MEANINGFUL REGRESSION COEFFICIENTS BUILT BY DATA GRADIENTS

Abstract

Multiple regression's coefficients define change in the dependent variable due to a predictor's change while all other predictors are constant. Rearranging data to paired differences of observations and keeping only biggest changes yield a matrix of a single variable change, which is close to orthogonal design, so there is no impact of multicollinearity on the regression. A similar approach is used for meaningful coefficients of nonlinear regressions with coefficients of half-elasticity, elasticity, and odds' elasticity due the gradients in each predictor. In contrast to regular linear and nonlinear regressions, the suggested technique produces interpretable coefficients not prone to multicollinearity effects.