# What to watch out for when regressing Y on X when not only Y influences X but also X influences Y?

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)?

• This wikipedia article on endogeneity should get you started en.wikipedia.org/wiki/Endogeneity_(economics) – chandler Jun 5 '13 at 21:56
• @chandler Note: I'm not trying to claim or "prove" causality 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 6 '13 at 10:17