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Here's another image for some intuition about what is going on: http://blog.statwing.com/wp-content/uploads/2012/12/ecologic...

You wouldn't be able to say anything with confidence about individuals without the individual data but this image helps me think about what individual data would be needed to back up or refute an inference based on group data.

If you can find data within some groups and they show very little to no relationship for X and Y then it's a little more likely that you can use the group inference. But in any case watch out!



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