二因素模型下可决系数平方研究计算 应用数学专业

二因素模型下可决系数平方研究计算摘要：两个及两个以上控制变量对观测变量产生显著影响的被称作多因素方差分析。多因素方差分析不仅能够分析多个因素对观测变量产生的独立影响，而且能够分析多个控制因素的交互作用对观测变量的分布是否会产生显著影响，找到最有利于观测变量的最优组合。可决系数（即复可决系数或多重可决系数）为解释变差占总变差的比重，用来表示解释变量对被解释变量的解释程度。可决系数可以作为综合度量回归模型对样本观测值拟合优度的度量指标。关键词：二因素模型；可决系数；修正可决系数Study and calculation of the Square of the determinable coefficient under the Two-Factor ModelAbsrtact: Two or more control variables have a significant effect on the observed variables, which are called multivariate anova. Multi-factor analysis of variance can not only analyze the independent effects of multiple factors on the observed variables, and can analyze multiple control factors in the interaction of the distribution of observation variables will have a significant impact, find the most beneficial to the optimal combination of the observed variables. The coefficient of determination (i.e., the complex or multiple deterministic coefficient) is used to explain the degree of explanatory variable to the explained variable. The coefficient of determination can be used as a measure to measure the goodness of the sample.Keywords: Two-factor model; determinability coefficient; modified determinability coefficient引言 在回归分析中，模型的拟合度一般采用可决系数（2R ）和修正的可决系数（2R ）来衡量，但2R 会受到自变量个数，样本数和可决系数本身大小等多重因素的影响，所以难以得到准确的分布函数及其特征。判断回归模型拟合优度程度优劣最常用的数量是指标可决系数（又被称为决定系数），是建立在对总离差平方和进行分解的基础上。可决系数是对回归模型拟合程度的综合度量，2R 越大，模型拟合程度越高。2R 越小，则模型对样本的拟合程度越差。然而可决系数在实际的模型运用中往往会受到许多因素的...