An iterative approach for deriving and solving an accurate regression equation

This paper introduces a method for deriving an accurate regression equation based on a set of any paired data, and a technique for solving the equation. For a practical example, we used five hundred seventy-one pairs of sediment concentration and river flow data to derive an accurate sediment rating equation. The graphs of the measured and predicted sediment concentrations matched each other, and data correlation showed Nash–Sutcliffe efficiency (NSE) of 0.9999860, coefficient of determination (R2) of 0.99998679, root mean square error (RMSE) of 0.0345, mean average error (MAE) of 0.0067, volume error (VE) of 1, and sum of square error (SSE) of 0.678631. To explain the technique of deriving and solving the accurate regression equation, separate files of video presentation and excel spreadsheet are provided as supplementary materials. In general, the method can be used to model any processes, and any calibration and validation processes can be addressed.

本研究提出一种基于任意配对数据集推导高精度回归方程的方法，以及该方程的求解技术。作为实证案例，本研究采用571组泥沙浓度与河流流量配对数据，推导得到高精度输沙率方程。实测与预测泥沙浓度的拟合曲线高度吻合，数据相关性指标显示：纳什-萨克利夫效率（Nash–Sutcliffe efficiency, NSE）为0.9999860，决定系数（coefficient of determination, R²）为0.99998679，均方根误差（root mean square error, RMSE）为0.0345，平均绝对误差（mean average error, MAE）为0.0067，体积误差（volume error, VE）为1，残差平方和（sum of square error, SSE）为0.678631。为详细阐释该高精度回归方程的推导与求解技术，本研究附带了视频演示文稿与Excel表格两类补充材料。总体而言，该方法可用于建模任意过程，同时可适配各类校准与验证流程。