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Given two sets, lets say:

enter image description here

Can I say that they are related to the same phenomenon, given their mean and correlation?

P.S.: Both sets have same correlation (x1 and y1; x2 and y2)

P.S.2: x1 and x2 have the same mean, so as y1 and y2

This question was related with Anscombe's quartet. More info about it here: https://en.wikipedia.org/wiki/Anscombe%27s_quartet

But I'm still looking for some details. Descriptive statistics alone is not enough here, so what must we use? Plot data? Some advanced regression models? I know we should go further, but to where?

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  • $\begingroup$ Can you add the data as text rather than images please ? (so that others can use them for examples more easily) $\endgroup$ – baxx Apr 12 '20 at 0:32
  • $\begingroup$ @baxx I would like to add data as table, but I can't so I posted it as image. $\endgroup$ – Victor Leal Apr 12 '20 at 1:13
  • $\begingroup$ You can - worse case you could just put the raw output of a csv file there and someone would be able to edit that quite easily $\endgroup$ – baxx Apr 12 '20 at 13:32
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You need an underlying model or metric by which one can describe 'sameness'. The quantitive description of data depends on the origin of the data.

In this case it seems like (meaningless) fabricated data. The y2 values look like following a smooth curve without much noise. You can see this also in a plot of the 2nd order derivative (computed by taking the difference of the difference).

Whether this is relevant to you and whether measures like just correlation are meaningful or not, depends on your viewpoint and interpretation of the data.

But, if you have fabricated data then anything will be meaningless. So not much can be said about this particular case without context.

See more about the philosophy behind these graphs here: https://www.jstor.org/stable/2682899

plot

plot 2nd order derivative

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