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双因素试验回归分析和方差分析的转化

发表时间:2009-07-15  浏览量:1509  下载量:476
全部作者: 李晓燕,胡锡健
作者单位: 新疆大学数学与系统科学学院
摘 要: 简要介绍了回归分析和方差分析的基本原理,并根据实际问题中双因素无重复试验的具体实施情况,分别采用回归分析法和方差分析法进行了分析讨论。在回归分析法中,首先对试验数据进行观测,研究自变量及结果变量的相关性和变化规律,给出假定的回归模型并对参数及其置信区间进行估计推断;在方差分析法中,双因素试验观测数据虽较多,但在因素水平较少的情况下,可以通过重新调整数据结构设置,使其变为正交试验设计模式,从而可单独对某因素进行显著性影响的评判,即方差分析。最终得出对同一问题在适当条件下2种方法的可实现性。
关 键 词: 数理统计;回归分析;方差分析;最小二乘原理;离差平方和;双因素
Title: The transformation between regression analysis and variance analysis about double factors experiments
Author: LI Xiaoyan, HU Xijian
Organization: College of Mathematics and System Sciences, Xinjiang University
Abstract: This paper introduced the fundamental rules of regression analysis and variance analysis and discussed the two methods by giving a practical example of double factors experiment without repetition in the real world. For regression analysis, the experiment data should be observed carefully and the relativity between independent variables and resultant variables and the changing rules should be studied. The proposal model was presented and the values of the parameters and corresponding credible intervals were assessed. For variance analysis, although the number of data was great, when the factor levels were not too much, the experiment design mode could be changed into orthogonality by adjusting the data structure, and thus the judgement on the effects arose by some factor could be carried out independently (variance analysis). And it came to a conclusion that under some appropriate conditions one method can be replaced by another to explain the phenomena.
Key words: statistics; regression analysis; variance analysis; the least squares principle; the sum of the warp square; double factors
发表期数: 2009年7月第13期
引用格式: 李晓燕,胡锡健. 双因素试验回归分析和方差分析的转化[J]. 中国科技论文在线精品论文,2009,2(13):1392-1395.
 
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