SSCP: Get confidence ellipse area...


A command to query the selected SSCP object for the area of a confidence ellipse.
Algorithm
The algorithm proceeds as follows:

1. The four array elements in the SSCPmatrix that correspond to the chosen dimensions are copied into a twodimensional matrix S (symmetric of course).

2. The eigenvalues of S are determined, call them s_{1} and s_{2}.

3. The lengths l_{1} and l_{2} of the two axes of the ellipse can be obtained as (see for example Johnson (1998), page 410):
l_{i} = scaleFactor · √ (s_{i} ), 

where
scaleFactor = √ (f · p · (n – 1) / (n · (n – p))), 

in which f =
invFisherQ
(1 – confidenceLevel, p, n – p), where p is the numberOfRows from the SSCP object and n the numberOfObservations.

4. The area of the ellipse will be π·l_{1}·l_{2}.
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© djmw, May 25, 2000