MATH 5305 Statistical Models
Instructor
Dr. Jesse Crawford Office phone: (254) 968-9536
Email: Office: Math 332
Website: faculty.tarleton.edu/crawford
Office Hours
MW 1:00 – 2:00
TR 2:30 – 3:30
You are highly encouraged to visit my office for help.
Course Meeting Times
MW 5:15 – 6:30 in Math 213
Required Materials
Statistical Models: Theory and Practice, revised edition, by David Freedman.
Optional Materials
Applied Linear Statistical Models, by Kutner et al.
Applied Logistic Regression, 2nd ed., by Hosmer and Lemeshow.
Multivariate Data Reduction and Discrimination with SAS Software, by Khattree and Naik.
Homework
Homework will be assigned almost every class meeting and will be due a week later. It is crucial to keep up with the homework to succeed in this course.
Grades
Course averages will be computed as follows.
Assignment / % of GradeHomework / 40%
Midterm Exam / 30%
Final Project / 30%
Students with Disabilities: It is the policy of Tarleton State University to comply with the Americans with Disabilities Act and other applicable laws. If you are a student with a disability seeking accommodations for this course, please contact Trina Geye, Director of Student Disability Services, at 254.968.9400 or . Student Disability Services is located in Math 201. More information can be found at or in the University Catalog.
Academic Integrity: The Tarleton University Mathematics Department takes academic integrity very seriously. The usual penalty for a student caught cheating includes an F in the course. Further penalties may be imposed, including expulsion from the university.
Student Learning Outcomes
Knowledge outcomes: Students will demonstrate knowledge of the following topics
a)Basics of experimental design, such as the distinction between observational studies and experiments, randomization, blinding, and confounding variables.
b)The mathematical assumptions of statistical models, such as simple and multivariate linear regression models and logistic regression models.
c)Techniques of estimation and hypothesis testing for these models, including ordinary least squares, generalized least squares, maximum likelihood estimation, t-tests, F-tests, and likelihood ratio tests.
Skill outcomes: Students will demonstrate proficiency in the following skills
d)Using software to fit statistical models to real data sets and make predictions.
e)Assessing the appropriateness of models with diagnostics, such as the Shapiro-Wilk test, Brown-Forsythe test, Durbin-Watson test, and various residual plots.
f)Addressing problems with models using remedial measures such as Box-Cox transformations and generalized least squares.
g)Analyzing empirical papers that use statistical models.
Sections of Primary Interest
Statistical Models: Theory and Practice, by David Freedman
1 Observational Studies and Experiments
1.1 Introduction
1.2 The HIP trial
1.3 Snow on cholera
1.4 Yule on the causes of poverty
Exercise set A
1.5 End notes
2 The Regression Line
2.1 Introduction
2.2 The regression line
2.3 Hooke’s law
Exercise set A
2.4 Complexities
2.5 Simple vs multiple regression
Exercise set B
2.6 End notes
3 Matrix Algebra
3.1 Introduction
Exercise set A
3.2 Determinants and inverses
Exercise set B
3.3 Random vectors
Exercise set C
3.4 Positive definite matrices
Exercise set D
3.5 The normal distribution
Exercise set E
3.6 If you want a book on matrix algebra
4 Multiple Regression
4.1 Introduction
Exercise set A
4.2 Standard errors
Things we don’t need
Exercise set B
4.3 Explained variance in multiple regression
Association or causation?
Exercise set C
4.4 What happens to OLS if the assumptions break down?
4.5 Discussion questions
4.6 End notes
5 Multiple Regression: Special Topics
5.1 Introduction
5.2 OLS is BLUE
Exercise set A
5.3 Generalized least squares
Exercise set B
5.4 Examples on GLS
Exercise set C
5.5 What happens to GLS if the assumptions break down?
5.6 Normal theory
Statistical significance
Exercise set D
5.7 The F-test
“The” F-test in applied work
Exercise set E
5.8 Data snooping
Exercise set F
5.9 Discussion questions
5.10 End notes
Applied Linear Statistical Models, 5th ed., by Kutner, Nachtsheim, Neter, and Li.
3Diagnostics and Remedial Measures
3.1 Diagnostics for Predictor Variable
3.2 Residuals
3.3 Diagnostics for Residuals
3.4 Overview of Tests Involving Residuals
3.5 Correlation Test for Normality
3.6 Tests for Constancy of Error Variance
3.7 F Test for Lack of Fit
3.8 Overview of Remedial Measures
3.9 Transformations
9 Building the Regression Model I: Model Selection and Validation
9.1 Overview of Model-Building Process
9.2 Surgical Unit Example
9.3 Criteria for Model Selection
9.4 Automatic Search Procedures for Model Selection
9.5 Some Final Comments on Automatic Model Selection Procedures
9.6 Model Validation
Applied Logistic Regression, 2nd ed., by Hosmer and Lemeshow.
2 Multiple Logistic Regression
2.1 Introduction
2.2 The Multiple Logistic Regression Model
2.3 Fitting the Multiple Logistic Regression Model
2.4 Testing for the Significance of the Model Coefficients
4 Model-Building Strategies and Methods for Logistic Regression
4.1 Introduction
4.2 Variable Selection
4.3 Stepwise Logistic Regression
4.4 Best Subsets Logistic Regression
Multivariate Data Reduction and Discrimination, by Khattree and Naik.
5 Discriminant Analysis
5.1 Introduction
5.2 Multivariate Normality
5.4 Discriminant Analysis: Fisher’s Approach
5.5 Discriminant Analysis for k Normal Populations