Multiple Linear Regression Based On Multiple Cointegration Correction

The economic structure of Henan Province is in a transition period from high growth to high quality development,as the regional economic development has made a great leap from2001 to 2020.In the process of economic development in transition,it is particularly important to scientifically analyze the factors influencing economic development in Henan Province.However,when establishing regression models between multiple independent variables,multiple covariance between independent variables may occur,resulting in unstable regression coefficients,failure of ordinary least squares estimation,and too few filtered independent variables to effectively explain the influencing factors of development.This paper summarizes the theoretical methods for diagnosing and correcting multiple covariance and proposes that using improved stepwise regression,ridge regression and principal component-ridge estimation correlation theory can solve the problem of instability of regression coefficients caused by multiple covariance,and according to the regression coefficients can analyze the important influencing factors of regional GDP in Henan Province and correct the multiple covariance,so as to provide help for further analysis and forecasting.The article takes the data of 11 economic-related indicators in Henan Province from2001 to 2020 as an example,and screens the variables through stepwise regression based on the t-test,so as to achieve the purpose of correcting the multiple covariance;based on the correction effect,it further proposes to use ridge regression and principal component-ridge regression for correction.The eigenvalues and eigenvectors of the design matrix were first calculated quantitatively using MATLAB to diagnose the degree of multiple covariance;then the regression analysis of the factors influencing the regional GDP was carried out with the help of the relevant theories of principal component-ridge regression and ridge regression.Finally,a stepwise regression equation and a ridge regression equation were established based on the modified independent and dependent variables to forecast the GDP of Henan Province from 2021 to 2023,the results of the study provide an effective scientific basis for the Henan Provincial Party Committee,the provincial government and relevant departments to formulate corresponding economic policies and development strategies.