Regression Analysis Method Based On Differential Equations

Statistics is the science dealing with data,it provides a set of methods and tools for data analysis.Regression analysis,as an analysis method to study the relation-ship between numerical independent variables and numerical dependent variables,has become one of the most commonly used statistical tools.Regression analysis method can be divided into linear regression and nonlin-ear regression according to model structure,the process of linear regression can be roughly divided into the estimation of regression coefficients,the significance test of regression equation and the estimation and prediction.In traditional nonlinear re-gression,the first step is to determine the form of function,and several possible curve functions can be selected preliminarily.Next,the variables should be transformed,for the regression equation can be transformed into a linear equation,and then we can estimate the parameters by the linear regression analysis method.Finally,a comparative analysis is conducted to select the optimal quantitative relation.Because of the complexity in operation and the large errors in fitting process of traditional nonlinear methods,this paper presents a regression analysis method based on differential equations.This method does not need to change the original variables,and is suitable for linear and nonlinear models.At the same time,there is no requirement for the number of independent variables,it can be applied to both univariate and multivariate regression analysis.The structure of the paper is divided as follows:Chapter 1 introduces the research background and current situation of regression analysis at home and abroad,then briefly describes the research content of this paper.Chapter 2 introduces the main contents of traditional regression analysis method and analyses its existing problems.In Chapter 3,a differential equation model is introduced,and a regression analysis method based on differential equations is proposed on the basis of processing a set of actual data.In the fourth chapter,one new differential equation model is proposed,then use traditional and new methods to process data;and the fitting results are compared and analyzed.Finally,this paper is summarized in the fifth chapter.