I have the following plot, which appears to have two pretty distinct trends.

enter image description here

The plots shown here and here depict similar situations. Is there a name for data that have two or more distinct trends, particularly when the distinct trends cannot be attributed to different factors?

  • 2
    $\begingroup$ As a descriptive term, some people would use "mixture" to reflect the apparent superposition of two bivariate densities that themselves might be capable of simple characterizations (they might each be Binormal, for instance). "Trend" is not really apt, because the vertical point cloud isn't a trend in the ordinary sense of the word (of describing how the response changes with the predictor) because the response is literally all over the place. $\endgroup$
    – whuber
    May 17 at 23:15
  • $\begingroup$ What are you measuring there? Would those variables be ratios of other quantities for example? $\endgroup$
    – Glen_b
    May 18 at 2:48
  • $\begingroup$ @whiber – It’s true that the word ‘trend’ is not applicable to vertical lines in the predictor-and-response sense. I guess I was wondering about a more general sense where the lines could be in any direction, but I wanted to include the vertical possibility. $\endgroup$ Jun 24 at 22:43
  • $\begingroup$ @Glen_b – the variables certainly could be ratios, but they aren’t necessarily ratios. I’m interested in the general sense where the variables could be anything. $\endgroup$ Jun 24 at 22:45
  • $\begingroup$ It wasn't an idle question, it impacts the answer. You gave a picture. That picture either came from ratio data or it didn't. If they're ratios, the advice I'd give would be different. $\endgroup$
    – Glen_b
    Jun 25 at 3:24

1 Answer 1


First off, a hexagonal plot would help you to visualize this plot density much better.

To me, there is only one trend, the seemingly flat line showing the expected response as a function of the predictor. There is also an incredibly powerful issue of heteroscedasticity where points within the central portion of the predictors distribution have a MUCH larger variance.

Another way to view it is that the bivariate density of these two variables has a mode that's distributed compactly along the orthogonal (vertical and horizontal) axes of the plane. The "mode" of a distribution need not be a finite set of points, but could be said to comprise an area. But to my first point, I can't be totally sure of it when the points are swarming like squid in a black cloud of ink!


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