Biplot basics - Understanding Biplots - page 37

Ta b l e 2 . 2 The data of Table 1.1 normalized to have zero means and
equal sums of squares.

Aircraft SPR RGF PLF SLF

a FH-1 − 1.000 − 1.868 − 0.016 − 2.122

b FJ-1 − 0.942 − 1.332 − 0.151 − 2.122

c F-86A − 0.704 0.609 0.108 0.606

d F9F-2 − 0.752 0.373 1.213 − 1.148

e F-94A − 0.577 − 0.590 1.473 − 1.245

f F3D-1 − 1.073 − 1.158 − 0.196 − 1.343

g F-89A − 0.697 − 0.811 − 1.887 0.119

h XF10F-1 − 0.594 0.262 − 0.568 − 0.466

i F9F-6 − 0.518 − 1.016 − 0.140 0.021

j F100-A 0.311 0.688 − 0.331 0.898

k F4D-1 0.320 − 1.048 0.920 1.191

m F11F-1 − 0.090 − 0.259 − 0.275 0.509

n F-101A 0.856 0.073 0.052 0.216

p F3H-2 − 0.395 − 0.006 0.120 0.703

q F102-A 0.021 1.430 − 0.748 0.703

r F-8A − 1.428 0.799 − 1.797 0.353

s F-104A 1.801 0.026 0.943 0.411

t F-105B 1.130 1.130 2.239 0.606

−

u YF-107A 0.952 1.698 0.692 0.606

−

v F-106A 1.385 1.446 0.884 0.898

w F-4B 1.995 − 0.448 0.616 0.606

problem with this figure is that the scales on the biplot axes are in terms of the normalized
values of the variables. It is easy to convert these to their original units of measurement,
using as input to PCAbipl the original aircraft data as given in Table 1.1 setting argument
scaled.mat = TRUE . The resulting biplot is given in Figure 2.17.
As before, we may improve legibility by moving the origin and rotating axes, as has
been done in Figures 2.18 and 2.19. Arguments orthog.transx = rep(3.43, 4)
and orthog.transy = rep(-0.68, 4) are used in producing Figure 2.18. Reflec-
tion, rotation and orthogonal translation are needed for the biplot in Figure 2.19. These
operations are carried out with the following argument settings:

orthog.transx = rep(2.35, 4), orthog.transy = rep(2.5, 4),
exp.factor = 2.5, reflect = "y", rotate.degrees = 214.2

2.6 A closer look at biplot axes

So far, we have been concerned entirely with the visualization of Table 1.1. Since our
aim is to use a biplot analogous to a scatterplot, we would like to use the biplot axes to
read off the values of SPR , RGF , PLF and SLF for any of the aircraft. To be precise,
we would like to use projection onto the biplot axes to read off approximate values of the
variables in Table 1.1 for each of the 21 points marked with aircraft names. This process
we term prediction . Our biplot functions contain an argument predictions.sample
to visually aid the prediction process. As an illustration we set predictions.sample