The Application Of Principal Component Regression And Quantile Regression On Two Types Of Data

In the process of analysing the actual data, the multivariate statistical analysismethod is widely used as the actual problem is often multivariate. The two kinds ofdata were researched and analyzed by the principal component regression andquantile regression in this thesis. Firstly, the characteristics of the two methods wascompared, then the two methods were combined in order to analyze the data morecomprehensively.The independent variables of the two sets of data this thesis selects havedifferent levels of multicollinearity, principal component regression is a morecommonly used regression method which is to overcome the multicollinearityamong the independent variables. Quantile regression can get different regressionequations due to the difference of the quantile. By comparing the significance andthe magnitude of parameter of the quantile regression equation, estimate the effectof independent variable on the dependent variable among different quantiles.Compared with the principal component regression, quantile regression analyzes thedata more comprehensively. Median component regressions to the two kinds of dataselected and contrastive analyze its result and the result of principal componentregression, it could be find that the collinearity between models will let the medianregression equation deviate from the actual situation, which did not have referencevalue. Considering that the principal component in the principal componentregression is linearly independent, the quantile regression of principal component isstudied in this thesis.For using quantile regression to principal component can not only overcomethe influence of multi-collinearity among the independent variables, but also reducethe number of variables and simplify the regression equation. Quantile regressionunder principal component can get each principal component of different subsites’influence on the dependent variable, combining with each principal component’srepresentation on each independent variable information we can get the influence ofdifferent quantiles primitive variable on the dependent variable. But the principalcomponent is a linear combination of the independent variables, and it is limited forthe representation of the independent variable information, therefore, the result maybe with some error. In order to get the independent variables’ specific impact oneach subsites, and then using regression quantile to each independent variable, so itcan avoid collinearity between variables’ influence on the result. Combining theresults of principal component of the quantile regression and the actual situation, We can make judgments and predictions about the relationship between thedependent variable and independent variables. For the model with multicollinearity,quantile regression under principal components and the quantile regression ofindependent variables have their own advantages and disadvantages.Thecombination of both can explanate the model more objective and reasonable, andhas more guiding significance to practical application.