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In-Depth Information
Figure 3.9
Interpolation biplot axes (in blue) fitted to the biplot display in the two-
dimensional biplot plane.
3.3 Measures of fit for PCA biplots
For any observed vector
x
decomposed into a fitted part
x
and residual
x
−
x
, it follows
that
x
=
x
+
(
x
−
x
).
(3.9)
The quality of the fit may be assessed by the
variance accounted for
ratio:
x
x
x
x
.
ss
(
x
)
ss
(
x
)
=
(3.10)
The expression 'variance accounted for' is used loosely and assumes, at least, that
x
is expressed in deviations from the mean. Much more important is that the ratio is
meaningful only when the decomposition is orthogonal, that is,
ss
(
x
)
=
ss
(
x
)
+
ss
(
x
−
x
).
(3.11)
