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Let’s say we have correlation between x and y as corr(x,y) and correlation between y and z as corr(y,z). What can be said of the correlation between x and z i.e. corr(x,z)?
Thank you for reading.
I don’t think you can say much.
The correlation function is not even transitive – in other words if both
corr(x,y) > 0andcorr(y,z) > 0, you can’t say ifcorr(x,z) > 0,= 0or< 0, unless those 2 correlations are especially high (corr(x,y)2+ corr(y,z)2) > 1)…See for example this article:
ftp://163.25.117.117/gyliao/TODylan/Is%20the%20Property%20of%20Being%20Positively%20Correlated%20Transitive.pdf(for some reason I can’t insert a clickable link)