Study On The Regression Method Based On Quasi-linear Function

Regression analysis is a mathematical method used for dealing with the relationship between variables, which is the most commonly used method of mathematical statistics. Regression has a profound and vivid real background. it comes from the production practice and science and technology. Regression has been proved to be a powerful tool for analyzing and solving problems in modern science and technology. It has a very important and widely used in solving the prediction and control, production process optimization, industrial and agricultural production and scientific research and other fields.Regression analysis is generally divided into linear regression analysis and non-linear regression analysis, in this paper, we focus on the following three aspects:unitary linear regression, unitary non-linear regression and unitary quasi-linear regression.Firstly, we introduce the modeling process and parameter estimation of unitary linear regression. Then we analyze the characteristic of nonlinear regression. There are some defects of nonlinear regression which directly affect its application in real life, such as the objective function after linear transformation is inconsistent with the original objective function:the selection strategy of non-linear regression function is not effective; parameter estimation of higher order equations is difficult and so on.Base on the concept of quasi-linear function, we establish the quasi-linear regression model (denoted by QRM, for short). Because the points of junction are uncertain, we can not get the estimated parameters through analytical methods. so we give a solution method combining with Genetic Algorithm (GA-QRM). GA-QRM can simplify the computing process. And we can control the genetic algorithm parameter settings to reflect different decision-making consciousness.Finally. we varify the performance of GA-QRM by a concrete example, and analyze the fitting results by residual analysis. The results show that QRM not only contains the linear regression method, but also could slove a class of nonlinear regression problems. The application of QRM will be widely used in prediction and management, industrial and agricultural production and scientific research and other fields.