Course Archives Statistical Quality Control & Operations Research Unit
Course: Multivariate Data Analysis
Level: Postgraduate
Time: Currently not offered
Past Exams

Syllabus: Analysis of Multivariate data: Multivariate data summarization, Plots. Univariate and multivariate analyses similarities. Special problems associated with multivariate analysis Dimensionality reduction.
Multivariate normal distribution: Elementary properties. Inference on mean vectors in multivariate populations Mahalanobis D2, Hotellings T2 ,MANOVA.
Principal Component Analysis:
PC Analysis based on the population covariance matrix, based on the sample covariance matrix; use of principal components.
Factor analysis: Module, communality, variance of a factor & total variance; estimation of Parameters, choosing number of factors; selection of loading rotation.
Discriminant Analysis and classification: Fishers discriminant function,classification rule based on expected cost of misclassification; rule for classifying into two normals/K normals.
Cluster analysis, Multidimensional scaling, Correspondence analysis: Similarity measures, clustering methods and algorithms; multidimensional scaling basic algorithm; correspondance analysis algebraic development, inertia, interpretation.
Conjoint analysis: Introduction, methods.
Methods for multivariate SPC: Multivariate control charts, Multivariate process capability analysis.
Multivariate Linear Regression: Multivariate Linear Regression Model, Least square Estimation. Tests and confidence Intervals, Model Adequacy checking, Problems of Multicollinearity, Ridge Regression, Principal component Regression.

Reference Texts:
1. Applied Multivariate Methods for Data Analysis: By Johnson D.E., Duxbury Press (1998)
2. Multivariate Data Analysis: By Hair, J.F. Jr., Anderson, R.E., Tatham, R.L. and Black, W.C.. Pearson Education (Fifth Edition) (2006)
3. Applied Multivariate Techniques: By Sharma S. Wiley (1996)
4. Multivariate Statistical Process Control with industrial Applications: By Mason, R.L. and Young, J.C. ASA SIAM Series in Statistics and Applied Probability (2001)
5. Marketing Research: By Malhotra, N. Prentice Hall (Fifth Edition) (2006)

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Past Exams
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[Indian Statistical Institute]