I have used an approach to the second method to examine (or to orthonalize) a factor's "independence" vis-a-vis other factors. In addition to looking at R^2, also examining each factor's sensitivity and its t-stats.
If the intercept of the regression is statistically different from zero then it would indicate the "dependent" factor contributes more than the explanatory factors. If it is statistically zero (abs(t-stat) <= 2) then the dependent factor is subsumed by the explanatory factors.