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 SSCP-matrix that correspond to the chosen dimensions are copied into a two-dimensional matrix S (symmetric of course).
2. The eigenvalues of S are determined, call them s1 and s2.
3. The lengths l1 and l2 of the two axes of the ellipse can be obtained as (see for example Johnson (1998), page 410):
    li = scaleFactor · √ (si ),
     where
scaleFactor = √ (f · p · (n – 1) / (n · (np))),
     in which f = invFisherQ (1 – confidenceLevel, p, np), where p is the numberOfRows from the SSCP object and n the numberOfObservations.
4. The area of the ellipse will be π·l1·l2.

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© djmw, May 25, 2000