SSCP: Get confidence ellipse area...
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A command to query the selected SSCP object for the area of a confidence ellipse.
Algorithm
The algorithm proceeds as follows:
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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).
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2. The eigenvalues of S are determined, call them s1 and s2.
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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 ), |
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where
scaleFactor = √ (f · p · (n – 1) / (n · (n – p))), |
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in which f =
invFisherQ
(1 – confidenceLevel, p, n – p), where p is the numberOfRows from the SSCP object and n the numberOfObservations.
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4. The area of the ellipse will be π·l1·l2.
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