Use of Linearized Nonlinear Regression for Simulations Involving Monte Carlo

The material presented furnishes an extension of regression analysis in two respects. First, a type of nonlinear regression function is developed that seems to (1) have substantial curve-fitting flexibility, (2) be satisfactorily determined from an acceptably small number of observations, (3) permit isolation of important combinations of effects, and (4) be computationally manageable. Second, in conjunction with this general type of regression function, a probability model is developed that is applicable under exceedingly general conditions. Namely, each of the independent observations utilized can be from a different statistical population and the shapes of these populations are not necessarily restricted or related in any specific manner. An important aspect of the model is selection of the kind of “average” that the regression represents Estimates, tests, and confidence intervals are developed for investigating the regression coefficients. The methods and results presented are especially useful for Monte Carlo type simulations that are performed by use of a computer. This paper represents a report of research in progress, since many additional results should be obtainable on the basis of the concepts and methods that are presented.