线性回归模型中多重共线性问题的研究

发布时间：2018-06-28 15:56

本文选题：线性回归模型 + 多重共线性　；参考：《渤海大学》2017年硕士论文

【摘要】：在多元线性回归模型的实际应用中,解释变量之间几乎不存在完全不相关的现象。尤其是在研究某经济问题时,往往涉及多个变量,各个变量之间普遍存在着多重共线性的现象,因而会给模型造成一定的影响。其不仅会影响参数的估计,还会使模型的误差扩大,导致模型的稳定性遭到破坏。因此,本文主要针对这一问题进行了讨论与研究。现如今,随着科学的进步与发展,人们已经探究出很多理论与功能各不相同的方法来解决多重共线性问题,通过它们的优劣,为人们选择具体适当的模型提供了有力的依据。本文主要介绍了两种方法:岭回归方法和主成分回归方法,理论与实际相结合,对这两种方法做出了诠释。首先,从理论上分析了两种方法的基本理念;其次,通过例子具体来说明两种模型的不同作用和特点。除此之外,本文还介绍了岭回归分析中广义岭估计的一种改进方法。通过计算,比较均方误差与均方残差的数值大小,对模型的优劣加以区分,以便人们选择更好的适当的模型来解决问题。
[Abstract]:In the practical application of multivariate linear regression model, there is almost no complete disconnection between explanatory variables. Especially in the study of a certain economic problem, many variables are often involved, and there is a phenomenon of multiple collinearity between the variables, which will have a certain impact on the model. It will not only affect the estimation of parameters, but also enlarge the error of the model, and destroy the stability of the model. Therefore, this paper mainly discusses and studies this problem. Nowadays, with the progress and development of science, people have explored a lot of different theories and functions to solve multiple collinear problems. Through their merits and demerits, they provide a powerful basis for people to choose specific and appropriate models. This paper mainly introduces two methods: Ridge regression method and principal component regression method. Firstly, the basic concepts of the two methods are analyzed theoretically. Secondly, the different roles and characteristics of the two models are illustrated by examples. In addition, this paper introduces an improved method of generalized ridge estimation in ridge regression analysis. Through calculation, the numerical value of mean square error and mean square residual is compared, and the advantages and disadvantages of the model are distinguished, so that people can choose a better model to solve the problem.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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