Sequential Regression: A Neodescriptive Approach to Multicollinearity

Classical regression analysis uses partial coefficients to measure the influences of some variables(regressors) on another variable (regressand). However, a descriptive point of viewshows that these coefficients are very bad measures of influence. Their interpretation as anaverage change of the regressand is only valid if the regressors are weakly correlated, and theyare useless when the degree of multicollinearity is high. Despite these obvious flaws there is alack of alternative ideas to measure influences. On that score this paper proposes two newcoefficients of influence: (1) A supplementary coefficient measures the additional influence ofa regressor when certain variables are already taken into account. (2) A particular coefficient,which is a mean of certain supplementary coefficients, allocates the influence of a regressorwithin the collective influence of all regressors. Both new coefficients can directly be interpretedas average changes of the regressand.