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I am simulating a population of binary stars by generating many samples of orbital parameters. I'm investigating the relationship between the inclination of the orbit and the fraction of the acceleration* which is along the line of sight to the orbit. I produced this plot:
enter image description here To me, it seems clear that there is some relationship between these quantities: the higher the inclination, the higher the y-value below which most of the points for that inclination are concentrated. I can clearly see a line on the border between the low and high density of points. It looks like a linear relationship that got "filled in" below the line, and above it, we have a few random points. However, this is a really unconcise way to describe it and doesn't help me understand the relationship between the parameters. Is there a name, description, or mathematical statement of this type of relationship that would be helpful? Or am I just wishing for a pattern where there isn't one?

*change in velocity over a certain time interval

kjetil b halvorsen
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Sofia Splawska
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    Unfortunately, your plot obscures any relationship. It might even suggest an incorrect relationship. (For instance, if you simulate relatively few small inclinations, the apparent absence of high accelerations there could arise merely from a lack of samples.) You need to apply transparency, make the points much smaller, or use a technique like hexbin plots in order to see these data. – whuber Jul 06 '21 at 14:11
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    @whuber thank you, I just made the points smaller as well as applying transparency – Sofia Splawska Jul 06 '21 at 14:16
  • You could try some form of nonparametric regression, or an alternative visualization that could help is *vertical stacked histograms/density estimators*, as used at https://stats.stackexchange.com/questions/428445/how-can-i-visualize-an-ordinal-variable-predicting-a-continuous-outcome/428573#428573 – kjetil b halvorsen Jul 07 '21 at 00:37

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I don't know of a word for this kind of scatterplot. Yet, if you are trying to understand the relationship between the two, this post might be helpful.

Two other thoughts to help identify a relationship in a visual way.

  1. Add a loess line or spline.
  2. Consider whether there are groups in your data that might be meaningful to color separately and/or create a loess line/spline for each one. Seeing this, part of me wonders whether there is some group (or groups) that is bounded for some reason and another that is not.
Mark
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