AM 51500 Applied Linear Models                                                                Spring 2005

Instructor: C. Andy Tsao

 

I. Objectives

        Applied linear models for regression, analysis of variance and experimental design are widely used in various application domains. Starting with the simple linear models, we will cover the main topics in linear statistical models such as multiple linear regressions, ANOVA, logistic regression, etc. Students will be exposed to both theoretical and practical aspects of applied linear models. Selected topics such as statistical machine learning, variable selection and PCA will also be briefly addressed if time permits.

 

II. Prerequisites

  Statistics, Matrix algebra

 

III. Plan

        Some possible topics/problems for group projects will be announced early in the class. These projects will be integrated with lectures, data analysis, class discussion and presentation. The statistical freeware R will be used for data analysis. Outline of the course is as follow

 

Week

Topics

Contents

1

Introduction

Overview and motivation

Review of Simple Linear Regression

2

Simple Linear Regression

Inference and Diagnostics for Simple Linear Regression

3-4

Multiple Regression

Matrix Notation, Inference and Diagnostics for Multiple Regression

5

Model Selection

Forward, Backward Selection, etc.

6-7

Categorical Independent

Variables

Bridge to ANOVA

8-9

Midterm

One-way ANOVA

 

10-11

Two-way ANOVA

Multi-way ANOVA

Inference, Model validation

12-13

Logistic Regression

 

Inference and application; Generalized Linear Models

14-15

Special Topics: Discussion and Presentation

Topics such as statistical machine learning, variable selection under multicollinearity, PCA, etc.

16-17

Project Presentation/Discussion

 

18

Final Exam

 

 

 

VI. Evaluation (tentative)

Homework   （15％）Project and presentation（30%）

Midterm          （20%）Final （35%）

 

 

V. Referencgs

1.      Neter, J., Kutner, M.H., Nachtsheim, C.J. and Wasserman, W. (1990).  Applied Linear Statistical Models, 4th edition. Irwin Inc.

2.      Kutner, M.H., Nachtsheim, C.J., Neter, J. and Li, W. (2005).  Applied Linear Statistical Models, 5th edition. McGraw-Hill.

3.      Draper, N.R. and Smith, H. (1981). Applied Regression Analysis, 2nd edition. Wiley.

4.      Montgomery, D.C. and Peck, E. (1991).  Introduction to Linear Regression Analysis, 2nd edition. Wiley.

5.      Sen, A. and Srivastava, M. (1990). Regression Analysis: Theory, methods and applications. Springer.

6.      Lehmann, E.L. (1986). Testing Statistical Hypotheses. 2nd edition. Wiley.

7.      Scheffe, H. (1959). The Analysis of Variance. Wiley.

8.      R website: http://www.r-project.org/