Nonlinear analysis of retail performance

Abstract

A new class of models is proposed for use in economic correlation and forecasting. The new model, termed the multivariable polynomial regression (MPR) model, is essentially a multiple regression model with polynomial and cross-product (interaction) terms. For example, if Y is a function of Q, R, and S, terms can be included such as QR/sup 2/S or Q/sup 3/S. MPR models can be fitted using conventional multiple regression software, although an automated program facilitates the analysis. Only terms which are statistically significant are retained in the model. MPR models are likely to be applicable to low-to-moderate dimensionality problems as are encountered in economics. If the number of independent variables is not too great, MPR models compare favorably to artificial neural network (ANN) models: MPR models can provide a better fit with fewer coefficients; as a result there is less overfitting of "memorizing" of data; the fitting procedure converges absolutely; MPR models result in a simple explicit equation for prediction or analysis; standard statistical tests can be applied to all coefficients and forecast predictions. The technique was applied to correlation of the performance of retail stores to a set of thirteen potential causative variables. An MPR model was developed which was able to explain 82% of the variation in the gross margin of the stores under study.