The choice of a regression model of the body weight on the height via an empirical bridge

A. P. Kovalevskii ; E. V. Shatalin

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2015), pp. 35-47

Résumé

An empirical bridge can be used for analysis of correspondance between regression models and observed data. If a model does not describe data correctly, then its response values deviate systematically from the regression curve, and this deviation can be revealed by summing the regression residuals. One needs to know the limiting distribution of the process for centered and normalized partial sums of regression residuals to study significance of these deviations. This process is the empirical bridge. We obtain a limiting process for a simple linear regression model. The main goal of this article is to apply the empirical bridge for the analysis of regression models describing the dependence of an individual’s body weight on his height. We considered a number of regression models of this dependence and compared models based on their empirical bridges. We used data on the height and weight of female students of the first course of Volga State Medical University. The study revealed the best model $\ln W_i=a+2\ln H_i+\varepsilon_i$. This model should be used for analysis of deviations from the normal body weight.

Détail

Keywords: linear regression, empirical bridge, dependence of weight on height.