摘要
相关系数矩阵是用于表现变量之间相关关系的统计分析工具.然而,多元变量之间的相关关系极易受各种复杂因素的影响,因此并不能仅仅依据该矩阵中的数值来解释变量间的关系.而利用偏相关系数可以进一步地反映变量间的本质联系.系统研究了相关系数矩阵的逆矩阵与行列式中的深刻内涵,一方面讨论了相关系数矩阵的逆矩阵与偏相关系数之间的数量联系;另一方面,从数学上证明了相关系数矩阵的行列式与变量间各阶次偏相关系数的等式关系.此外,还进一步指出这些研究结论在多元线性回归建模中的指导意义.
The sample correlation coefficient matrix is used for manifesting the relationship between variables.However,due to multivaxiable variants＇ relationship is easily affected by some complicated factors,judging by the sample correlation coefficient matrix only is unadvisable.Partial correlation coefficient can further reflect the contact.The paper reveals a systematic analysis of the implied information,lying in both the inverse of correlation coefficient matrix and the determinant of correlation coefficient matrix.The connection between the sample correlation coefficient matrix and the partial correlation coefficient has been discussed.Also a quantitative relationship between the determinant of sample correlation coefficient matrix and partial correlation coefficients of each order is achieved.Furthermore,the paper indicates the significance of the proposed theory in multiple linear regression modeling.
出处
《数学的实践与认识》
北大核心
2015年第6期180-185,共6页
Mathematics in Practice and Theory
基金
国家自然科学基金重点国际合作项目"海量高维混合数据的统计建模方法及其应用"(71420107025)
关键词
相关系数矩阵
偏相关系数
多元线性回归
correlation coefficient matrix
partial correlation coefficient
multiple linear regression
