Information Technology Reference
In-Depth Information
6
6
5
4
j
5
v
3
q
u
t
k
c
p
r
w
m
s
n
2
g
h
i
0.1
4
d
1
e
f
SPR
0
2
4
6
8
10
0
a
b
0.2
3
−
1
−
2
0.3
2
−
3
0.4
−
4
PLF
Figure 2.15
The biplot of Figure 2.5 with orthogonal parallel translation rotated and
reflected such that the
SPR
-axis is horizontal, with increasing calibrations from left to
right similar to the first Cartesian axis of a scatterplot.
These operations are purely cosmetic but the results reinforce the close relationship
that biplots have with conventional Cartesian plots.
2.5 Scaling the data
All the above biplots of the aircraft data have dealt with the raw data of Table 1.1.
However, the variables are not on commensurable scales. In particular,
PLF
is measured
on a much smaller scale than the other variables, a fact that manifests itself in the figures
by the insignificant role played by this variable. This lack of commensurability is a
serious problem because certain types of biplot are not scale-invariant. In such cases a
common practice is to adjust for it by normalizing all variables to have the same sum
of squares about their mean, as is done in Table 2.2. The chosen sum of squares is
immaterial; typical values are unity, the sample size
n
or even
n
- 1, as in Table 2.2.
We may proceed as with Table 1.1 using the data of Table 2.2 as input to our functions
for constructing the biplot and, corresponding to Figure 2.5, we have Figure 2.16. The
