The Countermeasures And Several Improvements Of Multicollinearity In Linear Regression Model

When we solve many actual questions,prediction equations are formed by the explanatory variables and the response variables,but collinearities among the explanatory variables will be found with the correlations of the response variables,or with any number of observation is less than the number of the explanatory variables.If we still use ordinary least square to form the model,then the multicollinearity is harmful to the estimate of the parameters , expanding the error of the model, and destroying the robustness of the model.The paper set forth three methods of soloving multicollinearity:ridge regression,principal component regression,partial least square regression.and discuss and investigate the three of mothods,and to summarize the properties of them.Especialy we summarize the calculation process of principal component regression and patial least square regression when we figure out the multicollinearity.The paper dicuss dificiencies of the ridge regression ,principal component regression and patial least square.In the ridge regression we adopt a new method of searching ridge parameter K;We substitute weighted sum of squares for sum of squares what filter eigenvalue's method , which is obviously amended the systemic error,and greatly raised the precision of model in principal regression;In patial least square regression we commence the constraint condition of calculationg,analysing idea contradiction that there are much information in explanatory martrix and with higher correlations ,and put forward a method of orthogonal projection, the components in the explanatory martrix which are irrespective to response varibles are deducted,the explanatory matrix is transformed by above which does not exist much messages which are irrespective to response varibles,and even so which widens the application scope of the partial least square .When we choose the number of principal components by cross-validity in the partial least squares,we discover that cross-validity is not always effective.and we explain through a example.We adopt a rule of selectingthe number of principal components which bases on residual error of dicrease's rate associative the rule of Qj;.Certainly, the rule is logical whether or not which must being validated in practice.