It attempts to identify underlying variables,or factors,that explain the pattern of correlations within a set of observed variables,and to eliminate multi-collinearity.

Four methods dealing with multi-collinearity are introduced, they are Stepwise Regression, Ridge Regression, Principal Component Regression and Partial Least Squares.

But when it is too muchindependent variable related in an actual problem, it is difficult to find a groupindependent variable, in which each of them is irrelevant, and it will bring themulti-collinearity problem.

Advantage of ridge regression ouer LS in solving multicollinearity;

Result indicates that Fuzzy Principal Component Method can improve multicollinearity of Least Squares Estimate.

Peguin & Terasvirta(1999) made a general extension based on the Taylor expansion,which was applied to the test of nonlinear causality,and they dealt with the problem of collinearity by means of drawing principal components.

The author establishes an econometrical model with the cross-section data of provinces in 2003,by the method of F-test,t-test,test for heteroscedasticity and test for multi-collinearity.