CURVES

A Five-Function Curve-Fitting Computer Program

by H. E. Boren

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Description and listing of an all-FORTRAN IV program that makes least-squares determinations of the parameters of any of five mathematical functions selected by the user, given a set of observations on the dependent and independent variables of interest (up to 200 data points per curve). The functions available are those most commonly used in developing cost-estimating relationships: line, parabola, power, asymptotic-power, and exponential. Up to three independent variables may be used for the line and power functions. The Y-intercept may be specified for the line, parabola, or asymptotic-power functions. The program is designed to be user-oriented and easily workable rather than to emphasize computational efficiency. Exact and unique solutions for the line and parabolic functions are obtained by standard algebraic methods. Since the other three choices are not linear in all parameters, they are solved iteratively: the power and exponential by a modified Gauss-Newton iteration, starting from the exact logarithmic solution (as described in RM-4879-PR), and the asymptotic-power function by a special iterative method described in the RM. In addition to directions for program use, the RM includes a discussion of the characteristics of the functions and mathematical considerations involved in nonlinear least-squares solutions.

This report is part of the RAND Corporation research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

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