20250227 Multivariate Analysis

Homework 1, make the boxplot for the mileage of American, Japanese and European cars (from left to right).

Josh Included in R

Published 2025-02-27 Updated 2025-03-02 765 words 4 minutes views

Contents

Introduction

This assignment requires us to draw boxplots of car mileage for the United States, Japan, and Europe as shown in the textbook.

The dataset carc.txt and the R script MVAboxcar.R for generating the image can be downloaded from https://github.com/QuantLet/MVA/tree/master/QID-1485-MVAboxcar.

Dataset

In R, we can use the following command to read the dataset.

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read.table("carc.txt")

Below is part of the dataset carc.txt.

V1	V2	V3	V4	V5	V6	V7	V8	V9	V10	V11	V12	V13
1	4099	22	3	2	2.5	27.5	11	2930	186	40	121	3.58
2	4749	17	3	1	3.0	25.5	11	3350	173	40	258	2.53
3	3799	22	NaN	NaN	3.0	18.5	12	2640	168	35	121	3.08
4	9690	17	5	2	3.0	27.0	15	2830	189	37	131	3.20
5	6295	23	3	3	2.5	28.0	11	2070	174	36	97	3.70
…	…	…	…	…	…	…	…	…	…	…	…	…

From Table 22.3 in the textbook, we know that the dataset contains 13 parameters and 74 vehicle types. The description of each parameter is as follows:

Variable	Symbol	Description
$X_1$	P	Price
$X_2$	M	Mileage (in miles per gallon)
$X_3$	R78	Repair record 1978 (rated on a 5-point scale; 5 best, 1 worst)
$X_4$	R77	Repair record 1977 (scale as before)
$X_5$	H	Headroom (in inches)
$X_6$	R	Rear seat clearance (distance from front seat back to rear seat, in inches)
$X_7$	Tr	Trunk space (in cubic feet)
$X_8$	W	Weight (in pound)
$X_9$	L	Length (in inches)
$X_{10}$	T	Turning diameter (clearance required to make a U-turn, in feet)
$X_{11}$	D	Displacement (in cubic inches)
$X_{12}$	G	Gear ratio for high gear
$X_{13}$	C	Company headquarter (1 for USA, 2 for Japan, 3 for Europe)

Boxplot

Below is an example of a boxplot drawn from the QuantLet/MVA repository on GitHub.

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# clear variables and close windows
rm(list = ls(all = TRUE))
graphics.off()

# load data
x = read.table("carc.txt")

# parameter settings
k      = 0
l      = 0
m      = 0
us     = NULL
japan  = NULL
europe = NULL
M      = x[, 2]
C      = x[, 13]

for (i in 1:dim(x)[1]) {
    if (x[i, 13] == 1) {
        k = k + 1
        us[k] = x[i, 2]
    } else if (x[i, 13] == 2) {
        l = l + 1
        japan[l] = x[i, 2]
    } else if (x[i, 13] == 3) {
        m = m + 1
        europe[m] = x[i, 2]
    }
}

m1 = mean(us)
m2 = mean(japan)
m3 = mean(europe)

# plot
boxplot(us, japan, europe, axes = FALSE, frame = TRUE)
axis(side = 1, at = seq(1, 3), label = c("US", "JAPAN", "EU"))
axis(side = 2, at = seq(0, 50, 5), label = seq(0, 50, 5))
title("Car Data")
lines(c(0.6, 1.4), c(m1, m1), lty = "dotted", lwd = 1.2)
lines(c(1.6, 2.4), c(m2, m2), lty = "dotted", lwd = 1.2)
lines(c(2.6, 3.4), c(m3, m3), lty = "dotted", lwd = 1.2)

(five = quantile(x[, 2], c(0.025, 0.25, 0.5, 0.75, 0.975)))

/1140227-multivariate-analysis/image/1740626790418.png — Boxplot for the mileage of different production locations.

Since we only need to draw boxplots of car mileage for different regions, we use only two parameters M = x[, 2] and C = x[, 13]. Here, M represents the miles per gallon, and C represents the company headquarters of the car manufacturer.

The original code was uploaded to GitHub by the author in 2016. We can now achieve the same result with a more concise approach. The updated code is as follows.

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# Clear variables and close graphics window
rm(list = ls(all = TRUE))
graphics.off()

# Load data
x <- read.table("carc.txt")

# Group data and compute mean values
groups <- split(x[, 2], x[, 13])
means <- sapply(groups, mean)

# Draw boxplot
boxplot(groups, names = c("US", "JAPAN", "EU"), frame = TRUE)
title("Car Data")
axis(2, at = seq(0, 50, 5))

# Add dotted lines for mean values
for (i in 1:length(means)) {
  lines(c(i - 0.4, i + 0.4), rep(means[i], 2), lty = "dotted", lwd = 1.2)
}

quantile(x[, 2], c(0.025, 0.25, 0.5, 0.75, 0.975)) # Quartiles

Environment

Operating System: Windows 11 24H2
Programming Language: R 4.4.2

References

Wolfgang karl härdle, léopold simar. (2015). Applied Multivariate Statistical Analysis (4th ed.). Springer. https://link.springer.com/book/10.1007/978-3-662-45171-7
Quantnet. (2025, January 27). MVA. Github. https://github.com/QuantLet/MVA