yes!
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can you say another 140 while I google “asymptotic independence”?
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@karlrohem Well, to posit an extreme example: suppose X is a Gaussian normal, and Y is defined to be = X if X \in [-1, 1]...
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...and if X not \in [-1,1], Y is randomly sampled from a Gaussian normal until it lands outside [-1,1].
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Then Y is actually Gaussian normal, and the scatter plot of X vs. Y looks like a Ø with a hard line segment in the center...
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...but the outer O is a Gaussian blur ring.
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So X and Y are perfectly correlated in the center, and uncorrelated outside it.
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A less extreme example would be a scatter plot where the points group close to the regression line in the middle but spread...
End of conversation
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.