Uncertain yield-density regression model with application to parsnips

Abstract

ABSTRACT Given the existing observations, regression is necessary to predict the relationship between the response variable and the explanatory variable. In general, we assume that the observed data are precise, but in actual life, precise observations are often difficult to be obtained, and most of them are imprecise interval data. As a result, the traditional regression analysis may lead to inaccurate results. When dealing with imprecise observations for more precise regression analysis, uncertainty theory is more appropriate. This paper will introduce the uncertain yield-density regression model and derive the optimal parameters by the least squares method. Besides, we provide residual analysis to obtain the distribution of the model's disturbance term and validate the appropriateness of the disturbance term using uncertain hypothesis testing. The predicted value and confidence interval for the model are also given. Moreover, three numerical examples of uncertain yield-density regression models will be given. Finally, this model will be successfully used in parsnips as an application.