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Error Analysis Using the Variance-Covariance Matrix

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Department of Chemistry, Moravian College, Bethlehem, PA 18018-6650
Cite this: J. Chem. Educ. 2000, 77, 9, 1239
Publication Date (Web):September 1, 2000
https://doi.org/10.1021/ed077p1239
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    Abstract

    The variance-covariance matrix for a linear fit to y = b + mx is defined, and its use in computing the errors for derived quantities from the fit is illustrated. The matrix formalism is used to derive analytical expressions for the vertical and horizontal error bands, calibration curve error bands, and the error in the area under the regression line. Although most spreadsheet regression routines do not make the complete variance-covariance matrix available, the missing covariance matrix element can be computed easily. An Excel spreadsheet is presented that uses the matrix formalism to compute the error in analyte concentration from a fit of standard additions data.

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