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 incorporate multiple and pairwise regressions into one objective we reduce this technique to an eigenproblem that represents a hybrid between regression and principal component analyses. We show that our approach corresponds to a specific scheme of ridge regression with a total matrix added to the matrix of correlations.