Analysis Of Linear Regression Model On The Outlier Problems

Outlier is an important concept in statistical diagnose theory. The research of detection of outliers in the linear regression model has been a hot topic all the time for the complexity of the real data. The identification and treatment of outliers are the keys to the success of statistical diagnose, while the process of identification is the base of diagnose.it is the key point is to know the concept, types, the difference between outliers and its influence on the linear regressive coefficient. In this paper, the linear regression model launched on outlier analysis, on the basis of summing up the work of our predecessors, for the promotion has got several important conclusions.Firstly, we introduce the concept, cause and value of doing research in detecting outliers. Chapter two introduces the basic linear regression model and least square estimation, the projection matrix and the second projection formula as well as the basic concepts and methods of residual analysis, which lay the foundation for the subsequent analysis of the problem. The hat matrix plays an important role in the analysis of outliers. So the third chapter in detail introduces some properties of the hat matrix and adding or omitting observations have an influence on the hat matrix. The fourth chapter is the focus of this article, firstly gives the classification, difference and contraction of individual outlier and uses practical examples to distinguish. And then provides some methods to handle individual outlier. Describes a new method for identify many deviances. The goal of this method is to find this true partition and separate the "bad" from the outlying observations. Proposed the new method does not need to know the number of outlier in the observation points but we can choose a significance level a to see if the observations are considered to be the outliers. What’s more studying the influence of the two having some correlation between outliers on the regression coefficients with mean-shift outlier model and case deletion model, pointed out that if mean shift occurs in several observations of the dependent variable in the same arguments, and the amount of upward drift is equal to that of downward drift, then in the corresponding mean-shift model, the least squares estimate of coefficients is exactly equal to that of the original model, while the estimate of the amount of drift is the residual in its original model. At same time, discussing the equivalence role of this two models in testing anomalies.