Timeline for Is it possible that 3 vectors have all negative pairwise correlations?
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Jan 24, 2018 at 22:40 | history | tweeted | twitter.com/StackStats/status/956295706666569728 | ||
| Jan 24, 2018 at 21:19 | comment | added | gung - Reinstate Monica | Related: Bound for the correlation of three random variables. (cc, @amoeba) | |
| Jan 24, 2018 at 21:18 | comment | added | amoeba | @R.M. There is no contradiction between whuber and Heikki. This question asks about data matrix $X$ of $n\times 3$ size. Normally we would talk about $n$ data points in 3 dimensions, but this Q is talking about three "vectors" in $n$ dimensions. Heikki says that all negative correlations cannot happen if $n=2$ (indeed, two points after centering are always perfectly correlated, so correlations must be $\pm 1$ and cannot be all $-1$). Whuber says that 3 vectors in $n$ dimensions can effectively lie in a 2-dimensional subspace (i.e. $X$ is rank 2) and suggests to imagine a Mercedes logo. | |
| Jan 24, 2018 at 21:15 | comment | added | Michael M | @R.M: take a factor with $m$ levels of the same size. Their dummy variables will all have negative pairwise correlation that gets weaker for growing $m$. | |
| Jan 24, 2018 at 21:09 | comment | added | karakfa | @amoeba, added the solution for your interesting follow-up question. | |
| Jan 24, 2018 at 21:04 | comment | added | R.M. | @AnttiA It seems like many people answering seem to be thinking you're specifically interested in 3-vectors (that is, vectors in 3D space). If that's not the case, and you're interested in vectors of arbitrary dimensionality, you might want to edit the post/title to clarify. | |
| Jan 24, 2018 at 20:59 | history | edited | amoeba | CC BY-SA 3.0 |
added 24 characters in body; edited tags; edited title
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| Jan 24, 2018 at 20:58 | comment | added | R.M. | @whuber Your comment seems to contradict Heikki Pulkkinen's answer, which claims it's impossible for vectors in a plane. If you stand by it, you should turn your comment into an answer. | |
| Jan 24, 2018 at 20:57 | comment | added | amoeba | @karakfa An interesting question will be, what is the lowest possible correlation that all three pairs can simultaneously have? You might want to add this to your answer below. | |
| Jan 24, 2018 at 20:54 | answer | added | karakfa | timeline score: 8 | |
| Jan 24, 2018 at 20:27 | comment | added | karakfa | They cannot be completely negatively correlated ($\rho=-1$), but in general there can be some negative correlation, again bounds set by the other correlations. | |
| Jan 24, 2018 at 15:52 | comment | added | whuber♦ | Negative correlations mean, geometrically, that the centered vectors mutually make obtuse angles. You should have no problem drawing a configuration of three vectors in the plane that have this property. | |
| S Jan 24, 2018 at 15:44 | history | suggested | John Coleman | CC BY-SA 3.0 |
changed the wording (which was about 2 correlations) to better reflect the actual question concerning 3
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| Jan 24, 2018 at 15:17 | answer | added | John Coleman | timeline score: 3 | |
| Jan 24, 2018 at 15:09 | review | Suggested edits | |||
| S Jan 24, 2018 at 15:44 | |||||
| Jan 24, 2018 at 12:59 | answer | added | Kozolovska | timeline score: 10 | |
| Jan 24, 2018 at 10:54 | answer | added | Heikki Pulkkinen | timeline score: 19 | |
| Jan 24, 2018 at 9:58 | review | First posts | |||
| Jan 24, 2018 at 13:20 | |||||
| Jan 24, 2018 at 9:54 | history | asked | Antti A | CC BY-SA 3.0 |