A Modified Algorithm Of Partial Least Squares Regression And Its Application

Partial least squares regression (PLSR) is a sophisticated multivariate analy-sis method ,which was first raised by economist Herman Wold and others in Swe-den in 1964.It is Mainly used to solve multivariate regression analysis of multiplevariables relevance or variable sample points more than the actual cases. As Itcombines multiple linear regression analysis, principal components analysis andcanonical correlation analysis of the basic functions of integration. Therefore it isknown as the second generation of multivariate statistical analysis. The methodhas been widely used in chemical measurement, industrial design, econometrics,and other areas.The main content of this paper can be summarized as follows :The first part deals mainly with the partial least squares method of historyand current situation as well as the recent hot issues summarized.The second part details the partial least squares regression to the basic idea,mathematical principles and single dependent variable PLS algorithm is derived.And the method is used to control for the study of sandstorms, finding inhibitionfrom the fundamental approach is not treating the desert, but to control and curbthe desertification of land bare farmland dust.The third part of the regression analysis, there is often too many variablesexist between multiple and related phenomena, In order to find the variablesare important among all variables, this paper presents a forward-stepwise-partialleast squares, and the method carried out a detailed theoretical derivation. Mean-while,by the use of SAS software, the results showed that this method is easyto operate with a certain practicality. In addition, multiple indicator systemto establish a comprehensive evaluation index, often encountered indicator vari-ables exist between multiple sets related issues, and the traditional principalcomponent analysis does not solve the problem, according to this situation, this paper use PLS Path Analysis and Construct comprehensive evaluation indicatorsfor China's western city's comprehensive evaluation of empirical analysis. Theforth part , Partial least squares regression is unable to predict the future value ofthe issue, therefore we presented the PLS and time series forecasting model. Onone hand, address the multiple factors related phenomenon, using partial leastsquares regression modeling, so clearly the result of variable factors on the extentof the impact. On the other hand, according to the data form factor character-istics, using AR (p) model for the future-value forecast, then their generationhas been built into the partial least squares regression equation which forecaststhe future value of the dependent variable. We used the method to analyze thewater consumption of Yantai City.