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Given a dataset with 3 variables A, B, C, you observe a value for the correlation between A and B, and another value for the correlation between B and C.
Question: what are the possible values of the correlation between A and C?
Answer (due to![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
en_ki): if your dataset has n points, center it, and consider A, B and C as vectors in ℜn. The empirical correlation between two variables is the cosine of the angle between them.
Thus the question becomes easy: what are the possible values of the angle AC, given the angles AB and BC?
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Question: what are the possible values of the correlation between A and C?
Answer (due to
en_ki): if your dataset has n points, center it, and consider A, B and C as vectors in ℜn. The empirical correlation between two variables is the cosine of the angle between them.Thus the question becomes easy: what are the possible values of the angle AC, given the angles AB and BC?
---
Original post, for the record: ( Read more... )