Principal component analysis biplots - Understanding Biplots - page 104

Ta b l e 3 . 1 7 Adequacies and predicitivities for the
two-dimensional biplot of the normalized aircraft data.

SPR RGF PLF SLF

Adequacy 0.4557 0.3824 0.7528 0.4091

Predictivity 0.8124 0.7202 0.9065 0.8118

The overall quality of the two-dimensional PCA biplot is

0 . 8127 = ( 41 . 0083 + 24 . 0087 )/( 41 . 0083 + 24 . 0087 + 9 . 2851 + 5 . 6979 ).

Comparing Table 3.17 with the corresponding entries in Table 3.6, PLF now becomes
the most adequately approximated variable, with RGF the least adequate. It may be
verified from Table 3.17 that the average predictivity agrees with the overall quality of
0.8127. The fit measures for all four dimensions are obtained with the call

PCA.predictivities(aircraft.data[,-1], scaled.mat = TRUE)
The axis predictivities and quality are summarized in Figure 3.25. Even in one dimen-
sion, all variables start at a gratifyingly high level, except for PLF which from a bad start
catches up immediately in the two-dimensional fit. A possible explanation is that most
variables involved with aircraft development improve, which means that they increase

Mean = Quality
SPR
RGF
PLF
SLF

1 2 3 4

Dimension of subspace

Figure 3.25 Plot of axis predictivity against dimensionality for the normalized air-

craft data.