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Sep 4, 2024 at 16:05 history edited kjetil b halvorsen
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Apr 24, 2024 at 19:09 answer added Mehdi timeline score: 6
Feb 24, 2024 at 4:07 history edited User1865345 CC BY-SA 4.0
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Feb 24, 2024 at 4:05 history bumped CommunityBot This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
Jan 18, 2024 at 18:02 answer added Marcus Chiu timeline score: 6
Nov 10, 2022 at 3:28 comment added Sycorax Another way to consider Stephan's comments is that every regression you could estimate for the two variables in your plot is, in a sense, a correlation measurement. Testing and comparing arbitrarily many regressions has problems with false discovery and statistical validity, so "just try stuff" isn't a great way to go about it: you need to be specific about what questions you want to ask your data & how you want to ask it. The plot you show is roughly monotonic & Spearman's correlation would characterize the extent. Lots of nonlinear functions are monotonic, so Spearman's is an answer.
Nov 9, 2022 at 22:39 history edited Sycorax CC BY-SA 4.0
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Nov 9, 2022 at 7:42 comment added Stephan Kolassa ... (2) Especially for inference, the question comes up whether you want to test a specific polynomial correlation, or a general second-order polynomial, or a general polynomial of up to second order. Perhaps you could explain what you want to do with such a nonlinear correlation?
Nov 9, 2022 at 7:41 comment added Stephan Kolassa (1) What do you mean by "measuring"? If you want a measure of the "strength" of such a correlation, then you could indeed run a polynomial regression and report the MSE. Possibly cross-validated, otherwise if you re-ran this for higher order polynomials, you would "find" that the "second-order correlation" is smaller than the "third-order correlation" and so on. Conversely, if you want to do statistical inference, the null and alternative hypotheses will need some thinking about - are $x$ and $x^3$ for $-1<x<1$ "significantly second order correlated"? ...
Nov 9, 2022 at 6:59 comment added Dave Interesting question. Some of the trouble of defining a curved correlation will be deciding on what kind of curvature you want to measure. After all, a logarithm-type of graph has different curvature than a quadratic. Further, determining the sign will be challenging, since many curves (such as quadratics) allow for increasing and decreasing sections. I’ve wondered if the concavity of a parabola (up-opening vs down-opening) could be used for this, but parabolas are just one type of curve. (Maybe you can do this if you restrict to convex or concave functions.)
Nov 9, 2022 at 0:24 history edited stats_noob CC BY-SA 4.0
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Nov 8, 2022 at 23:44 history asked stats_noob CC BY-SA 4.0