A non‐sinusoidal regression function for least‐squares fitting of rhythmic data

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Abstract
The frequently used cosine as regression function is, in general, not suited for the extrapolation of maximum, minimum, and over‐all mean of rhythmic data, as it is not a priori clear that the rhythm is sinusoidal, and curve‐fitting to non‐sinusoidal data leads to erroneous results. For rhythms with one peak and one trough the 5‐parameter function is suggested as regression function. With this function maximum and minimum may be any distance apart and have independently any shape and height. The parameters are determined by a nonlinear regression computer program, weighted least squares being used for repeat measurements. Formulas for the calculation of maximum, minimum and mesoras well as first order estimates of their standard errors are given.

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