
475Multivariate Analysis I
The communalities are the squares of the elements of A or the diagonal terms of AA
T
h
2
=
0 996
0 942
0 992
.
.
.
Adding up all communalities we get 2.93, which is equal to the rst eigenvalue of AA
T
, which is
the only nonzero eigenvalues. The total correlation for three variables would be 3.00. Therefore
2.93/3 = 0.976. Therefore, this FA explains 97.6% of the variance.
Write the cor(u) as diagonal matrix
cor(u) =
0 005
00058 0
000 009
.
.
.
and now we can see that
AA cor(u)
T
+ =
−
−
100097 099
097100 097
099097 100
...
.. .
.. .
(14.43)
which is equal to the correlation matrix R of X.
14.8 CORRESPONDENCE A ...