多元线性回归模型及其应用
摘要
本文介绍了多元线性回归模型，其过程分为模型构建、模型参数估计、模型检验和模型预测等几
个方面。通过对与我国物价指数 CPI 相关的几个因素建立初始多元线性回归模型，分析 CPI 的影响因素，
之后对该模型进行各种统计检验，在模型检验中发现初始模型中有部分变量的系数不能通过检验，可能
存在多重共线性的问题，最后采用逐步回归分析法来进行去除显著性不高的变量，并且建立新的模型，
最终找出了影响 CPI 的关键要素是农业生产资料价格和人均 GDP，通过最终确定的 CPI 与其影响因素之
间的线性回归方程可以清晰地得到各个指标对 CPI 的影响大小，进而为我国控制 CPI 提供方向性的建议
指导。
关键词
多元线性回归 CPI 影响因素 逐步回归
Multiple linear regression model and its application
Abstract
This article introduces the multiple linear regression model, and its process is divided into
several aspects: model construction, model parameter estimation, model testing and model
prediction. By establishing an initial multiple linear regression model on several factors related to
China's price index CPI, analyzing the influencing factors of CPI, and then carrying out various
statistical tests on the model, it is found in the model test that the coefficients of some variables in
the initial model cannot pass Test, there may be a problem of multicollinearity, and finally use a
stepwise regression analysis method to remove less significant variables, and establish a new
model, and finally find out that the key factors affecting CPI are agricultural production materials
prices and GDP per capita, Through the final linear regression equation between the CPI and its
influencing factors, we can clearly get the impact of various indicators on the CPI, and then provide
directional recommendations for the control of CPI in China.
Key words
Multiple linear regression CPI influencing factors stepwise regression
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