Correlation Conundrum

Number Theory Level 3

For statistical events A, B, and C,

A is correlated with B, and B is correlated with C.

Does this imply that A is correlated with C?

Yes No

Geoff Pilling by Geoff Pilling , 53, USA

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2 solutions

David Vreken
Nov 20, 2018

Good weather makes me happy. Good food makes me happy. This means good weather correlates to my happiness, and my happiness correlates to good food. However, good weather does not correlate to good food.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Hahahaha... Nicely put, David!

Geoff Pilling - 2 years, 6 months ago
Geoff Pilling
Nov 20, 2018

For example if A and C are uncorrelated, but if B=A+C then B is correlated with both A and C.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice question! I hadn't considered whether correlation was transitive or not before. One demonstration of your example is to consider the following unit vectors:

A = < 0 , 1 > , B = < 1 2 , 1 2 > , C = < 1 , 0 > A = < 0, 1>, B = < \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} >, C = <1,0> .

While correlation is not transitive could we possibly infer some degree of partial correlation?

Brian Charlesworth - 2 years, 6 months ago

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Ah yes.. and A and C are clearly orthogonal in the true sense of the word! :)

Geoff Pilling - 2 years, 6 months ago

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