| 几种一元拟线性回归中的问题与改进措施 |
| |
| 引用本文： | 王仲锋,冯仲科.几种一元拟线性回归中的问题与改进措施[J].东北师大学报(自然科学版),2006,38(4):45-52. |
| |
| 作者姓名： | 王仲锋 冯仲科 |
| |
| 作者单位： | 北京林业大学资源与环境学院,北京,100083;长春工程学院勘查与测绘学院,吉林,长春,130021;北京林业大学资源与环境学院,北京,100083 |
| |
| 基金项目： | 国家自然科学基金，国家高技术研究发展计划(863计划)，北京市自然科学基金 |
| |
| 摘 要： | 讨论幂函数、指数函数、双曲函数及S型曲线通过换元进行线性回归时,所满足的最小二乘条件,指出换元线性化回归存在的问题,提出了改进措施,并给出幂函数和双曲函数回归的实际算例.理论分析与实验表明,换元后的因变量具有异方差性,致使拟线性回归参数的精度较低,但拟线性回归的参数精度可通过加权回归的方法得到大幅度提高.
|
| 关 键 词： | 回归分析 拟线性回归 幂函数 指数函数 双曲函数 S型曲线 异方差性 |
| 文章编号： | 1000-1832（2006）04-0045-08 |
| 收稿时间： | 2006-02-22 |
| 修稿时间： | 2006年2月22日 |
On the problem and improved measure in some quasi-linearization regression with one argument |
| |
| WANG Zhong-feng,FENG Zhong-ke.On the problem and improved measure in some quasi-linearization regression with one argument[J].Journal of Northeast Normal University (Natural Science Edition),2006,38(4):45-52. |
| |
| Authors: | WANG Zhong-feng FENG Zhong-ke |
| |
| Institution: | 1. College of Resources and Emvironment, Beijing Forestry University,Bijing 100083, China; 2. School of Prospecting and Surveying,Changehun Institute of Technology, Changchun, 130021, China |
| |
| Abstract: | This paper discusses the least square condition that is needed by power function,exponential function,hyperbolic function and S-shape curve when they are made linear regression by substitution,points out the problem to use the linearization method,narrates the improved linearization method,and gives two practical calculated examples of power function and hyperbolic function regression.It is proved by theoretical analysis and experiments that dependent variables after substitution have heterscedasticity,and it makes the precision of the parameters estimated by quasi-linearization regression become lower,but the parameters precision of quasi-linearization regression can be improved substantially by giving weights to the dependent variables after substitution. |
| |
| Keywords: | regression analysis quasi-linearization regression power function exponential function hyperbolic function S-shape curve heteroscedasticity |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
