The Diagnosis And Process Solutions In Multicollinearity Of Multiple Regression Model

In the multiple regression model, due to the multicollinearity amongindependent variables, the parameter estimations will increase and the models willturn unstable. Sometimes some regression coefficients do not even match theircorresponding realistic meanings. By studying the solutions to multicollinearity, abetter solution to a certain kind of models has been found and therefore, the impactof multicollinearity on the model is reduced.The diagnosis methods and solutions to multicollinearity are analyzed in thisthesis. For diagnosis methods, variance inflation factor, latent roots and conditionnumbers are mainly used to detect the existence of multicollinearity, while solutionsinclude ridge regression method, principle component regression method and partialleast squares method. Moreover, their respective scopes of application areconcluded from the study of their basic principles, properties and procedures, andthe analysis of their relative pros and cons.These theoretical methods are creatively applied in the NBA scoring model inthis thesis. Firstly, the player scoring model is built based on the statistics of NBAplayers. Although all the parameters of this model meet all the requirementsseemingly, further diagnosis analysis of multicollinearity towards this model revealsthe existence of multicollinearity in this model. Secondly, the ridge regressionmethod, principle component regression method and partial least squares methodare applied in this model respectively to find a better solution to this model, andeven to the all the models of this kind. Simulating experiments show that the partialleast squares method is not applicable for this model, while principle componentregression method and ridge regression method can reduce the multicollinearity inthis model. Further analysis based on comparison between other parameters showsthat principle component regression method is a better solution for this model,which can eliminate the multicollinearity more effectively than the other method.The conclusion reached in this thesis can be applied to most of the models of thiskind and eliminate the influence of multicollinearity and stabilize the modelseffectively.