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Regression analysis is an important branch of statistics , it is widely used in the field of business management, economics , social , medical and biological sciences . From the beginning of the 19th century Gauss counting by the method of least squares , regression analysis has been 180 years of history , the beginning of the twentieth century , more statisticians into this area , a series of regression analysis theory and application papers, the last three decades , have a series of more mature results of regression analysis . Regression analysis, multicollinearity phenomenon between the independent variables , the estimated value of the regression coefficients will be unstable , the variance , which is bound to adversely affect problem , thus eliminating multicollinearity regression analysis an important part in the parameter estimates . Eliminate multicollinearity commonly used parameters improved principal component regression and ridge regression . This paper briefly describes the existence of the principal component regression of the principle and the advantages and disadvantages of the principal component estimation methods ; focusing on different ideas from different angles departure , in-depth discussion of the most common Ridge Regression Estimation : ridge parameter K , ridge estimator , the ridge parameter K . Since 1970 Hoerl and Kennard [ 1 ] , [ 2 ] since the ridge estimate , ridge regression estimation methods have been widely used in practice . In this paper, multiple linear regression model typical form for the study , from the perspective of reducing the mean square error , the existence of the ridge parameter K and ridge estimator in a certain range . Ridge parameter K is determined dependent on the unknown parameters , but a good sample inference , it will make a lot of experience and information role unable to play . Ridge trace method to determine the value of K there is a certain subjective factors , this man just let me qualitative and quantitative analysis combine to improve the method of Hoerl and Kennard . This paper analyzes the mean square error function monotonic , K narrowed it down to a relatively small range . Approximation of the K value , how to achieve the extreme points, needs further study. Finally summarized and presented the problem to be solved .
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