Surely all scientists are acquainted with the method of least squares (LS) for fitting data to a straight line, and by now many if not most also use it to fit data to more complex relations that require nonlinear LS (NLS) and weighting. (Note: Use here of “fitting data to models” is fully consistent with the attitude of W. Edwards Deming in his important book, Statistical Adjustment of Data.) Probably far fewer are aware that NLS can be used easily to (1) solve systems of equations, and (2) propagate uncertainty – applications where typically the number of data points equals the number of adjustable parameters, making the fits exact. Key to the first of these is the recognition that each of the n data points can be fitted to a different equation (a variation on “global” LS). The second requires use of the a priori covariance matrix, which is appropriate when the data variances are considered known and does not vanish for exactly fitting data. Algorithms will be illustrated for several chemical applications -- like coupled equilibria and Arrhenius analysis of temperature-dependent kinetics rate constants -- using KaleidaGraph and Excel. Similar procedures will be shown for NLS fitting of data having uncertainty in more than one variable.

Simple algorithms for some unconventional uses of the method of least squares

2019 Fall National Meeting

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