Application of DGM(1,1) and linear regression based on entropy weight method

Abstract

Grain security is an important strategic issue, which is associated with the development of economy, social stability and national independence. In order to ensure national grain security, one of the tasks of us is to make accurate forecast of grain production. Using a single forecasting method may lead to the lower forecasting accuracy due to the useful information missed. The combined model can overcome the disadvantages of the single model and effectively gather more useful information. Therefore, it is more suitable to use combined method to solve the problem of the complicated economic system with incomplete information. Grey system theory is widely used in many fields such as engineering control, management decision-making and social economy. The simplest of the grey forecasting model is GM (1,1). Dr. Xie Naiming proposed a discrete DGM model because the prediction accuracy of the traditional GM (1,1) model often troubles the researchers; Multiple linear regression analysis is used to forecast the grain yield in this paper. According to the number of influencing factors in the model and the relationship between the influencing factors and the predicted objects, regression analysis can be divided into one linear regression analysis, multiple linear regression analysis and nonlinear regression analysis; Regression analysis method predicts future or establishes the relationship of things based on mutual influence, interrelated, two or more factors of the measured or survey data. Then, through the determination of the future influencing factors, the process of indirectly exporting the data is measured; Arithmetic average method, variance reciprocal method, mean square reciprocal method, simple weighting method, binomial coefficient method and optimal weighting method are often used to weight in combined model. The paper adopts entropy method to combine linear programming model and grey prediction model. Then, this paper puts forward the grey linear regression combination model. The paper combines the DGM(1,1) model with multiple linear regression model, uses the entropy weight method to determine the weight of the results of two models, and forecasts the grain yield form 2010 to 2015. The results show that the average error of DGM(1,1), multiple linear programming and the combined model are 1.34%, 0.73% and 0.57%. It can be seen that the combined model of this paper improves the prediction accuracy on the basis of the two models, which can be better applied in the prediction of grain yield.