CurveFitting
Data Analysis (Damped Oscillations) Using the Genfit Function JCE
R. D. Poshusta, Washington State University
Shows how the Mathcad Genfit function does a general least squares fit of a model function to experimental data. Sampole data is provided. The template is easy for students to use.
Fitting a Polynomial to CP vs. T for Ag
Theresa Julia Zielinski, Monmouth University
This document demonstrates the method of fitting a polynomial of any reasonable power to a set of data and provides an example of how to use matrix methods to solve simultaneous equations in physical chemistry.
Nonlinear regression: Kinetics of sucrose inversion*
Theresa Julia Zielinski, Monmouth University
An introduction to nonlinear curve fitting using data using first order data. Explorqtion of the basic concepts of ploting data, writing the fitting function, estimating the fitting parameters and then finding the best fit parameters by minimizing the sum of the squares of the deviations (SSD) between the fitting function and the data.SSD from before and after obtaining the optimum parameters are compared. The document concludes withcalculation of residuals and a plot of residuals to demonstrate that points lie between. ? 2 sigma.
van der Waals and Redlich Kwong: Fitting Two Parameter Equations to Gas Data
Theresa Julia Zielinski, Monmouth University
The Mathcad document given here is a highly annotated application of non-linear curve fitting for determining the a and b parameters for the van der Waals and Redlich-Kwong equations. The document goes through the development of the sum of squares of deviations SSD, applies the Levenberg-Marquradt to minimize the SSD and then uses the F-test to determine the equation that best represents the data. The determination of the standard deviation of the fitting parameters is done through the explicit construction and inversion of the Hessian matrix.