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Non-Linear Least-Squares Regression

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Abstract

Nonlinear least-squares regression is often required in the physical chemistry laboratory. It is especially important for fitting functions that cannot be linearized. This template demonstrates various implicit and explicit methods for determining of the parameters of the regressed curve obtained by nonlinear curve-fitting. Through this worksheet students will be able to obtain the standard deviation of fit and the standard deviations of the parameters. Residual analysis is used to demonstrate techniques of removing bad data points from the fit. Data may be read into the template by using a Read statement. After minor editing the template can be used for a variety of applications in the student and research laboratories. As in Linear Least-Squares Regression, parameters can be tested to see if their addition to a model is statistically significant.

Figure 1. The residuals shown here for a linear function fitted to a set of data do not show a random distribution about zero. This residual plot suggests the addition of a quadratic term, because the residuals are parabolic as if following y = x² + c.

Figure 2. The residuals shown here for a quadratic function fitted to the same set of data as in Figure 1 show a random distribution about zero. This residual plot suggests that the addition of a quadratic term was appropriate.

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Mathcad	NonLinearLeastSquares.mcd

See also the following data file: nonlinear.prn

Version	Download
Mathcad	NonLinearLeastSquares.pdf

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Keywords

Domain: Analytical Chemistry; Laboratory Instruction; Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Chemometrics; Mathematics / Symbolic Mathematics;

JCE Citation