Large inefficiencies of unweighted least‐squares treatment of logarithmically transformed A exp(–kt) data

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Abstract
The standard deviations (σ) of the parameters of a single exponential function can vary strongly with the range of the data, the character of the underlying error structure and also with the inclusion or omission of the appropriate relative weights. These effects are studied quantitatively, for least squares analysis of uniformly spaced, ln‐linearized simulated data. The parameters, k and A, extracted are less precise when weighting is omitted, increasingly so as the range of the data increases, particularly for the case of equal amplitude errors for each A exp(–kti) datum. The results, expressed as efficiencies (σ2[using weights]/σ2[omitting weights]), show < 1% efficiency in some cases. This is tantamount to ignoring > 99% of the data and treating the remainder with proper relative weighting.
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