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Measurement errors and curve fitting

1. Results of unweighted fit results to Pearson’s data Method of calculation least-squares Slope To the Editor: In a recent paper, Brace (3) discussed the problem of fitting straight lines to experimental data when both variables are known to have errors, the errors themselves being unknown. A straightforward and effective method was presented to improve the regression coefficients calculated with the conventional’ leastsquares fit. Brace also noted that the improved value of the slope of the regression line obtained by applying his method is the same as that obtained by calculating the geometric mean of the slopes found by the regression of y on x and the regression of x on y. In the past few years, a number of investigators (1,49,11-16) have discussed methods of dealing with a closely related problem of interest, that of linear (and polynomial) least-squares fitting when both variables are known to have errors and the errors themselves are known. The known errors in both variables are used to weight the least-squares calculation. (For a brief review of this problem see Ref. 1.) One result (I, 16) of particular relevance to the reader of Brace’s paper is that, when errors exist in both http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png AJP - Regulatory, Integrative and Comparative Physiology The American Physiological Society

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