Ridge Estimation Method For Multicollinearity In Linear Regression Models

In this big data era,regression analysis is becoming more and more widely used in various fields,including economy,society,medicine,and bioinformatics.However,when studying the linear model in regression analysis,there will be multiple collinearity between the independent variables,which leads to the instability of the model,and even the problem that the regression coefficient does not match the actual meaning.This requires finding a solution to the multicollinearity problem in linear models.This article introduces the ridge estimation method to solve the multi-collinearity problem of linear models from two aspects of theoretical and experimental simulation.First,the diagnostic methods of multi-collinearity are introduced,such as: intuitive judgment method,eigenroot judgment method,variance expansion factor method,Conditional number discrimination method,etc.,used to know which models exist multicollinearity,and cited specific examples,followed by introducing solutions,such as:eliminating unimportant variables,increasing sample size,biased estimation of regression coefficients,etc.The focus is on the ridge estimation method.This article introduces the concept,basic idea,nature,and selection method of the ridge parameter k.In particular,the generalized ridge estimation and the universal ridge estimation are also applied to solve the multicollinearity problem.Finally,the theory of this paper is verified by examples.The program is written using SAS through data,and it is found that there are multiple collinearity between variables,and the ridge estimation method is used to establish the model and optimize the model to solve the problem.This paper lists the medical aspects of hemoglobin and trace elements.The relationship between the content,through the analysis of the data and the analysis of the results of the stepwise regression analysis,the ridge estimation method is more excellent;by examining the relationship between the import value and gross domestic product,savings,and total consumption,it is found that the original model is due to variables The multi-collinearity between them is inconsistent with economic theory.After using the ridge estimation method to solve the multi-collinearity problem,the sign of the regression coefficient is consistent with the economic theory,and compared with the partial least square method,the results show that the ridge estimation method is superior to the partial minimum The method of double multiplication has verified the superiority of the ridge estimation method;at the same time,the ridge estimation method can also predict the change trend of the passenger traffic volume of civil aviation.From the conclusions of several applications,the ridge estimation method can better reduce the impact of the multicollinearity problem on the model,visually see the improvement,and make the model more stable.