Multivariate Polynomial Regression (MPR) can be used for any input-output system, and is especially suitable for systems with many inputs that may interact with each other. Any numerical data that can be arranged in a table of rows and columns can be modeled by MPR. Each row represents a data point. Each column is a variable, one of which is the dependent variable, and the others are independent variables.

To put it more simply, MPR can be used to produce a model to predict an outcome based on one or many causative variables. We encounter such relationships every day. To give any idea of how common they can be, we have produced a list of hypothetical potential applications. Some are drawn from correlation examples in the literature, but the list is intended only to illustrate the kinds of problems that could be examined using MPR.

Science

Biology

• Population dynamics, predator-prey relationships;
• Plant growth or product yield vs. cultural factors.

Chemistry

• QSARs (quantitative structure-activity relationships)
• nonlinear free energy relationships;
• Equations of state.

Physics

• Time-series models of sunspot numbers,
• Correlation of property phase diagrams.
• Correlation of turbulent flow.

Sociology

• All correlations that would otherwise use multilinear regression should be replaced by MPR correlations; e.g. crime rates vs. socioeconomic factors

Engineering

Chemical

• System identification for process control.
• Convert physical property nomographs to explicit functional form.
• Correlations for mass transfer coefficients.

Civil

• Hydrologic response function;
  an explicit correlation for pipeline flow friction factor.
• Concrete strength vs. mix proportion

Environmental

• Lead concentration in drinking water vs. home age, piping, pH, alk, TDS, LSI, etc;
• Predict performance of biological process vs.loading factors.
• Hydrological Nonlinear hyetograph (flood-stage prediction).
• Create regional models of streamflow relationships.

Electrical

• Filtering, signal processing, data compression.

Mechanical

• Correlate helicopter performance (lift) with factors such as power, rpms, air temperature and pressure;
• Performance curves for pumps, motors, etc.
• Heat transfer coefficients for heat exchangers.

Clinical/Medical

• Epidemiology Cancer vs. age, exposure, nutrition, smoking, etc.
• Dynamics of epidemics (by time-series analysis).
• Pharmacology Dose/response relationships with confounding factors
  (age, sex, etc.)

Econometric

• Sales vs. advertising, market factors, or economic factors.
• Cost optimization.
• Estimating cost of housing using local factors and house attributes.
• Predicting changes in stock values using leading indicators.

Mathematics

• Prediction and analysis of chaotic processes.
• Generate explicit form for mathematical functions, such as probability distributions, Bessel functions, error functions, etc.

Industry and Manufacturing

• Statistical quality control; optimization.
• Load forecasting (power, water, etc.).
• Correlating product quality with manufacturing parameters (feedstock quality parameters, manufacturing machine speed or other settings, etc.)