| 多元线性回归的整体最小二乘解和几何分析 |
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| 引用本文： | 周世健,唐伟靖,鲁铁定.多元线性回归的整体最小二乘解和几何分析[J].江西科学,2010,28(6):719-721. |
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| 作者姓名： | 周世健 唐伟靖 鲁铁定 |
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| 作者单位： | 江西省科学院;东华理工大学测绘工程学院; |
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| 基金项目： | 国家自然科学基金，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： | 在多元线性回归中,考虑自变量为随机变量的情形,在总体最小二乘准则下求解,根据奇异值分解理论,讨论了其求解公式及步骤;结合求解准则与几何分析的基本原理,对多元线性回归的整体最小二乘解作了初步的几何分析和说明,供参考与讨论。
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| 关 键 词： | 多元线性回归 总体最小二乘 几何分析 |
The Total Least Squares and Geometric Ananysis of Multi-linear Regression |
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| ZHOU Shi-jian,TANG Wei-jing,LU Tie-ding.The Total Least Squares and Geometric Ananysis of Multi-linear Regression[J].Jiangxi Science,2010,28(6):719-721. |
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| Authors: | ZHOU Shi-jian TANG Wei-jing LU Tie-ding |
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| Institution: | ZHOU Shi-jian1,TANG Wei-jing2,LU Tie-ding2(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 multi-linear regression,the solutions should be obtained under the total least squares.The formuale for the total least squares of the multi-linear regression have been discussed based on singular value decomposition(SVD) theory.In light of the solution creation and the principle of the geometric ananysis,the geometric ananysis and explaination for the total least squares of the multi-linear regression have been analyses elementarily. |
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| Keywords: | Multi-linear regression Total least squares Geometric ananysis |
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