Multicollinearity In Multilinear Regression Models And Partial Least Squares Regression

The paper discusses two questions:one about multicollinearity, and the other about the weakness of Partial Least Square Regression.One hand, in the application of multilinear regression , the harm of multicollinearity is very serious, but the existence of multicollinearity is widespread. Now the usual regression models are the three ones:Ridge Regression, Princinpal Component Regression and Partial Least Square Regression(PLS).Which kind of models is the most adaptive one when a set of datums from actual sircumstances in which multicollinearity exists are suitable to be dealed with by the linear regression model ?The essay discusses this question in terms of two aspects of theory and example. Above all, the paper analyzes .the principle how the three models overcome multicollinearity and the different function. And then ,with aid of SAS program , the paper examplifies the concrete performances of the three models used to overcome the multicollinearity, evaluates objectively characteristics of the several methods and their strength and weakness. This finding provides the basis to the choice of the concrete model.On the other hand, partial Least Square Regression which is called the second generation regression method has got good result in handling the multicollinearity in multilinear regression;But under some circumstances the result of such a regression is not satisfactory. The thesis focuses on the weakness of this regression model. First, this model has no robustness for influential poinds in that one or more influential points can seriously change the results of the regression . The next, the components withdrawed from PLS regression process are not all ideal, and among them there is a kind of component which has bigger covariance, however this component is weak in accounting for the dependent variables, which is primarily due to the fact that the independent variables is sneaked into more excrescent influences in that the variance becomes bigger.The article puts out this sircumstance unsuitabe for this model .By combining theoretical analysis with verification in example , the study puts forward a method to improve this model, whichwidens the application scope of PLS.