Information Technology Reference
In-Depth Information
abbreviations used for the variables in Table 1.1. This is done by issuing the following
instructions from the R prompt:
> aircraft.mat <- aircraft.data[, 2:5]
> aircraft.mat
SPR RGF PLF SLF
a 1.468 3.30 0.166 0.10
b 1.605 3.64 0.154 0.10
.......................
v 7.105 5.40 0.089 3.20
w 8.548 4.20 0.222 2.90
Next,
we
construct
a
scatterplot
of
the
two
variables
SPR
and
RGF
with
the
instructions:
> plot(x = aircraft.mat[,1], y = aircraft.mat[,2], xlab = "",
ylab = "", xlim = c(0,10), ylim = c(2,6), pch = 15,
col = "green", yaxp = c(2,6,4), bty = "n")
> text(x = aircraft.mat[,1], y = aircraft.mat[,2],
labels = dimnames(aircraft.mat)[[1]], pos = 1)
> mtext("RGF", side = 2, at = 6.4, line = -0.35)
> mtext("SPR", side = 1, at = 10.4, line = -0.50)
The scatterplot in Figure 2.1 is an example of what is probably the simplest form
of an asymmetric biplot. It shows a plot of the columns
SPR
and
RGF
, giving perfor-
mance figures for power and range of the 21 types of aircraft introduced in Table 1.1.
It is a scatterplot of two variables referred to orthogonal axes. The familiar elements of
Figure 2.1 are:
•
points representing the aircraft;
•
a directed line for each of the variables, known as a coordinate axis, with its label;
•
scales marked on the axes giving the values of the variables.
Note also the convention followed of labelling the axes at the end where the calibra-
tions are at their highest values. It is an asymmetric biplot because it gives information
of two types, (i) concerning the 21 aircraft and (ii) concerning the two variables, which
cannot be interchanged. When a point representing an aircraft is projected orthogonally
onto an axis, one may read off the value of the corresponding variable and this will
agree precisely with the value given in Table 1.1. Indeed, this is not surprising, because
the values of the variables were those used in the first place to construct the coordi-
nate positions of the points. Notice the difference between the top and bottom panels of
Figure 2.1. Which of
k
and
n
is nearest to
j
? From the top panel, it appears to be
n
, but
a simple calculation shows the true distances to be
0
.
021
2
dist
(
j
,
k
)
=
+
1
.
1
2
=
1
.
10,
1
.
288
2
+
0
.
39
2
dist
(
j
,
n
)
=
=
1
.
34,
