总体最小二乘求解线性回归模型的迭代算法

An iteration algorithm of total least squares for linear regression models

根据线性回归模型的特点,推导了一种解线性回归参数的总体最小二乘算法。并对其单位权中误差的评定进行了探讨,通过理论推导表明按常规的总体最小二乘解法求得的线性回归单位权中误差与实际不符,并对其进行了纠正。通过算例分析且与常规的总体最小二乘解法进行比较,结果表明了算法的正确性和可靠性。

According to the characteristics of the linear regression model,an algorithm of total least squares for solving linear regression parameters is derived.And the evaluation of the error of the mean square error of unit weight is discussed.The theoretical derivation shows that the error estimation of the general least squares solution for the conventional linear regression does not tally with the actual mean square error of unit weight,and corresponding corrections are applied.Through example analysis and comparing with conventional total least squares method,the results show the correctness and reliability of the algorithm.