Introduction to multivariate analysis : linear and nonlinear modeling The aim of statistical science is to develop the methodology and the theory for extracting useful information from data and for reasonable inference to elucidate phenomena with uncertainty in various fields of the natural and social sciences. The data contain information about the random phenomenon under consideration and the objective of statistical analysis is to express this information in an understandable form using statistical procedures. We also make inferences about the unknown aspects of random phenomena and seek an understanding of causal relationships. Multivariate analysis refers to techniques used to analyze data that arise from multiple variables between which there are some relationships. Multivariate analysis has been widely used for extracting useful information and patterns from multivariate data and for understanding the structure of random phenomena. Techniques would include regression discriminant analysis principal component analysis clustering etc. and are mainly based on the linearity of observed variables. In recent years the wide availability of fast and inexpensive computers enables us to accumulate a huge amount of data with complex structure and or high dimensional data. Such data accumulation is also accelerated by the development and proliferation of electronic measurement and instrumentation technologies. Such data sets arise in various fields of science and industry including bioinformatics medicine pharmaceuticals systems engineering pattern recognition earth and environmental sciences economics and marketing. Multivariate techniques are used to analyze data that arise from more than one variable in which there are relationships between the variables. Mainly based on the linearity of observed variables these techniques are useful for extracting information and patterns from multivariate data as well as for the understanding the structure of random phenomena. This book describes the concepts of linear and nonlinear multivariate techniques including regression modeling classification discrimination dimension reduction and clustering