Multiobjective regression modifications for collinearity

In this work we develop a new multivariate technique to produce regressions with interpretable coefficients that are close to and of the same signs as the pairwise regression coefficients. Using a multiobjective approach to i ncorporate multiple and pairwise regressions into one objective we reduce t his technique to an eigenproblem that represents a hybrid between regressio n and principal component analyses. We show that our approach corresponds t o a specific scheme of ridge regression with a total matrix added to the ma trix of correlations.