An empirical analysis of the quantitative effect of data when fitting quadratic and cubic polynomialsA study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.
Document ID
19740051007
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
Authors
Canavos, G. C. (NASA Langley Research Center Hampton, Va., United States)
Date Acquired
August 7, 2013
Publication Date
January 1, 1974
Subject Category
Mathematics
Meeting Information
Meeting: Symposium on Nonlinear Estimation Theory and Its Applications