Comparison of theoretical derivations, simple linear regressions, multiple linear regression and principal components for analysis of fish mortality, growth and environmental temperature data

Abstract

Natural mortality of fish populations is difficult to estimate, and parameters for growth and environmental temperature, which are easier to estimate, have been applied to predict fish natural mortality using multiple linear regression. There are theoretical relations among all of the variables applied in the multiple linear regression, and there is high multicollinearity; the results of the multiple regression differ considerably from the theoretical relations among the variables. Simple linear regression results agree with the theoretical results but they are not as precise for prediction of mortality as multiple linear regression. A principal components analysis correctly identifies the important variables and the relations among variables but it is more complex than multiple linear regression and yet is not any more precise for predictions. A plot of the first two principal components separated the data into two groups: one was temperate water species and one was warmer water species. The analysis confirms the limitations and advantages of different data analysis methods. Copyright © 2001 John Wiley & Sons, Ltd.