基于主成分分析的经济统计方法及应用_许莉莉.pdfVIP

第34卷第10期 煤炭经济研究 Vol.34 No.10 2014年 10月 CoalEconomicResearch Oct. 2014 基于主成分分析的经济统计方法及应用 许 莉 莉 （河南理工大学 经济管理学院，河南 焦作 454000） 摘 要：常用的线性回归方法只将因变量视为随机变量，其回归结果随坐标系选取的不同将发生相 应改变。受统计分析中主成分分析法的启发，提出了一种新的具有坐标无关性的一元线性回归方法 ——主成分分析法。用仿真例及实例验证了新方法与常规的最小二乘法相比回归系统偏差小，回归 精度高。主成分分析法是数值解，其计算量上的优势使其具有广阔的应用前景。 关键词：一元线性回归；经济统计方法；主成分分析；坐标无关性 中图分类号：F019 文献标志码：A 文章编号：1002－9605 （2014）10－0054－04 DOI:10.13202/ki.cer.2014.10.013 Economic StatisticMethodandApplicationbasedPrincipal ComponentAnalysis XULi⁃li （SchoolofEconomicsandManagement,HenanPolytechnicUniversity,Jiaozuo 454000, China） Abstract: A conventional linear regression method was only to consider a dependent variable as a random variable and the re⁃ gression results would be relevantly varied with the coordinate selected. With an illumination of a principal component analysis method applied in the statistic analysis, a new unary linear regression method with a coordinate independence- principal com⁃ ponent analysis method was provided. A simulation example and case were applied to verify a small deviation of the regres⁃ sion system in comparison with the new method and the conventional least square method and the regression accuracy was high. The principal component analysis method is a numerical solution and the advantage of the calculation value would have awideapplicationprospect. Key words: unarylinearregression; economic statistic method; principal component analysis;coordinateindependence 一重一元线性回归是最基本的问题，推导如下。 0 引 言 x,y