 Principal components analysis
computes the underlying factor that accounts for the
maximum variance held in common among a set of
intercorrelated variables.
 Then it computes a second
uncorrelated (orthogonal) factor to account for
the maximum remaining variance.
 It proceeds to calculate separate,
uncorrelated factors until all variance in the original
matrix is exhausted.
 The number of factors extracted
depends on the intercorrelations in the
matrix.
 The lower the correlations, the
less common variance, so more factors are needed to
account for large proportions of the
variance.
Two
Principal Components Accounted for 98.5 Per Cent of
Total Variance from Eight Rectangle Tests on One
Hundred Cases



First
Component

Second
Component

(also "Latent
Root")

Eigenvalue

5.96

1.93


Per Cent of
Variance

74.4

24.1






Variable

Factor
I

Factor
II

1

Length

0.85*

0.52

2

Width

0.63

0.76

3

10Length +
e

0.86

0.50

4

10Width +e

0.63

0.74

5

20L + 10Width +
e

0.98

0.18

6

20L + 20Width +
e

0.99

0.08

7

10L + 20Width +
e

0.93

0.37

8

40L + 10Width +
e

0.94

0.34

*This value (0.85), which is called
the factor "loading,"
is the correlation of that variable
(length) with the underlying factor.
We know (from constructing the data) that
the only variance not accounted for by the first two factors
is error variance due to the error term. Let's see a
plot of this analysis.
Continue to page 5: A
plot of the unrotated factors
