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My data (about 20-30 data points) seems to be following a quadratic pattern, and it's quite plausible that they influence each other:

For $X < 16$, the influence (direction of "Granger-causality") seems to go from $Y$ to $X$, while for $X > 16$ the direction of causality seems to be reversed.

In other (interpretative) words: Two effects may be present, where one of them dominates up until $X < 16$, while the other takes over beyond that point.

Is it fine just to quote the $R^2$-value(s) and the $p$-value(s) for either $Y$ on $X$ or $X$ on $Y$, or must some alarm bells go off if the two variables influence one another (i.e., the dependent variable effectively becoming the independent variable, and vice versa, for half the data-set)?

nutty about natty
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  • [With correlation you don't have to think about cause and effect. You simply quantify how well two variables relate to each other. With regression, you do have to think about cause and effect as the regression line is determined as the best way to predict Y from X.](http://stats.stackexchange.com/a/2129/26535) – nutty about natty Jun 05 '13 at 20:29
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    This wikipedia article on endogeneity should get you started http://en.wikipedia.org/wiki/Endogeneity_(economics) – chandler Jun 05 '13 at 21:56
  • @chandler Note: I'm *not* trying to claim or "prove" [causality](http://stats.stackexchange.com/questions/8453/can-you-use-r2-and-regression-to-estimate-cause-and-effect?rq=1) here. I'm just wondering whether it's fine to quote R² and p-values for Y on X (even though some kind of endogeneity, cross-dependence, bias or (in-)consistency may be at play - sorry for misusing/abusing technical terms here, plz do correct me)... – nutty about natty Jun 06 '13 at 10:17

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