What is the difference between uncorrelation and independence?

 

Answer

Uncorrelation means that there is no linear dependence between the two random variables, while independence means that no types of dependence exist between the two random variables. For example, in the figure below \(Y_1\) and \(Y_2\) are uncorrelated (no linear relationship) but not independent.

The plot below shows graphically what uncorrelation (lack of linear dependence) but there still being some sort of dependence. The plot shows a parabolic curve that signifies some sort of quadratic dependence, however, if you were to fit a linear line to this plot it would be a flat horizontal line signifying no correlation.

This means that independent random variables are always uncorrelated, but uncorrelated random variables may not be independent. In other words, independence is a stronger statement than uncorrelation.

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  • Last Updated Apr 23, 2021
  • Views 16072
  • Answered By Dorian Frampton

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