[R] Scatterplot and Causality

[Lorenzo Isella]

Dear All,
I hope this is not too off topic.
I am given a set of scatteplots (nothing too fancy; think about a
normal x-y 2D plot).
I do not deal with two time series (indeed I have no info about time).
If I call A=(A1,A2,...) and B=(B1, B2, ...) the 2 variables (two
vectors of numbers most of the case, but sometimes they can be
categorical variables), I can plot one against the other and I
essentially I need to determine whether

A=f(B, noise) or B=g(A, noise)

where the noise is the effect of other possibly unknown variables,
measurement errors etc.... and f and g are two functions.

Without the noise, if I want to test if A=f(B) [B causes A], then I
need at least to ensure that f(B1)!=f(B2) must imply B1!=B2 (different
effects must have a different cause), whereas it is not ruled out that
f(B1)=f(B2) for B1!=B2 (different causes may lead to the same effect).

However, in presence of the noise, these properties will hold only
approximately so....any idea about how a statistical test, rather than
eyeballing, to tell apart A=f(B, noise) vs B=g(A, noise)?
Any suggestion is welcome.

Lorenzo