The advantages and difficulties of application of Pad\'e approximants to two-dimensional regression analysis are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations in case of rational functions. The possibility of using Tikhonov regularization technique to avoid overfitting is demonstrated in this approach. To illustrate the efficiency of the suggested method, several practical cases from physics and reliability theory are considered.

翻译：讨论了将Pad\'e 近似物应用于二维回归分析的优点和困难,在最小方块方法中建议了残留物的新表述方式,在合理功能情况下导致一个线性方程系统,在这种方法中说明了利用Tikhonov正规化技术避免过度调整的可能性,为说明所建议的方法的效率,考虑了物理学和可靠性理论的一些实际案例。