线性回归模型中一类式子的推导  

A Class of Formulas' Derivation in Linear Regression Model

作　　者：甘胜进[1] 林娟[1] 

机构地区：[1]福建师范大学福清分校数学与计算机科学系,福建福清350300

出　　处：《福建师大福清分校学报》2013年第2期23-25,共3页Journal of Fuqing Branch of Fujian Normal University

基　　金：福建师范大学福清分校科研项目(KY2012025)

摘　　要：线性回归中的最小二乘估计具有线性无偏估计类中方差最小的性质,而这个性质的证明较为复杂,许多文献都予以省略,复相关系数的定义更是直接给出,并未从统计意义上加以解释,回归方程显著性检验所给出的统计量往往是从约束最小二乘出发得到,本文利用简单方法来推导这些性质,并且导出检验统计量的分布,解释了复相关系数的统计意义,以及回归模型中不相关的推导.Least square estimator has the minimum variance of the all linear unbias estimates.However,the proof of this property is complicated,and some references ignore it.The definition of the correlation coefficient is given directly without explaining the statistical sense.The significant test statistic of regression equation generally is obtained by constrained least squares estimation.This article adopts a simple method to derive these properties,and derive the distribution of the test statistics.It also explains the statistical significance of the multiple correlation coefficients and gives the cause of the uncorrelation in the definition of the regression model.

关 键 词：LS估计 BLU估计 投影阵 复相关系数 

分 类 号：G65[文化科学—教育学]