Study On The Methods Of Testing Heteroscedasticity In Regression Model

Regression analysis is often used to measure the relationship between variables.In many regression models,one of the general assumptions about error items is that for all observations,the variance of the model error item should be constant.Unfortunately,in practical applications,such as in the pharmaceutical,geographical,economic and other fields,due to the measurement errors,omission of explanatory variables and the influence of stochastic factors,the variance of error items is usually not constant,which is called heteroscedasticity.The generation of heteroscedasticity poses difficult problems for researchers in various fields,that is why the existence of heteroscedasticity should be tested before regression analysis.The importance of studying heteroscedasticity is mainly that if there is no variance in the model,the best linear unbiased estimator(BLUE)and nonpartial difference estimation of model parameters can be obtained by using the least squares(OLS)theory,thus reducing the process of model construction to a great extent,otherwise,if there is heterogeneous variance in the model,and it is not tested and handled properly,which will eventually lead to the estimation of the wrong model parameters.There are many traditional methods to test heteroscedasticity,such as graphic test,Breusch-Pagan test,White test,Goldfeld-Quandt test,Park test,Glejser test,Spearman rank correlation coefficient test and so on.The main research results of this paper are as follows:(1)In view of the heteroscedasticity in the regression model,the existence of heteroscedasticity in the model is tested by Breusch-Pagan test using the bptest()function in the lmtest package by using R stastical software.The results show that there is heteroscedasticity in the model.This method is simple and quick to use,and the test results are more accurate.(2)The multivariate regression model in this paper is tested by White test,and the heteroscedasticity test is carried out under the condition of constructing different forms of auxiliary regression equations.The results show that there is heteroscedasticity in the model.However,the operation of this method is more complex,if the regression independent variables are more,it will take a lot of experimental time.(3)The Goldfeld-Quandt test is used to test the existence of heteroscedasticity,which is also called two-sample test.Ordinary least square regression is performed on two sample respectively to construct Fstatistic,and finally to judge whether there is heteroscedasticity or not.(4)In this paper,an improved Glejser test method is proposed to construct an auxiliary regression model based on the fitting value as a new variable.Through case analysis and simulation,the results show that the test method is feasible and convenient.This paper focuses on the study of Glejser test,and puts forward an improved Glejser test.Through case analysis and simulation analysis,the implementation of this method is simpler and more effective than the traditional Glejser test before.