I am new to statistics, reading the elements of causal inference:
On section 4.2.1 Additive Noise Models, appears:
Left regress Y on X. Right regress X on Y
The fitted functions are shown in the top row, the corresponding residuals are shown in the bottom row. Only the direction X->Y yields independent residuals... Therefore the correct direction should be X->Y.
Overall I understand the example, but I am not able to relate to it. For example if I think about smoking->cancer, or yearsExperience->salary.
The way I see it, if I do
cancer=f(smoking)+noise it should be pretty similar to doing
My question is: what is the intuition behind getting non-independent residuals for the wrong direction?
My intuition tells me that I can predict cancer seeing smoking the same as predict smoking seeing cancer (and similarly for yearsExperience and salary).