Solved – Correlation coefficient for sets with non-linear correlation

What method can I use to test if there is a correlation between two sets of data? The correlation coefficient works if there is a linear association, but if I have two sets that are clearly (visually by graph) correlated in a non-linear way, how can I test that? Is there a coefficient or a special method?

In case of non-linear correlation Spearman's Rank-correlation is one method

and one more method is called Kendall's Tau

R code for Spearman's rank correlation:

cor(X, Y ,method= "spearman") 

R code for Kendall's rank correlation:

cor(X, Y ,method= "kendall") 

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