In article <[EMAIL PROTECTED]>,
Derek Ogle <[EMAIL PROTECTED]> wrote:
>Members,
>Can anyone provide me (a description or a reference will suffice) with a
>convincing argument or demonstration of WHY the first eigenvector-eigenvalue
>of the variance-covariance matrix represents the direction and magnitude of
>the greatest variability in the "cloud of multivariate data"? I can convince
>the students that this is what happens but I can't convince them of the why
>this is what happens. Thank you in advance for your help.
Just use the idea of concentration ellipsoids. The use of
orthogonal transformations (rotations) makes the
characteristic vectors the direction vectors of the rotated
axes, and the values the lengths of the axes.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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