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Principal components of 100 Rectangles
Consider 100 rectangles --

of random lengths and widths

Let's treat Length (1) and Width (2) as two variables and then create six other variables as functions of (1) and (2)--adding random error terms--to create these variables in inches for all 100 arbitrarily-drawn rectangles:

Variable #
Description
Mean
1
Length
17.8
2
Width
11.7
3
10Length + e
190.6
4
10Width +e
119.1
5
20L + 10W + e
476.3
6
20L + 20W + e
591.5
7
10L + 20W + e
416.1
8
40L + 10W + e
831.3
This example comes from William W. Cooley and Paul R. Lohnes, Multivariate Procedures for the Behavioral Sciences. New York: John Wiley, 1962, pp. 154-157.

Go to the next page, # 3: The correlation matrix for measures of 100 rectangles