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Yes, you need strong correlations in the first two combinations and you will have less of it in the third, it is impossible to make the two planes orthogonal with true correlations in the first two couples.

Pierre
by Pierre on Tue Feb 24th, 2009 at 11:58:16 AM EST
[ Parent ]
do you happen to actually have the formula of the angle at hand ?

Pierre
by Pierre on Tue Feb 24th, 2009 at 11:59:14 AM EST
[ Parent ]
The correlation coefficient is the cosine of the angle. Is that what you mean? You then apply spherical trigonometry to the triangle. Assuming all three variables are on a plane, you get upper and lower bounds (from cosine of sum and cosine of difference formulas).

This all follows from considering that "covariance" is an "inner product". The Cauchy-Schwarz inequality gives you "covariance is less than the product of standard deviations".

Does that answer your question?

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith

by Migeru (migeru at eurotrib dot com) on Tue Feb 24th, 2009 at 12:10:16 PM EST
[ Parent ]
yes

Pierre
by Pierre on Tue Feb 24th, 2009 at 12:42:15 PM EST
[ Parent ]

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