I have an x variable and a y variables. I have done a simple scatter plot. I however don't really know how to interpret (if there is anything to interpret) the plot. I can't find any other similar examples
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I would think that this suggests that you have several different populations being analysed with a few outliers that may or may not be freak instances. Perhaps 9 or 10. Perhaps different atomic isotopes or similar species of organic molecules might show these sorts of results.
I think the answer strongly depends on what are the variables. In general, one can perform correlation analysis (Pearson or Spearman, however I think the latter is more appropriate). However, there is strong evidence (I mean by visual inspection) that in fact there are different classes of something in the plot. If indeed the response is on the vertical axis, and if this is somewhat related to quantum mechanics, I'd suspect there are discrete realisations of an observable, possibly obscured with some kind of noise (thermal most likely, if it relies strongly on electronic devices; or cosmic radiation, or...). Or, if this is some kind of resonant behaviour, this may show position of resonances in some mixing system (bifurcations ring a bell, but that would be going too far with this amount of information). An so on. If you are asking for what to do statistically, I would say that nearly everything; it depends what are the data, what are you looking for, what's the aim of collecting these data, etc.