Multivariate Polynomial Regression
(MPR) can be used for any inputoutput 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, predatorprey relationships;
 Plant growth or product yield vs. cultural factors.
Chemistry
 QSARs (quantitative structureactivity relationships)
 nonlinear free energy relationships;
 Equations of state.
Physics
 Timeseries 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 (floodstage 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 timeseries 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.)
