Is the Property of Being Positively Correlated Transitive?
- 1 November 2001
- journal article
- Published by Taylor & Francis in The American Statistician
- Vol. 55 (4) , 322-325
- https://doi.org/10.1198/000313001753272286
Abstract
Suppose that X, Y, and Z are random variables and that X and Y are positively correlated and that Y and Z are likewise positively correlated. Does it follow that X and Z must be positively correlated? As we shall see by example, the answer is (perhaps surprisingly) “no.” We prove, though, that if the correlations are sufficiently close to 1, thenX and Z must be positively correlated. We also prove a general inequality that relates the three correlations. The ideas should be accessible to students in a first (postcalculus) course in probability and statistics.Keywords
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