Applied Multivariate Statistical Modeling

Data driven decision making is the state of the art today. Engineers today gather huge data and seek meaningful knowledge out of these for interpreting the process behaviour. Scientists do experiments under controlled environment and analyse them to confirm or reject hypotheses. Managers and administrators use the results out of data analysis for day to day decision making. As the data collected and stored are multidimensional, to extract knowledge out of it requires statistical analysis in the multivariate domain. The aim of this course is therefore to build confidence in the students in analysing and interpreting multivariate data. The course will help the students by:(i) Providing guidelines to identify and describe real life problems so that relevant data can be collected,(ii) Linking data generation process with statistical distributions, especially in the multivariate domain,(iii) Linking the relationship among the variables (of a process or system) with multivariate statistical models,(iv) Providing step by step procedure for estimating parameters of a model developed,(v) Analysing errors along with computing overall fit of the models,(vi) Interpreting model results in real life problem solving, and(vii) Providing procedures for model validation.INTENDED AUDIENCE : Students of BTech/BE/MTech/ME/MS/MSc/PhD/MBA/PGDBM in Data Science, Engineering, Management, Economics, Other Sciences including Mathematics, and Professionals including Data Scientists, Engineers, Academicians, Managers, Economists, Policy Makers, and Administrators can take itPRE-REQUISITES : Basic Knowledge of Probability and StatisticsINDUSTRY SUPPORT : Nil.

Week 1. Introduction to Multivariate statistical modelling; Assignment - 1Week 2. Univariate descriptive statistics; Sampling Distribution; Assignment - 2Week 3. Estimation; Hypothesis Testing; Assignment-3Week 4. Multivariate descriptive statistics; Assignment-4Week 5. Multivariate normal distribution; Assignment-5Week 6. Analysis of variance (ANOVA); Assignment-6Week 7.Multivariate analysis of variance (MANOVA); Assignment-7Week 8. Multiple Linear Regression (MLR): Introduction, Sampling, & Adequacy checking: Assignment-8Week 9. MLR: Test of assumption, and diagnostic study; Assignement-9Week 10. Principal Component Analysis (PCA): Introduction, estimation, adequacy checking, & interpretation; Assignment – 10Week 11. Factor Analysis (FA): Introduction, estimation, adequacy checking, factor rotation, & factor scores; Assignment – 11Week 12. Structural Equation Modeling (SEM): Introduction, measurement model, & structural model; Assignment – 12