Regression with Differential Equation Models

Abstract

Regression analysis normally implies the use of algebraic equations to describe a system; however, some cases would better be modeled by differential equations. This is accomplished by assuming a differential equation model for a given set of data and estimating the values of the unkown parameters within the model. These values are then systematically perturbed to generate particular solutions which are superimposed to yield a better estimate of the unknowns. This process is repeated until a specified accuracy is met. Through an analysis of variance, the statistical characteristics of linear regression can be generated for most nth order differential equations. This provides a basis for evaluating the 'acceptance or rejection' of the regression. The characteristics generated consist of an ANOVA table (uncorrected), general F test on the regression, the R2 value, covariance matrix of the superposition constants, an estimate of the variance about the regression, an estimate of the variance of the parameters, and the confidence intervals on these estimates.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1976
Accession Number
ADA026446

Entities

People

  • Craig D. Hunter

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Analysis Of Variance
  • Classification
  • Computer Programming
  • Confidence Limits
  • Differential Equations
  • Engineering
  • Equations
  • Linear Differential Equations
  • Linear Systems
  • Maintenance
  • Plastic Explosives
  • Probability
  • Random Variables
  • Regression Analysis
  • Statistical Analysis
  • Training
  • Universities

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Statistical inference.