Shalabh
shalab@iitk.ac.in
shalabh1@yahoo.com
Department of Mathematics & Statistics
Indian Institute of Technology Kanpur, Kanpur - 208016 (India)

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MTH 416 : Regression Analysis

Syllabus: Simple and multiple linear regression, Polynomial regression and orthogonal polynomials, Test of significance and confidence intervals for parameters. Residuals and their analysis for test of departure from the assumptions such as fitness of model, normality, homogeneity of variances, detection of outliers, Influential observations, Power transformation of dependent and independent variables. Problem of multicollinearity, ridge regression and principal component regression, subset selection of explanatory variables, Mallow's Cp statistic. Nonlinear regression, different methods for estimation (Least squares and Maximum likelihood), Asymptotic properties of estimators. Generalised Linear Models (GLIM), Analysis of binary and grouped data using logistic and log-linear models.
 

Grading Scheme: Quizzes: 20%, Mid semester exam: 30%, End semester exam: 50%

 

Books:  1. Introduction to Linear Regression Analysis by Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining (Wiley), Low price Indian edition is available.

                2. Applied Regression Analysis by Norman R. Draper, Harry Smith (Wiley), Low price Indian edition is available.

                3. Linear Models and Generalizations - Least Squares and Alternatives by  C.R. Rao, H. Toutenburg, Shalabh, and C. Heumann (Springer, 2008)

                4. A Primer on Linear Models by John F. Monahan (CRC Press, 2008)

                5. Linear Model Methodology by Andre I. Khuri (CRC Press, 2010)

Assignaments:

Assignment 1

Assignment 2

Assignment 3

Assignment 4

Assignment 5

Assignment 6

Assignment 7

Assignment 8

 

Lecture notes for your help (If you find any typo, please let me know)

Lecture Notes 1 : Introduction

Lecture Notes 2 : Simple Linear Regression Analysis

Lecture Notes 3 : Multiple Linear Regression Model

Lecture Notes 4 : Model Adequacy Checking

Lecture Notes 5 : Transformation and Weighting to Correct Model Inadequacies

Lecture Notes 6  : Diagnostic for Leverage and Influence

Lecture Notes 7  : Generalized and Weighted Least Squares Estimation

Lecture Notes 8  : Indicator Variables

Lecture Notes 9  : Multicollinearity

Lecture Notes 10  : Heteroskedasticity

Lecture Notes 11  : Autocorrelation

Lecture Notes 12  : Polynomial Regression Models

Lecture Notes 13  : Variable Selection and Model Building

Lecture Notes 14  : Logistic Regression Models

Lecture Notes 15  : Poisson Regression Models

Lecture Notes 16  : Generalized Linear Models