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I have two two datasets. Each contains two variables. There is one variable that is present in both datasets.

When I plot each dataset to see the relationship between the two variables in each, I find that in one dataset the data follows an exponential decay function while the other the data follows a square root function.

For each dataset, I would like to measure the expected change in one variable per unit change in the other variable (always within the same dataset). Then, I would then like to compare the magnitude of the expected change across my two datasets.

StatsScared
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  • This question is predicated on a possible misunderstanding of Pearson correlation, which can be applied and interpreted in this situation. Could you explain what you really mean by "magnitude of correlation or association"? That would help determine how to respond. – whuber Sep 09 '22 at 13:56
  • @whuber, thank you. By "magnitude of correlation or association" I mean the strength of the correlation between the two variables in each dataset. – StatsScared Sep 09 '22 at 18:59
  • By definition, Pearson's $\rho$ measures that. But there are other measures, depending on what exactly you mean by "correlation." You need to explain your meaning. – whuber Sep 09 '22 at 21:23
  • @whuber, always appreciate the rigor. Updated the question, I believe I am after what is usually the β coefficient in a regression, but I'm not entirely convinced.. – StatsScared Sep 09 '22 at 22:48
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    The problem with "measure the expected change in one variable per unit change in the other variable" is that it's inconsistent with a nonlinear relationship. In a linear relationship, that expected change is constant. Nonlinearity implies the expected change varies with the explanatory variable. An example of how to analyze such relationships is at https://stats.stackexchange.com/a/36110/919 -- and there are many more examples like that in other threads if you need more guidance of that nature. – whuber Sep 09 '22 at 22:48
  • Thanks for that. Are you not able to provide any particular pointers? I cannot follow the advanced math on those links. I guess I need to transform my variables from exponential or square root into something that can be compared via a regression. Is that it? – StatsScared Sep 09 '22 at 23:39
  • In my posts I have tended to avoid all advanced math (including Calculus). I cannot provide specific pointers because your question is too vague for that. – whuber Sep 10 '22 at 15:04

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