关键词: 总体最小二乘法, 回归参数, 奇异值分解法, 迭代算法, 显著性检验

Abstract: The adjustment model based on total least squares is superior to the ordinary least squares when coefficient matrix and
observation vector include errors. Singular value decomposition method and Euler-Lagrange approximation algorithm are two
commonly used regression parameter estimation methods for total least squares, but its derivation process involves Eckart-Young-
Mirsky matrix approximation theory, which is complicated and difficult to understand, making many learners feel unacceptable, which
limits its application. Therefore, this paper introduces a new iterative algorithm for regression parameter estimation. The theoretical
basis is rigorous and sufficient, the derivation process is clear and easy to understand, and the specific calculation is also easy to
program. Practical examples are used to verify the feasibility and effectiveness of the method. The test results show that the linear
regression model obtained by the algorithm has a good fitting effect.

Key words: total least squares, regression parameters, singular value decomposition method, iterative algorithm, significance tests