摘要
针对自变量为随机变量情形,在最小二乘准则下,一元线性回归所得到的回归参数估计及其拟合直线存在二义性问题,为确保解算结果的唯一性和一致性,需用总体最小二乘准则进行解算,对总体最小二乘准则进行了描述,利用奇异值分解方法,讨论了解算公式,最后用一数字算例,用最小二乘和总体最小二乘方法进行了计算和结果分析,得到了一些结论,此方法对于工程实践的数据分析具有较大的参考价值。
The independent variables are the stochastic variables in the practice, the regression parameters and the fitting straight for a lipear regression are the ambiguity problem under the Least Squares criterion. The total least squares has been imported to insure the uniqueness and consistency of the computation results. The criterion of the total least squares has been described in this paper, the computation formulae has been discussed using the singular value decomposition methodology. Finally, the conclusions have been obtained that the numerical example calculated using the least squares and the total least squares, the results show the method is reference to the data processing of the engineering practice.
出处
《江西科学》
2011年第6期681-683,690,共4页
Jiangxi Science
基金
国家自然科学基金项目(40874010)
江西省自然科学基金项目
江西省科技支撑计划项目
关键词
总体最小二乘
线性回归
奇异值分解
解算分析
Total least squares, Linear regression, Singular value decomposition, Computation analysis
作者简介
周世健（1966-），男，江西安福人，博士，教授，研究方向：空间数据处理理论与应用分析。
