Regression with Differential Equation Models
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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.
- Statistics and Probability
- Computer Programming and Software