Note that one technique that does not work in offsetting the effects of multicollinearity is orthogonalizing the explanatory variables ( linearly transforming them so that the transformed variables are uncorrelated with each other ) : By the Frisch Waugh Lovell theorem, using projection matrices to make the explanatory variables orthogonal to each other will lead to the same results as running the regression with all non-orthogonal explanators included.
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