The Introduction Of Several Multivariate Statistical Method And Its Application

The science of multivariate statistical analysis is a series of theories and methods which solve multivariate problems by mathematical statistical methods. It contains regression analysis, discrimination analysis, cluster analysis, principal component analysis, factor analysis, correspondence analysis and so on.’The Exact Distribution of Covariance Matrix of the Samples from Multivariate Normal Population’which wrote by Wishart and published in1928was the beginning of the multivariate analysis and Fisher,Hotelling, Roy’s strong complement to it on the basis of this made its theory knowledge more prefect and its development more quickly. From then on the application of multivariate analysis appears in many areas. But the problem of large amount of computation in the practical application of multivariate analysis hadn’t been solved for a long time in the social environment at that time, which made the statistical method suffer from a developing retard and even stop developing. Thanks to the development of computer technology the multivariate statistical analysis was widely applied in subjects of geology, medicine, sociology, meteorology and so on in the mid-1950s. In1960s scholars improved the theories of multivariate statistics and developed many new theories and methods by practice, which made the application of multivariate statistics wider. In the past30years the scholars in our country had got remarkable achievement in the area of multivariate statistical analysis and reached international advanced level in some areas.Comprehensive evaluation is a procedure that determines the level and order of every subject we evaluate in whole in the form of quantity by collecting all information of the subjects. Multivariate statistical analysis is one of important methods for integrated data processing in comprehensive evaluation which is involved in many fields such as economic, society, education, technology, etc. In this paper, we made the comprehensive evaluation by the method of multivariate statistical analysis which is used to deal with multi-issue and complex correlation problems.In this paper, we introduce the theories and application of the cluster analysis, principal component analysis and factor analysis. Firstly we introduce the theories and application examples of several multivariate statistical analysis methods then we specially illustrate the application of multivariate statistical analysis in comprehensive evaluation of the living environment in all regions of the country. We use an index system which contains nine subsystems in the process of comprehensive evaluation of the living environment in all regions of the country. The specific process is as follows: Firstly we divide the whole information system of living environment into nine subsystems which are exhaust gas processing subsystem, exhaust emissions subsystem, wastewater discharge and treatment subsystem, industrial emissions system, industrial waste gas disposal subsystem, industrial wastewater discharge and treatment subsystem, garbage collecting and processing subsystem, industrial solid waste generation subsystem and industrial solid waste treatment and utilization subsystem. Secondly we make a comprehensive evaluation of all regions of the country in every subsystem by the method of multivariate statistical analysis and get the integrated score of every one. Finally we define the nine integrated scores as new variables of every region and calculate every region’s value of comprehensive evaluation and sort all the regions by the same method.Besides the forewords and conclusion, the paper is mainly divided into four major parts. The first part mainly introduces the theories and application example of the cluster analysis-the use of cluster analysis on evaluation of per-capita income of rural residents. The second part mainly introduces the theories and application example of principal component analysis-the use of principal component analysis on evaluation of students achievements. The third part mainly introduces the theories and application example of factor analysis-the use of factor analysis on evaluation of students achievements. The fourth part mainly introduces the use of multivariate statistical analysis on the comprehensive evaluation of the living environment of every region in the country and analyzes the result of comprehensive evaluation. In this part, we also give some advice according to problems revealed by the result and propose the application of the comprehensive evaluation which combined with the multivariate statistical analysis in other fields.