Consider I have an observable which is depend on one state variable of the system much more than other variables. The dependency can be linear or nonlinear (and there is no linear correlation). Is there any way to find that the observable is carrying information from one of the states more than the others. For example, in the following figures, f depends on x and seems weak or non-dependent on y.
Is there any way to figure it out from data itself?
f vs x (dependency can be observed visually):
f vs y seems scattered:
