NPTEL : NOC:Applied Multivariate Statistical Modeling (Mathematics)

Co-ordinators : Dr J Maiti


Lecture 1 - Introduction to Multivariate Statistical Modeling

Lecture 2 - Introduction to Multivariate Statistical Modeling: Data types, models, and modeling

Lecture 3 - Statistical approaches to model building

Lecture 4 - Statistical approaches to model building (Continued...)

Lecture 5 - Univariate Descriptive Statistics

Lecture 6 - Univariate Descriptive Statistics (Continued...)

Lecture 7 - Normal Distribution and Chi-squared Distribution

Lecture 8 - t-distribution, F-distribution, and Central Limit Theorem

Lecture 9 - Univariate Inferential Statistics: Estimation

Lecture 10 - Univariate Inferential Statistics: Estimation (Continued...)

Lecture 11 - Univariate Inferential Statistics: Hypothesis Testing

Lecture 12 - Hypothesis Testing (Continued...): Decision Making Scenarios

Lecture 13 - Multivariate Descriptive Statistics: Mean Vector

Lecture 14 - Multivariate Descriptive Statistics: Covariance Matrix

Lecture 15 - Multivariate Descriptive Statistics: Correlation Matrix

Lecture 16 - Multivariate Descriptive Statistics: Relationship between correlation and covariance matrices

Lecture 17 - Multivariate Normal Distribution

Lecture 18 - Multivariate Normal Distribution (Continued...)

Lecture 19 - Multivariate Normal Distribution (Continued...): Geometrical Interpretation

Lecture 20 - Multivariate Normal Distribution (Continued...): Examining data for multivariate normal distribution

Lecture 21 - Multivariate Inferential Statistics: Basics and Hotelling T-square statistic

Lecture 22 - Multivariate Inferential Statistics: Confidence Region

Lecture 23 - Multivariate Inferential Statistics: Simultaneous confidence interval and Hypothesis testing

Lecture 24 - Multivariate Inferential Statistics: Hypothesis testing for equality of two population mean vectors

Lecture 25 - Analysis of Variance (ANOVA)

Lecture 26 - Analysis of Variance (ANOVA): Decomposition of Total sum of squares

Lecture 27 - Analysis of Variance (ANOVA): Estimation of Parameters and Model Adequacy tests

Lecture 28 - Two-way and Three-way Analysis of Variance (ANOVA)

Lecture 29 - Tutorial ANOVA

Lecture 30 - Tutorial ANOVA (Continued...)

Lecture 31 - Multivariate Analysis of Variance (MANOVA): Conceptual Model

Lecture 32 - Multivariate Analysis of Variance (MANOVA): Assumptions and Decomposition of total sum square and cross products (SSCP)

Lecture 33 - Multivariate Analysis of Variance (MANOVA): Decomposition of total sum square and cross products (SSCP) (Continued...)

Lecture 34 - Multivariate Analysis of Variance (MANOVA): Estimation and Hypothesis testing

Lecture 35 - MANOVA Case Study

Lecture 36 - Multiple Linear Regression: Introduction

Lecture 37 - Multiple Linear Regression: Assumptions and Estimation of model parameters

Lecture 38 - Multiple Linear Regression: Sampling Distribution of parameter estimates

Lecture 39 - Multiple Linear Regression: Sampling Distribution of parameter estimates (Continued...)

Lecture 40 - Multiple Linear Regression: Model Adequacy Tests

Lecture 41 - Multiple Linear Regression: Model Adequacy Tests (Continued...)

Lecture 42 - Multiple Linear Regression: Test of Assumptions

Lecture 43 - MLR-Model diagnostics

Lecture 44 - MLR-case study

Lecture 45 - Multivariate Linear Regression: Conceptual model and assumptions

Lecture 46 - Multivariate Linear Regression: Estimation of parameters

Lecture 47 - Multivariate Linear Regression: Estimation of parameters (Continued...)

Lecture 48 - Multiple Linear Regression: Sampling Distribution of parameter estimates

Lecture 49 - Multivariate Linear Regression: Model Adequacy Tests

Lecture 50 - Multiple Linear Regression: Model Adequacy Tests (Continued...)

Lecture 51 - Regression modeling using SPSS

Lecture 52 - Principal Component Analysis (PCA): Conceptual Model

Lecture 53 - Principal Component Analysis (PCA): Extraction of Principal components (PCs)

Lecture 54 - Principal Component Analysis (PCA): Model Adequacy and Interpretation

Lecture 55 - Principal Component Analysis (PCA): Model Adequacy and Interpretation (Continued...)

Lecture 56 - Factor Analysis: Basics and Orthogonal factor models

Lecture 57 - Factor Analysis: Types of models and key questions

Lecture 58 - Factor Analysis: Parameter Estimation

Lecture 59 - Factor Analysis: Parameter Estimation (Continued...)

Lecture 60 - Factor Analysis: Model Adequacy tests and factor rotation

Lecture 61 - Factor Analysis: Factor scores and case study