### Linear Models and Regression Analysis-II (STAT-7103)

Introduction

Regression models are ubiquitous in applied as well as methodological statistical research. In all research dimensions, we are often interested in outcomes that do not follow a normal distribution, such as binary outcomes (survived/died, successful/unsuccessful therapy) and counts (number of infections/cases of cancer/complications at a hospital or in a county). Understanding the fundamentals of these models is critical for anyone in statistical research. Regression diagnostics for outlier and influential observations are the other core objectives of this course.

Learning outcomes

• To compute and interpret the regression diagnostics
• To perform Stein rule sharinkage estimation
•  To perform bootstrapping and cross validation
•  To carry out Robust Regression for Non-normal Errors

Textbooks

1. Christensen, J. (2002). Advanced Linear Modeling. Springer Texts in Statistics
2. Draper, N.R. and Smith, H. (2004). Applied Regression Analysis. John Wiley and Sons.
3. Graybill F.A. (1990). An Introduction to Linear Statistical Models. McGraw Hill Book Company Inc. New York.
4. McCullegh P. And Nelder J.A. (1990). Generalized Linear Models. Chapman and Hall, New York.
5. Montgomery, D.C., and Peck E.A.   (1992).    Introduction    to    Linear    Regression Analysis.  John Wiley and sons Inc. New York.
6. Weisburg, S. (1980). Applied Linear Regression.  John Wiley and Sons.

Course Plan

Week

## Books

1

Assumptions of the linear model

Applied Regression Analysis

2

Regression diagnostics: Outlier detection methods

Applied Regression Analysis

3

Regression diagnostics: Influential observation detection methods

Applied Regression Analysis

4 Multiple-case Diagnostics Applied Regression Analysis

5

Regression diagnostics estimation and computation with R and Mathematica

Applied Regression Analysis

6

Recent Developments, and High-Breakdown Diagnostics

Applied Regression Analysis

7

Stein-Rule Shrinkage Estimator: Motivation for Shrinkage: Stein-Rule in the Regression Context.

Introduction    to    Linear    Regression

Analysis

8

Properties of the Stein-Rule Estimator and its Extensions.

Basic Econometrics

9

Robust Regression for Non-normal Errors

Basic Econometrics

10

Testing a Nonlinear Specification

Basic Econometrics

11

Measures of Nonlinearity.

Applied Regression Analysis

12

Orthogonality

Applied Regression Analysis

13

Applied Regression Analysis

14

Resampling Techniques

Introduction    to    Linear    Regression

Analysis

15

Jackknifing, Bootstrapping.

An Introduction to Generalized Linear Models, Generalized Linear Models

16

Robust regression estimation, Resampling, bootstrapping and Jackknifing approaches with r

An Introduction to Generalized Linear Models, Generalized Linear Models

Description of system of Evaluation

Exam: Mid (30%), Final (50%), Sessional (20%): Assignments, Presentations, Class Participation Quizzes

Lecture TIme: Tuseday (9:00 AM to 12:00 PM)