Statistics 211: The Mathematics of Regression
  Fall 2021

Course Home Page

Course Description

In this course, we learn the mathematics underpinning linear regression and logistic regression, the two most common models used in applied statistics. We see how matrix algebra enables a very practical representation of regression modeling, helps us understand how and why regression works, and offers convenient maximum likelihood estimation of regression model parameters. In STA 211, we emphasize mathematics and theory over data analysis (whereas STA 210 emphasizes data analysis over theory), although we continuously connect to topics in data analysis. This course is 0.5 credits.

Course Objectives

Logistics

Prerequisites

The course is designed for students who have completed linear algebra (Math 216/218/221 or the equivalent). Students should have completed STA 210 (or an equivalent course on applied regression modeling) or be taking it concurrently. The course is a prerequisite or co-requisite for STA 360.

Readings

Readings and course videos will be posted on the STA 210 course web site on Sakai.

Computing

We will use the statistical software package R to implement regression models using matrix algebra.  It can be downloaded for free at http://www.r-project.org/.

Schedule of Topics

We will cover the topics in the table below.  We may spend different amounts of time on each topic than shown, depending on the interests of the class participants.

Introduction and reviews of linear regression, maximum likelihood estimators (MLEs), and key linear algebra concepts 2 lectures
Parameter estimation for simple linear regression (MLEs and their properties, least squares, inferences)
 1 lectures
Matrix representation of simple linear regression model (concepts, geometrical interpretations, estimation, predictions, diagnostics)
 2 lectures
Matrix representation of multiple linear regression model (concepts, geometrical interpretations, estimation, predictions, diagnostics, dummy variables, co-linearity, contrasts)
 3 lectures
Maximum likelihood for logistic regression model (Newton-Raphson algorithm)
 2 lectures


Graded work

Graded work for the course will consist of one term exam and methods assignments.  There is no final exam.  Students' final grades will be determined as follows:
 
Methods Assignments
 75%
Term Exam
 25%

There are no make-ups for exams or assignments except for medical or familial emergencies or for reasons approved by the instructor before the due date.  See the instructor in advance of relevant due dates to discuss possible alternatives.

Descriptions of graded work

Methods Assignments:

Methods assignments are posted on the Statistics 211 course web site on Sakai.  Students should upload their work to the Assignments folder in Sakai by the due date.  Students are permitted to work with others on the assignments, but each person must write up and turn in their own answers.  The Methods assignments include questions on the computational and the mathematical aspects of regression modeling. Assignments that involve computing must be turned in using R Markdown.

Term Exam:

The exam will cover mathematical aspects of regression models.   The exam will be towards the end of the course.

Academic honesty

Students are expected to abide by Duke's Community Standard for all work for this course.  Violations of the Standard will result in a zero grade for the relevant assignment and will be reported to the Dean of Students for adjudication. Additionally, there may be penalties to the final grade for the course.   Ignorance of what constitutes academic dishonesty is not a justifiable excuse for violations.

For the exam, students are required to work alone.  For the Methods assignments, students may work with a study group but each student must write up and submit their own answers.

Attendance policy related to COVID symptoms, exposure, or infection

Student health, safety, and well-being are the university's and my top priorities. To help ensure your well-being and the well-being of those around you, please do not come to class if you have symptoms related to COVID-19, have had a known exposure to COVID-19, or have tested positive for COVID-19. If any of these situations apply to you, you must follow university guidance related to the ongoing COVID-19 pandemic and current health and safety protocols. If you are experiencing any COVID-19 symptoms, contact student health: 919-681-9355. To keep the university community as safe and healthy as possible, you will be expected to follow these guidelines. Please reach out to me and your academic dean as soon as possible if you need to quarantine or isolate so that we can discuss arrangements for your continued participation in class.

Mask wearing policy

Per Duke policies related to COVID-19, the instructor, teaching assistants, and all students will wear masks while engaged in course-related activities indoors.

Mental health and wellness

Student mental health and wellness is of primary importance at Duke, and the university offers resources to support students in managing daily stress and self-care. Duke offers several resources for students to seek assistance on coursework and to nurture daily habits that support overall well-being, some of which are listed below.

If your mental health concerns and/or stressful events negatively affect your daily emotional state, academic performance, or ability to participate in your daily activities, many resources are available to help you through difficult times. Duke encourages all students to access these resources.