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Linear Least-Squares Regression

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Abstract

Linear least-squares regression is the workhorse mathematical tool of the physical chemistry laboratory. This Mathcad worksheet and its accompanying data files demonstrate various implicit and explicit methods for determination of slope and intercept of a regressed line. It also produces the correlation coefficient, 95% confidence ranges, standard deviation of fit, and standard deviations of slope and intercept. Residual analysis is used to demonstrate techniques of determining and removing questionable data points from the fit. Since this worksheet can import data from external files, one may use it as a general laboratory tool. Instructors can easily prepare simplified versions of the worksheet for students from this template. The worksheet also contains an introduction to weighted least-squares methods. It shows how a quadratic term can be included and tested during the fitting process for data that are poorly fit with a linear least-squares model. A second set of data is provided for this activity. The worksheet includes a discussion of how to determine whether the quadratic term is statistically significant. This testing method is general and can be used for all fitted parameters obtained by least-squares fitting. The worksheet is fully annotated and contains interactive exercises for student practice.

Downloads

Version	Download
Mathcad	LinearLeastSquares.mcd

See also the following data files: data1.prn, exercise22x.prn, exercise22y.prn, linear_x.prn, linear_y.prn

Version	Download
Mathcad	LinearLeastSquares.pdf

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Commentary

Other Information

Keywords

Domain: Analytical Chemistry; Laboratory Instruction; Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Chemometrics; Mathematics / Symbolic Mathematics;

JCE Citation