Multiple linear regression can be applied for predicting an individual value of dependent variable y by the given values of independent variables x. But it is not immediately clear how to estimate percent change in y due to changes in predictors, especially when those are correlated. This work considers several approaches to this problem, including its formulation via predictors adjusted by their correlation structure. Ordinary least squares regression is used, together with Shapley value regression and another model based on solving some system of differential equations. Numerical estimations performed for a real marketing research data demonstrate meaningful results. The considered techniques can be very useful in practical estimations of the percent change of dependent variable by the change in predictors.
Lipovetsky, S. (2017). Prediction of Percent Change in Linear Regression by Correlated Variables. Journal of Modern Applied Statistical Methods, 16(2), 347-358. doi: 10.22237/jmasm/1509495480