Functional Regression and Correlation Analysis

Abstract

In fisheries, many applications of regression analysis are based on functional relations, but application of predictive regression results in two regression equations. Ricker proposed application of a method developed by Teissier to estimate the geometric mean functional relation when the parameters of a functional relation are of biological significance. Functional regression results in a single equation relating variables as opposed to the two equations that result when predictive regression is applied. The geometric mean functional relation also is given by bivariate normal correlation analysis when the correlation coefficient is 1. Bivariate normal correlation analysis provides a model for functional regression. An equation for variation of observed values about the functional regression line is obtained, and functional regression is compared with predictive regression. If the model assumptions are met, the one equation of functional regression is less precise for prediction than the two equations of predictive regression. However, the confidence intervals for the estimates of the slopes for functional and predictive regression are nearly the same.