0

enter image description here How would I go about generating data with the same pearson's correlation, But different dependence structure as can be seen above. Basically I want to show short coming of linear correlation as a descriptive measure of dependence.

Many Thanks

Vladimir
  • 65
  • 1
    Take a rv $X$ with any centered nontrivial distribution. Then $X,X^2$ are uncorrelated but of course not independent. More counterexamples can be found by playing with or simulating copula models. – Horst Grünbusch Jun 25 '17 at 16:10
  • 1
    Have you looked at Anscombe's quartet that as four such datasets all on Wikipedia already and try this paper – machazthegamer Jun 25 '17 at 19:19
  • This question is illustrated in our many posts about Anscombe's quartet and answered (in the language of univariate regression) at https://stats.stackexchange.com/questions/152028/i-have-a-line-of-best-fit-i-need-data-points-that-will-not-change-my-line-of-be/152034#152034. However, an answer that might best meet your needs would be one that proposes using a copula. – whuber Jun 26 '17 at 17:01

0 Answers0