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It is folklore that the standard error of the estimate of a least-squares linear fit in logarithmic space to the curve y = axb approximates the percentage error of estimates made using that curve. This report explains in non-probabilistic terms the relationship between nonlinear-least-squares-fit characteristics in arithmetic space and the corresponding linear-least-squares-fit characteristics in log space. The relationship between the parameter values and the standard errors of the estimate in arithmetic and log space is derived by a Taylor-series analysis.
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Philip H. Young (1999) studied this question.
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