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Taylorfit Multivariate Polynomial Regression

Simetrica provides software and services for engineering, science, and business modeling and simulation applications.

Its major product is TaylorFit Software for empirical modeling of complex systems. TaylorFit is a software implementation that helps a user to develop Multivariate Polynomial Regression (MPR) models.

  • Do linear models leave you flat?
  • Do artificial neural networks make you nervous?
  • Are you in search of a higher correlation?

MPR is new class of models for use in forecasting and correlation analysis. An 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 QR2S or Q3S.

MPR models can be fitted using conventional multiple regression methods, and only terms that are statistically significant are retained in the model. MPR models are applicable to low-to-moderate dimensionality problems as are encountered in science, engineering and business.

MPR models can replace linear modeling techniques such as multilinear regression and ARMA (Box-Jenkins) models, and can produce far superior results because they incorporate nonlinear effects. If you have used one of these linear methods in the past, you should dust off your data and take another look with TaylorFit. Otherwise you could be missing important behaviors in your data.

MPR models compare favorably to artificial neural network (ANN) models: MPR models can provide a better fit with fewer coefficients; it is easier to control overfitting, or "memorizing" of data; the fitting procedure is less computationally intensive and converges absolutely; MPR models do not require a priori selection of model structure; they give a simple explicit equation for prediction or analysis; standard statistical tests can be applied to all coefficients and forecast predictions.

MPR models can also be used in most applications to which artificial neural networks have been applied. However, MPR models have a number of advantages, especially that they are easier to understand and use, and they make it easier to avoid overfitting errors.