水文相关中的最小二乘回归问题探讨

在研究了水文相关中利用最小二乘原理进行回归分析方法的基础上，指出了传统水文回归分析方法的使用条件、局限性和存在的问题。提出了不同性质的变量在回归分析时应区别对待的概念。结合水文观测的实际情况，研究了相关变量观测值均存在误差情况下，以变量的观测误差作权进行回归分析的概念，提出了建立基于最小二乘原理基础上的双加权回归模型，并研究了该模型的解算方法。同时推导了估计参数和预测值的误差估计公式，通过估计参数和模型误差的研究，有助于提高水文变量回归的精度和误差估计水平。

Study on the Regression with Least Square Applied in Hydrology Correlation

On the basis of researching the hydrologic correlation regression with least square method, this paper not only puts forward the using condition, limitation and problems existing in the traditional hydrologic regression analyzing method, but also gives a new idea that variables of different types should be differentiated in regression. In consideration of the present hyclrometric fact that the values of non-relevant variables can be obtained infallibly, the regression method based on the weight of observational biases was explored, the double-weighted regression model using least square method was proposed, and the approaches and formulas of bias estimation both for the model and for parameters were presented. The research on estimating the bias of the model and parameters redounds to the improvement in the accuracy and precision for hydrologic variables regression and bias estimation.