Evaluation of parameter uncertainties in nonlinear regression using Microsoft Excel Spreadsheet
Background Nonlinear relationships are common in the environmental discipline. Spreadsheet packages such as Microsoft Excel come with an add-on for nonlinear regression, but parameter uncertainty estimates are not yet available. The purpose of this paper is to use Monte Carlo and bootstrap methods to estimate nonlinear parameter uncertainties with a Microsoft Excel spreadsheet. As an example, uncertainties of two parameters (α and n) for a soil water retention curve are estimated. Results The fitted parameters generally do not follow a normal distribution. Except for the upper limit of α using the bootstrap method, the lower and upper limits of α and n obtained by these two methods are slightly greater than those obtained using the SigmaPlot software which linearlizes the nonlinear model. Conclusions Since the linearization method is based on the assumption of normal distribution of parameter values, the Monte Carlo and bootstrap methods may be preferred to the linearization method.... [Show full abstract]
© 2015 Hu et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.