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December 1, 1968BioScience196 citations

Calculation and Miscalculation of the Allometric Equation as a Model in Biological Data

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JZJerrold H. Zar

Key Points

  • This research aims to evaluate the effectiveness of the allometric equation as a regression model in biological data and its commonly used fitting method.
  • Examined the fitting of the allometric equation Y = βXα using least squares method.
  • Utilized logarithmic transformation for both variables to approximate parameters β and α.
  • Provided an example highlighting the pitfalls of the current transformation procedure.
  • Demonstrated that the logarithmic transformation often leads to poor approximations of β and α.
  • Showed that erroneous conclusions can arise from the current method of fitting this model.
  • Recommended an alternative procedure for a more accurate approximation.

Abstract

The allometric equation Y = βXα is widely used as a regression model in biology. The common procedure for fitting this model by the method of least squares involves the logarithmic transformation of both variables: log Y = log β + α log X. This transformation procedure results in a least squares solution which only approximates β and α and often the approximation is a poor one. That erroneous conclusions may arise from the use of the logarithmic transformation is demonstrated with an example, and a preferred procedure is recommended.

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Cite This Study

Jerrold H. Zar (1968) studied this question.

synapsesocial.com/papers/69f3ee9bdc238f81977998b8https://doi.org/10.2307/1294589
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