| 一元总体最小二乘线性回归与解算分析 |
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| 引用本文： | 周世健,鲁铁定.一元总体最小二乘线性回归与解算分析[J].江西科学,2011,29(6):681-683,690. |
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| 作者姓名： | 周世健 鲁铁定 |
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| 作者单位： | 1. 江西省科学院,江西南昌,330029
2. 东华理工大学测绘工程学院,江西抚州,344000 |
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| 基金项目： | 国家自然科学基金项目，江西省自然科学基金，江西省科技支撑计划项目 |
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| 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...
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| 关 键 词： | 总体最小二乘 线性回归 奇异值分解 解算分析 |
The Total Least Squares for Linear Regression and Computation Analysis |
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| ZHOU Shi-jian,LU Tie-ding.The Total Least Squares for Linear Regression and Computation Analysis[J].Jiangxi Science,2011,29(6):681-683,690. |
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| Authors: | ZHOU Shi-jian LU Tie-ding |
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| Institution: | 1.Jiangxi Academy of Science,Jiangxi Nanchang 330029 PRC; 2.Faculty of Geomatics,East China University of Technology,Jiangxi Fuzhou 344000 PRC) |
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| Abstract: | 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. |
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| Keywords: | Total least squares Linear regression Singular value decomposition Computation analysis |
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