Stern School of Business
Statistical Inference and Regression Analysis
UB.0015.01, GB-3302.30

Professor: William Greene, Stern Departments of Economics and IOMS

BS The Ohio State University, 1972 (Operations Research); MA Wisconsin, 1974 (Economics); PhD Wisconsin, 1976 (Econometrics); History: Cornell 1976-1982; Real world, 1982-1983; Return to ivory tower at Stern (then GBA) NYU, 1983-2008; Toyota Motor Corp Professor, 2007-2011, Robert Stansky Professor, 2012-2017. Publications: Articles - see vita on home page; Books: Modeling Ordered Choices, 2010, Econometric Analysis, 8th Ed (2018); Applied Choice Analysis (2015); Software, NLOGIT (www.nlogit.com), Editor in Chief, Foundations and Trends in Econometrics. Editor in Chief, Journal of Productivity Analysis, Associate editor, Journal of Economic Education, Journal of Choice Modeling, Economics Letters, Journal of Business and Economic Statistics. Research interests: econometric methodology, discrete choice modeling, efficiency and productivity analysis, health economics, transportation, nonlinear estimation, entertainment and media.
Office:  MEC 7-90, Ph. 998-0876
Professor: e-mail: wgreene@stern.nyu.edu

Professor: Home Page: http://people.stern.nyu.edu/wgreene

Abstract

This course has two parts. In the first we will develop topics in mathematical statistics including distribution theory, estimation theory for the method of moments and maximum likelihood estimation, and principles of statistical inference including confidence intervals and hypothesis testing. The second half of the course will examine linear, loglinear and nonlinear regression models. The course is intended to provide background for research and practice in statistical and actuarial science.

Prerequisites

I will assume that students are familiar with algebra, calculus, linear algebra and basic probability theory. A prior course in probability and statistics is assumed. The linear algebra will be basic and can be picked up during the course.

 

Course Requirements and Course Grades

 

Final grades for the course will be determined on the basis of the following components and weights:

 

*   Mid-term exam: 40%. (Old sample questions 1) (Old sample questions 2) (2015 midterm with solutions) (2016 midterm with solutions)

 

*   Final exam: 40% (2015 final exam with solutions) (2016 final exam with solutions)

 

*   Homework assignments (details below): (6 @ 3.33%) 20% (in aggregate).

 

Students may work in groups of up to 4 and submit a single report for the group.

 

All examinations are open book, open notes, closed telephone. You may bring use tablet if you have your class materials stored on it. Do bring a hand calculator to both exams.

 

Course Materials

 

*    The text for this course is Hogg, R., McKean, J., and Craig, A;, Introduction to Mathematical Statistics 7th Edition, Pearson, 2013. Labeled HMC below.

 

*    The second half of the course (the sessions on regression modeling) will draw heavily on Greene, W., Econometric Analysis, Eighth edition, Prentice Hall, 2018. Students need not purchase this book - access to electronic copies of the relevant chapters will be provided in class.

Chapters from Greene, Econometric Analysis:

1. Introduction
2. The Linear Regression Model
3. Least Squares
4. The Least Squares Estimator

5. Hypothesis Tests
6. Functional Form and Structural Change
7. Nonlinear Regression Models
9. The Generalized Regression Model and Heteroscedasticity
Appendix A. Matrix Algebra

 

*    Some useful notes on several subjects. These include the bare bones theoretical results and lots of examples.

 

Notes on the gamma distribution
Notes on Bayesian Statistics
Application of Bayesian Estimation
A Test About Binomial Success Probability

 

*    We will do some computer exercises during the course. Software will be provided (for free) and will be introduced in class.

Other Stuff

*    Please remember to turn off your cell phone before you come to class.

*    Please try to arrive early. Late entrances are disruptive.

*    As a general rule, laptops are an annoyance during class, particularly when you are checking your email, playing with Facebook or angry birds, tweeting or watching YouTube videos while others are studying statistics. If you absolutely must use your laptop to take notes, so be it, but you will be asked to submit a copy of your class notes via email within an hour of the end of class.

Course Outline and Schedule

Session 1 (Thursday 2/8): Probability and distribution theory.
Reading: HMC, Chapters 1.1-1.7, 2.1-2.3, 3.1-3.5
Materials: (Notes 1-Slides: Probability Theory)

Session 2 (Thursday 2/15):Moments, Functions of Random Variables, Covariance and Correlation, Conditional Moments; Limit Theorems, Law of Large Numbers, Central Limit Theorem, Asymptotic Distribution.
Reading: HMC, Chapters 1.8, 1.9, 2.3-2.6.1,5.1-5.3
Materials: (Notes 2-Slides: Moments and Limit Theorems)

Session 3 (Thursday 2/22): Point Estimation; method of moments, maximum likelihood estimation, Bayesian estimation.
Reading: HMC, Chapters 4.1-4.4, 6.1-6.2, 11.1-11.2.2
Materials
(Notes 3-Slides: Estimation Theory)  

Session 4 (Thursday 3/1): Normal family of distributions, t, F, chi-squared; Statistical inference, point and interval estimation, confidence intervals, bootstrapping
Reading:
HMC Chapters 3.4-3.6, 4.2-4.4, 4.9
Materials: (Notes 4-Slides: Inference)

Session 5 (Thursday 3/8): Hypothesis testing, Neyman-Pearson lemma, likelihood ratio tests, nonparametric tests.
Reading: HMC Chapters 4.5-4.7, 6.3-6.5, 8.1, 8.3

Materials: (Notes 5-Slides: Hypothesis tests)

(Thursday 3/15): NO CLASS (Spring Break)

(Thursday 3/22): MIDTERM EXAM,

Session 6 (Thursday 3/29): Regression model, part 1.
Reading:
Greene Chapters 2-4.
Materials: (Notes 6-Slides: Regression Part 1)

Session 7 (Thursday 4/5): Multiple regression model, part 2.
Readings: Greene, Chapters 2-4

Materials: (Notes 7-Slides: Regression Part 2)

 

Session 8 (Thursday 4/12): Multiple regression model, part 3.
Materials: Greene, Chapters 2-4
Materials: (Notes 8-Slides: Regression Part 3)

Session 9 (Thursday 4/19): Multiple regression model, part 4.
Reading: Greene, Chapters 2-4, 6, 9.
  
Materials: (Notes 9-Slides: Regression Part 4)

Session 10 (Thursday 4/26): Advanced topics in regression modeling.
Reading: Greene, Chapter 7,

Materials: (Notes 10-Slides: Nonlinear Regression)

(Thursday 5/3): FINAL EXAM

Problem Sets

Students may work with one or more of their colleagues on these homework assignments and submit your assignment as a group.

Problem set 1 (due 2/15) Problem set 1 solutions
Problem set 2 (due 3/1) Problem set 2 solutions
Problem set 3 (due 3/22)
 Problem set 3 solutions
Problem set 4 (due 4/5) Problem set 4 solutions 
Problem set 5 (due 4/19) Problem set 5 solutions
Data for Problem set 5: Right click to download, left click to launch
(Rice-14_40 minitab) (Rice-14_40 nlogit) (Rice-14_40 Excel)

(Baseball Data minitab) (Baseball Data nlogit) (Baseball Data Excel)

Problem set 6 (due 5/3) Problem set 6 solutions

Data for Problem set 6: Right click to download, left click to launch
(Cornwell and Rupert minitab) (Cornwell and Rupert nlogit ) (Cornwell and Rupert Excel)

(Labor Market Data minitab) (Labor Market Data nlogit) (Labor Market Data Excel)