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2001
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Information • Textbooks • Media • Resources
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Computer Bulletin Board
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Curve Fitting, Confidence Intervals and Envelopes, Correlations, and Monte Carlo Visualizations for Multilinear Problems in Chemistry: A General Spreadsheet Approach
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Paul Ogren, Brian Davis, and Nick Guy
Department of Chemistry, Earlham College, Richmond, IN 47374-4095
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June 2001
Vol. 78 No. 6
p. 827
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| Abstract |
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A spreadsheet approach is used to fit multilinear functions with three adjustable parameters: ƒ = a1X1(x) + a2X2(x) + a3X3(x). Results are illustrated for three familiar examples: IR analysis of gaseous DCl, the electronic/vibrational spectrum of gaseous I2, and van Deemter plots of chromatographic data. These cases are simple enough for students in upper-level physical or advanced analytical courses to write and modify their own spreadsheets. In addition to the original x, y, and sy values, 12 columns are required: three for Xn(xi) values, six for Xn(xi)Xk(xi) product sums for the curvature matrix [a], and three for yi Xn(xi) sums for (b) in the vector equation (b) = [a](a). The Excel spreadsheet MINVERSE function provides the [e] error matrix from [a]. The [e] elements are then used to determine best-fit parameter values contained in (a). These spreadsheets also use a "dimensionless" or "reduced parameter" approach in calculating parameter weights, uncertainties, and correlations. Students can later enter data sets and fit parameters into a larger spreadsheet that uses Monte Carlo techniques to produce two-dimensional scatter plots. These correspond to Dc2 ellipsoidal cross-sections or projections and provide visual depictions of parameter uncertainties and correlations. The Monte Carlo results can also be used to estimate confidence envelopes for fitting plots.
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| Supplement |
The spreadsheets used for Tables 3-5 and a Monte Carlo spreadsheet used for Figure 6 are available. They were developed in a PC/Windows environment.
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 Contents |
DClFit.xls, I2fit.xls, MCmaster.xls, VanDeemfit.xls (Microsoft Excel); ReadMeFit.doc (Microsoft Word)
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| Download |
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| More Information |
Citation |
Ogren, Paul; Davis, Brian; Guy, Nick. J. Chem. Educ. 2001 78 827.
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Keywords |
Chromatography; Laboratory Computing / Interfacing; Physical Chemistry; UV-Vis Spectroscopy
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History |
Created:
Last Updated: |
May 8, 2001
August 31, 2005
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| Home > JCE Print > Journal of Chemical Education > Issues >
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