On Comparing Two Dependent Linear and Nonlinear Regression Models

Linear and nonlinear regression models are flexible methods of data analysis that may be appropriate whenever a quantitative response variable is to be examined in relationship to any other explanatory variables. This relationship can be expressed by different models and equations. In some fields, such as in agriculture, biology, hydrology, neural network, and psychology, researchers need to analyze whether the relationship between response variable and predictor variables differ in two fitted models on the same dataset. In other words, we are interested in the comparison of two regression models for a single dataset. In this article, we will use the nonparametric methods to establish hypothesis testing for the equality of two dependent regression models. Then, a simulation study is provided to investigate the performance of the proposed method. Also, the proposed method is applied to compare the different linear, quadratic, cubic, and exponential models that can be fitted on a real dataset.