A note on orthogonalization against multicollinearity in linear regression, with a consideration of spacetime as the common parameter domain

Abstract

In estimating/testing a functional relationship in Economics, one collects data - - both the dependent variable and the explanatory variables, which is not the same as an experiment in Physics with all the independent variables in full control by the analyst. This brings about the problem of multicollinearity in multiple linear regression to all fields that do not enjoy true degrees of freedom in the causal variables of a regression model. This note presents a simple example, where a pair of variables, u and v, seeks to explain y, but u(t, s) and v(t, s) share one common parameter domain, t and s, so that it becomes evident that the regression model y = a + bu + cy + e is simply invalid. We thus recommend constructing regression models based on independent variables true to their definition of independence, such as time and space, by using a spatiotemporal sample.