Linear response surface analysis as a technique for visualizing linear models and data

Abstract

Linear Response Surface Analysis (LRSA) is a subset of the statistical field Response Surface Methodology (RSM). RSM is a research field dedicated to the optimization and forecasting of linear and non-linear models. These models are presented in terms of various "independent" variables that influence a dependent ( or response) variable. The feature that distinguishes LRSA from RSM in general, is that LRSA can be applied to both planned and raw data, compared to RSM that is applied mainly to planned data. The terms "planned" and "raw" are used to differentiate between data collected from a planned experiment and data for which the cases are collected randomly (e.g. observational studies). LRSA makes use of the mathematical programming technique Linear Programming to generate graphic representations of linear models and data. The objective of this study is to investigate the feasibility of these graphic results to reflect properties of linear models and data which will be useful for optimization and forecasting. Specific interest is shown in handling linear model building difficulties such as: • Interpretation of models in case of interdependence among "independent" variables. • Determining the importance of a variable to a model, relative to the other variables in the model. • Deciding which variables to include or exclude from a model in case of multiple linear regression. • Handling of state variables in case of optimization and forecasting. In addition to the above objectives, software was developed for an experimental decision support system with new improved functionality, e.g. using a robust linear program solver, using parametric programming for more effective visualization, generating multi-variable response graphs, and an implementation of a parallel algorithm to speed up execution. The outcome of the envisaged objectives was evaluated in the light of an empirical investigation using developed experimental software. In relation to each of the objectives stated it was shown that the graphic results generated with LRSA revealed important properties about the linear model and data that may aid the model building process. It is also. shown that the new functionality was implemented successfully.