Partial Least Squares Correlation Algorithm And Its Application

Partial least squares(PLS)is a multivariate statistical analysis method.It was put forward by Wood and S.Word(C.Albano)two experts in 1983 to solve the problem of quantitative chemistry.It is an improvement of traditional multiple linear regression model.The method combines the principal component regression and canonical correlation analysis,can solve the multicollinearity and the sample size is less than the number of variables,the variables so the application of partial least square from the field of chemistry to the rapid development of the application of medicine,biology,mechanics,economics and other fields.This paper mainly studies the two indicators of economic growth and energy consumption in Guizhou Province,the data index exists multicollinearity,so the construction of economic growth in Guizhou Province on the main components of the energy consumption of the regression model,and study the canonical correlation analysis between energy consumption and economic growth in Guizhou Province,but these two kinds of methods there are some limitations,and then by the partial least square method and the multi variable double screening method to establish the regression model between the two variables at the same time system,the prediction results and principal component regression are compared with each other,finally due to the regression variables gradually double selection is more superior.In addition to the typical variable correlation coefficient test,the first use of X~2 inspection based on the assumption of normality,but to avoid the distortion of inspection data was non normal,with the application of Bootstrap in non parametric test methods to test the correlation coefficient test,2 pairs of canonical variables correlation coefficient is significant correlation,and test results are consistent,but this is not affected by the assumption of normal constraints,and in the test of the partial least squares regression model parameters,using this test method,the test result was significant,it can enhance the reliability of the test.Through the statistical analysis on the economic and energy two variables of the system,the qualitative analysis between Guizhou province energy and economy;and through the comparison of Bootstrap test method and traditional test on coefficient,obtained by Bootstrap method is no longer normal restriction,has a good application.