### Linear Models and Regression Analysis-I (STAT-7101)

Introduction

This course is designed for M.Phil. in Statistics students. A researcher is often interested in using sample data to investigate relationships, with an ultimate goal of creating a model to predict a future value for some dependent variable. The process of finding this mathematical model that best fits the data involves regression analysis. Generally, regression analysis is collection of methods for determining and using models that explain how a response variable (dependent variable) relates to one or more explanatory variables (predictor variables).

Learning Objectives

• To analyze and interpret relationships between a response variable and one or more covariates.
• To identify the best regression model for better research output.
• To explore some of the wide range of real-life situations occurring in different fields that can be investigated using regression statistical models.

Textbooks

1. Annette J. Dobson and Adrian Barnett (2008). An Introduction to Generalized Linear Models. 3rd edition, Taylor and Francis, Text in Statistical Science.
2. Draper, N.R. and Smith, H (2004). Applied Regression Analysis. John Wiley and Sons.
3. Gujrati. D. (2005). Basic Econometrics. 5th edition, John Wiley, 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
6. .  John Wiley and sons Inc. New York.
7. Weisburg, S. (1980). Applied Linear Regression.  John Wiley and Sons.

Course Plan

Week

# Topics and Readings

## Books

1

Introduction to linear models

Applied Regression Analysis

2

Functionally related models mean related model

Applied Regression Analysis

3

Least squares and unbiased estimation

Applied Regression Analysis

4

Best Linear U                                                                                  Best Linear Unbiased Estimation.

Applied Regression Analysis

5

Multiple Regression Analysis: Estimation and exercises

Applied Regression Analysis

6

Multiple Regression Estimation through matrix approach and related exercises

Applied Regression Analysis

7

Various approaches of subset selection procedures

Introduction    to    Linear    Regression

Analysis

8

Heteroscedasticity: Definition, Reasons, Consequences, Detections and remedial measures

Basic Econometrics

9

Autocorrelation: Definition, Reasons, Consequences, Detections and remedial measures

Basic Econometrics

10

Multicollinearity: Definition, Reasons, Consequences, Detections and remedial measures

Basic Econometrics

11

Ridge Regression Estimation and Properties

Applied Regression Analysis

12

Choice of biasing parameters

Applied Regression Analysis

13

Predictions from Regression

Applied Regression Analysis

14

Choosing a Regression Model

Introduction    to    Linear    Regression

Analysis

15

Generalized Linear Models: Definition, Estimations with Examples

An Introduction to Generalized Linear Models, Generalized Linear Models

16

Some Generalized Linear Models i.e. Poisson, Logistic, Gamma, Inverse Gaussian Regression and applications

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 (2:00 PM to 5:00 PM)