This paper presents an efficient semi-parametric method of identifying regression models based on a parametric copula-based joint probability distribution of input and output variables. This regression-model identification method uses our recently-introduced rolling pin method of estimating joint probability distributions, and therefore it can model highly nonlinear and nonmonotonic relationships. As the proposed method does not require any assumptions on the homoskedasticity, it can model relationships with noise terms whose variances depend on input variables. Moreover, it allows the user to calculate confidence intervals of the identified regression model through the estimated joint probability distribution. As the model-training computational cost increases quadratically with the number of variables, the method is suitable for large-scale applications such as modeling relationships in industrial processing plants. The application and performance of the proposed method are shown using two examples. (C) 2015 Elsevier Ltd. All rights reserved.