Analyses of Two Different Regression Models and Bootstrapping

Abstract

Regression methods are used to explain the relationship between a single response variable and one or more explanatory variables. Graphical methods are generally the first step and are used to identify models that can be explored to describe the relationship. Although linear models are frequently used and they are user friendly, many important associations are not linear and require considerably more analytical effort. This study is focused on such nonlinear models. To perform statistical inference in this context, we need to account for the error structure of the data. The experimental design for the nutrition data that we use called for each subject to be studied under two different values of the explanatory variable. However, some participants did not complete the entire study and, as a result, the data are available for only one value of the explanatory variable for them. In the analysis section, the bootstrapping method will be used to re-sample the data points with replacement, which will then be used with a nonlinear parametric model. The confidence intervals for the parameters of the nonlinear model will be calculated with the reflection method for the nutrition data set. In addition, the break point of the spline regression will be determined for the same data set. Although the nutrition data set will be used for this study, the basic ideas can be used in many other fields such as education, engineering and biology.