I would like to ask the opinion of this community in regard to the following discussion between me and my colleague. The case is this: we have two variables, let's call them Y and X. The AIC of a simple linear regression of Y on X
(Y = b1*X + e) is A, and the AIC of the reversed model, regression of X on Y
(X = b2*Y + e) is B.
If B is much larger than A, can we say that the first model is preferable? I have never encountered such use of AIC, but I also couldn't find any references that would mention a restriction of the comparison based on AIC to models with same directionality. In other words, how close do the models in comparison have to be for an AIC-based comparison to be valid? Any references are welcome (with preferences for less technical ones, but anything is better than nothing). Thanks!