If I have two series of measurements, and I use a statistical test to show they are not independent of each other, can I infer a "shared" factor to produce a third series which represents the dependent factor?
for an x and y that are not independent
z === inferred factor between x and y
$x'$ === x excluding z (perhaps subtraction)
$y'$ === y excluding z (perhaps subtraction)
$f'$ === a variant of f that operates on $x' y' z$
how to find
$z, x', y'$
$f'(x', y', z) = f(x, y)$
What additional information do I need? What would be a better problem statement? What are some different approaches to take for a solution?
Also, I would appreciate pointers in the right direction as much as complete solutions. :)