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I have read some of the existing non-linear correlation analyses such are Maximal Information Coefficient (MIC) and Distance Correlation, both of them don't tell us about how the correlation is shaped (such as sinusoidal or polynomial). Is there any approach to know the shape of non-linear association between two variables?

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  • $\begingroup$ Fitting various models with non-linear terms, pruning them to include statistically significant terms only and comparing them using AIC, BIC and such. $\endgroup$
    – stans
    Commented Dec 5, 2022 at 8:32
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    $\begingroup$ Just a simple scatter plot, maybe add some smoothers... $\endgroup$
    – Maarten Buis
    Commented Dec 5, 2022 at 10:48
  • $\begingroup$ This page illustrates splines and "loess" fits for this task. $\endgroup$
    – EdM
    Commented Dec 5, 2022 at 13:44
  • $\begingroup$ Plot, plot, plot, plot, plot. $\endgroup$
    – usεr11852
    Commented Dec 19, 2022 at 13:01

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