The Theory And Applications Of Partial Least Squares Regression And Kernel Partial Least Squares Regression

With the development of the society, data analysis and its application has become increasingly important. Partial least squares regression and kernel partial least squares regression described in this article are two novel data analysis method. Ingredients were extracted from the dependent variable and the independent variables by partial least squares regression, and the number of selected components is determined by cross validation, then a multiple linear regression equation was set up. Kernel partial least squares regression is a method of transforming a nonlinear problem to a linear problem in different space through the kernel function and setting up a partial least squares regression model in different space.The main work is as follows:1. A high degree of linear correlation data is simulated in this paper, and a corresponding regression equation is established by partial least squares regression. By calculating the results of the simulation diagram and the multiple correlation coefficient, we obtained that the predicted value and the actual value is very close in this partial least squares regression. Then it is used to do some research in the real estate sales prices of three cities (Beijing, Changsha and Harbin). Taking the real estate sales prices as dependent variables, a partial least squares regression model is established and the independent variables are nine factors such as gross domestic product (GDP), real estate development investment, population density and so on. Combined with further calculations and analysis, we obtained that the real estate sales prices are mainly affected by gross domestic product, real estate development investment, per capital disposable income and total domestic money supply.2. The kernel partial least-squares regression models are respectively established with a set of high degree of linear correlation data and a set of nonlinear data, its show that kernel partial least squares regression is significant to solve these problems. Then the kernel partial least-squares regression model is set up in the research of the real estate sales prices. The results show that the model precision of kernel partial least squares regression is better than that of partial least squares regression.It can be seen through the research:when the sample size is not big enough and the number of independent variables is large, the fitting effect of partial least squares regression model is much better. Though kernel partial least squares regression is mainly used to solve the problem of nonlinear relationship between variables, but the fitting effect of it is also notable to solve linear regression in this article.