Research On Multivariate Lineaar Model And Ridge Regression

Regression analysis is a very important link in statistics. It has extensive application in such each field as business administration, economy, society, physic and bioscience etc. Regression analysis has a over 180-year history since Guass presented least squares estimation in 1800s. A lot of statisticians devoted themselves to this field since 1900s and came out with a series of papers on theory and applications . It has a series of pure conclusion in the latest 30 years. In regression analysis, the estimation of regression coefficients is in unstable and variance goes up when multicollinearity takes place , which harm to the question and model. Therefore, elimination the multicollinearity in independent variables is a very important part in the estimation of regression coefficients. The staple methods of elimination multicollinearity and betterment methods of parameters are principal component regression and ridge regression . Ridge regression is simply introduced in this paper, such as its principle, processes, advantages and disadvantages. The core of this paper is to analyze and probe into ridge regression from different ideas, such as the existence of ridge parameter K, the choiceness of ridge estimation K , the choice of ridge parameter K and the methods of regression coefficients. Ridge regression is widely put into practice since Hoerl and Kennard presented it in 1970. The investigation object of this paper is the standard canonical form. In order to the mean square error, I analyze the existence and choiceness of ridge regression K in some spectrum. The confirmation of parameter K relies on unknown parameters. In the same time, a lot of experience and information are losing if we analyze only stylebook. It is subjective that we confirm the ridge parameter according to ridge traces, but I integrate the qualitative analysis and quantitative analysis and improve on the methods of Hoerl and Kennard. This paper reduces the range of ridge parameter according to the monotonicity of mean square error function. To draw up the extremum is unexhausted. There is a summarization at the end of this paper and I present the unexhausted questions.