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Regression analysis is to establish the regression relationship between dependent variables and independent variables. The data of traditional regression model are often assumed to be observed precisely. However this assumption holds only sometimes. Due to the influence of various uncertain factors, the data in reality is often inaccurate. Therefore, We treat real data as uncertain variables. Uncertain regression analysis is likely to provide an effective analysis method. Based on the uncertainty theory, the residual analysis of verhulst-pearl model is discussed in this paper. We use the least square method to estimate the parameters. And we also obtained the confidence interval of the response variables for the new explanatory variables. In the uncertain regression analysis, we propose a leave- $p$ -out cross-validation method for model selection under imprecise observation. We end up the paper with a numerical example of uncertain Verhulst-Pearl regression model and show that the model has a better prediction accuracy.

Leave-$p$ -Out Cross-Validation Test for Uncertain Verhulst-Pearl Model With Imprecise Observations