摘要
主要讨论了最常用的一元线性回归问题,分析了同时顾及自变量和因变量误差回归解算的相关问题,对采用同时考虑自变量和因变量误差的条件平差解算法,通过分析得出其解算出回归参数的估值与不考虑自变量误差情况下回归参数的估值一致,同时给出了同时考虑自变量和因变量误差的整体最小二乘解法,通过算例分析得出了整体最小二乘法解算的有效性。
Regression has been widely applied in many management economics etc. This paper mainly explored fields, such as natural science, social science, the unitary linear regression. Some problems about unitary linear regression considering together the errors of independent variable and cause variable are analyzed. On the analysis of the conditional adjustment algorithm considering together the errors of independent variable and cause variable, the author derived that the results from the conditional adjustment algorithm is equal to results of the common regression. In order to solve the problem of together considering any errors in variables, algorithm based on total least squares is presented. Practical computations have shown that the TLS algorithm is correct and validity in the unitary linear regression when considering any errors in variables.
出处
《西安科技大学学报》
CAS
北大核心
2009年第2期200-204,共5页
Journal of Xi’an University of Science and Technology
基金
国家自然科学基金资助项目(40874010
40574008)
江西省自然科学基金资助项目(2007GZC0474
0650007)
江西省教育厅科技资助项目(赣教财2006[208])
地球空间环境与大地测量教育部重点实验室开放基金资助项目(0606)
数字国土江西省重点实验室开放基金资助项目(DLLJ200506)
地理空间信息工程国家测绘局重点实验室开放基金资助项目
关键词
一元线性回归
整体解算
整体最小二乘
unitary linear regression
total calculation
total least squares
