X,Y are r.v's exactly related by some unknown non-linear relationship.

Does there exist a neat analog of Correlation, that gives some information about a this relationship?

**Contents**hide

#### Best Answer

Were you looking for something like $Distance Correlation$?

http://en.wikipedia.org/wiki/Distance_correlation

This will be non-zero for any sort of relationship between your $x$ and $y$. Therefore this can trap arbitrary non-linear relationships though interpreting the values is harder than interpreting correlation.

If this is what you need try the "energy" library in R.

`set.seed(1234) x<-rnorm(1000,0,1) y<-x^2 cor(x,y) [1] -0.03908369 library(energy) dcor(x,y, R=500)) [1] 0.5478997 #to get a p-value for the distance correlation: dcov.test(x,y) dCov test of independence data: index 1, replicates 500 nV^2 = 140.74, p-value = 0.001996 sample estimates: dCov 0.3751596 `

### Similar Posts:

- Solved – Explaining the difference between Pearson correlation and distance correlation
- Solved – Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS
- Solved – Does zero correlation mean no causation?
- Solved – the relation between a loss function and an energy function
- Solved – Interaction in stepwise regression analysis