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Data Analysis and Statistics for Geography, Environmental Science, and Engineering
book

Data Analysis and Statistics for Geography, Environmental Science, and Engineering

by Miguel F. Acevedo
December 2012
Beginner content levelBeginner
557 pages
19h 5m
English
CRC Press
Content preview from Data Analysis and Statistics for Geography, Environmental Science, and Engineering
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
00
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 ...
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Publisher Resources

ISBN: 9781439885017