An iterative approach for deriving and solving an accurate regression equation

ABSTRACT

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 ($R^2$) 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.

KEYWORDS:

• Regression equation
• polynomial function
• sediment rating curve

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/13873954.2024.2313014

Additional information

Funding

This research was funded by the German Academic Exchange Service and Universität der Bundeswehr München.