylab = "₹/kg")

# Iris counts by species (one per row, but illustrative)
sp <- table(iris$Species)
barplot(sp, col = c("plum","skyblue","palegreen"),
        main = "Iris Sample by Species")

6. Residual Plots for Assumption Checking

After fitting a model with lm() or glm(), R provides four diagnostic plots through plot(model).

fit <- lm(mpg ~ wt + hp, data = mtcars)
par(mfrow = c(2, 2))
plot(fit)
par(mfrow = c(1, 1))

The four panels are:

1. Residuals vs Fitted — checks linearity & homoscedasticity. A flat red line ⇒ ok.
2. Normal Q-Q — residuals should lie close to the straight reference line if normally distributed.
3. Scale–Location — checks equal variance; should show no clear pattern.
4. Residuals vs Leverage — points outside Cook's distance contours are influential.

Other Useful Diagnostics

# Histogram of residuals
hist(resid(fit), breaks = 12, col = "lightgray",
     main = "Distribution of Residuals", xlab = "Residual")

# Q-Q plot for any data
qqnorm(resid(fit)); qqline(resid(fit), col = "red", lwd = 2)

# Shapiro-Wilk test for normality
shapiro.test(resid(fit))

fit <- lm(Sepal.Length ~ Petal.Length, data = iris)
par(mfrow = c(2, 2)); plot(fit); par(mfrow = c(1, 1))
shapiro.test(resid(fit))   # p > 0.05 ⇒ residuals plausibly normal

x <- 1:50
y <- x + x^2/40 + rnorm(50, 0, 3)    # quadratic relation + noise
fit <- lm(y ~ x)
par(mfrow = c(1, 2))
plot(x, y, main = "Data + Linear Fit"); abline(fit, col = "red")
plot(fit, which = 1)                  # curved residual pattern signals non-linearity
par(mfrow = c(1, 1))

7. Saving Plots

# PDF
pdf("myplot.pdf", width = 8, height = 6)
hist(mtcars$mpg, col = "skyblue", main = "MPG")
dev.off()

# PNG
png("myplot.png", width = 800, height = 600, res = 100)
boxplot(mpg ~ cyl, data = mtcars, col = "lightyellow")
dev.off()

# JPEG, SVG, TIFF — similar
svg("myplot.svg"); plot(1:10); dev.off()

8. Best Practices for Statistical Visualization

• Always add title, axis labels with units, and a legend when colours/shapes encode categories.
• Use colour-blind-friendly palettes (e.g., viridis package).
• Avoid 3-D effects and unnecessary decoration.
• For comparison, use side-by-side / grouped boxplots rather than overlaid histograms.
• Always inspect residual diagnostics after fitting regression / ANOVA.
• Save plots in PDF for publications (vector, infinite resolution) and PNG for web.

Key Take-aways

• hist() for distributions; boxplot() for spread & outliers; plot() for scatter; barplot() for categorical.
• Generic parameters: main, xlab, ylab, col, pch, lty, lwd.
• Multi-panel layout via par(mfrow = c(r, c)).
• plot(lm_object) auto-generates four diagnostic plots for residual assumption checking.
• Save plots with pdf(), png(), etc., followed by dev.off().