Evaluating Goodness-of-Fit in Comparison of Different Expressions for Length-Weight Relationship in Fishery Resources

Abstract:

To find out the optimal length-weight relationship expression of fishery species, eight different expressions were used to fit the length-weight relationships in 18 fishery species (nine fish species, two shrimp species, three cephalopoda species, three crab species and one mantis shrimp species), including Linear Regression Function, Body Mass Index, Power Regression Function and Polynomial Function, and the goodness-of-fit of each expressions were compared by adjusted R-square, Residual Standard Deviation (RSD), and Fitting Optimization Index of Curve Regression which is proposed by Zhang. The results turned out that the polynomial equation W = a + b * L³ + c * L² + d * L showed the best goodness-of-fit, while the linear equation W = a + b * L and BMI equation W = a * L² showed the worst goodness-of-fit. Combined with prediction curve of regression function, there may be over-fitting in the model of polynomial function. In this research, the expressions W = a + b * L^c was proved to show the best goodness-of-fit in length-weight relationship at given simples or populations, and the constant term ‘a’ as an error may not be zero for samples.

• Periodical: Applied Mechanics and Materials (Volumes 651-653)
• Pages: 337-343
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.651-653.337
• Online since: September 2014
• Authors: Hai Long Xu, Yong Chen, De Xian Gu, Xiu Ting Qiao*
• Keywords: Comparison, Goodness-of-Fit, Length-Weight Relationship

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