Unit-I

Multivariate Random variables and Distribution functions – Variance – covariance matrix – correlation – Bivariate normal distribution, Multivatiate normal density and its properties – Definition of Wishart matrix and its properties, Mahalanobis Distance. Sampling distributions of and , Large sample behaviour of and .

Unit-II

Classification for two populations, classification with two multivariate normal populations, Fisher’s discriminant functions for discriminating several population.
Principal components analysis, Dimensionality reduction, Factor Analysis- factor loadings using principal component analysis, Cluster Analysis- Cluster Analysis: Hierarchical Clustering and divisive clustering methods.

Unit-III

Simple Linear Regression- Properties, Least Squares Estimation of parameters, Hypothesis Tests in Simple Linear Regression, Interval estimation in simple linear regression, Coefficient of determination.
Multiple Linear Regression: Estimation of model parameters. Nonlinear Regression models, Examples of nonlinear regression models.

1. Anderson, T. W. (1983): An Introduction to Multivariate Statistical Analysis. 3rdEd. Wiley.
2. Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye. Probability and Statistics for Engineers and Scientists, Eighth Edition, Pearson Education Asia, 2007.
3. Douglas C. Montgomery and Elizabeth A.Peck and G.Geoffrey Vining. Introduction to Linear Regression Analysis”, Third Edition, John Wiley& Sons, Inc
4. Amir D. Aczel and Jayavel Sounderpandian. Complete Business Statistics, Sixth Edition, Tata McGraw-Hill Publishing Company, New Delhi. 2006.