STATS 401 is an intermediate course in applied statistics focusing on the linear model and its applications. The linear model is a fundamental tool for much of data analysis. We will learn to use the linear model for statistical analysis in applications drawn across the social sciences, the natural sciences, and elsewhere.
We will cover the following topics.
Introduction to command line statistical computing: getting started with R.
Introduction to the linear model: fitting a line by least squares.
Matrices: introduction to the matrix representation of the linear model.
Uncertainty: probability and random variables.
Statistical inference: hypothesis testing and confidence intervals for the linear model.
Model specification: diagnosis of misspecification, and the quest for an appropriate linear model.
Handling some common difficulties: collinear variables, interpreting linear models for observational versus experimental data, working with nonlinear relationships using a linear model, testing multiple hypotheses.
The listed pre-requisites are MATH 115 and one of (STATS 180 or STATS 250 or STATS 280, STATS 412 or ECON 451).
These pre-requisites are formally advisory, but you should not attempt STATS 401 without comparable preparation.
We will build on material in STATS 250. If you have some other background, you may like to check the STATS 250 notes available online.
STATS 280, STATS 412 and ECON 451 are more advanced and therefore entirely adequate preparation. AP Statistics (STATS 180) provides sufficient background, but at a somewhat lower level than STATS 250.
No previous experience with matrices is expected. If you have a course in linear algebra (MATH 214 or 217) you should consider taking STATS 413 instead of STATS 401.
No previous experience with statistical computing is expected. STATS 306 overlaps with our initial introduction to R, but after the first two weeks the courses head in different directions.
There is no textbook for this course. The lecture notes and lab notes will be posted online at https://ionides.github.io/401f18/.
A suitable reference book is “Applied Linear Statistical Models” by Kutner, Nachtsheim, Leter and Li (5th edition).
A previous version of STATS 401 is at https://ionides.github.io/401w18/. This may be a good guide to see where the course is heading, though some material will be new this year.
Your homework report must include a statement titled “Sources”.
Homework reports without a statement of sources will receive zero points.
The lowest homework score will be dropped in the calculation of the course grade.
The sources statement must list all books, internet resources or other people consulted while completing the homework. For example, “Sources: notes only,” or, “Sources: collaboration with X and Y; web site Z,” or, “Sources: notes and office hours.” Any material taken from any source, such as the internet, must be properly acknowledged. Directly copied text must be in quotation marks. Directly copied equations must be explicitly referenced to the source. Unattributed copying from any source is plagiarism, and has potentially serious consequences.
Homework will be graded on engagement with the material. This means that a homework report demonstrating sufficient thought about each problem can receive full credit, regardless of accuracy.
Homework reports that show only superficial engagement with the material will not receive full credit, even if all questions are attempted.
Ways to demonstrate engagement include writing justifications for a qualitative answer and showing your working for a quantitative answer. Simply writing a numerical answer, or responding with a few words to a verbal question, is usually not enough to show you have thought about the task.
Take advantage of this grade scheme to try working on the homework by yourself. Then consult other sources if you like, but you won’t gain extra credit for borrowing a solution online. Material researched online can help to demonstrate engagement with the task, but only if the homework also reports your own thoughts.
All homework, quiz and exam scores will be posted on Canvas. You are responsible for checking posted solutions. Please let us know as soon as possible if there is a grading error, or a missing score for work you turned in.
When possible, please raise gradebook concerns within a week of the score being posted.
Quiz and homework grading questions should be addressed to your GSI. Midterm and final re-grading requests will be considered by the instructor, though you are welcome to ask your GSI for an initial explanation.
Final grades will be based on an overall score, weighted as described above. Letter grades will follow a curve determined by the instructor, consistent with previous offerings of this course.
You are encouraged to bring a laptop to class, to follow along with the class notes and to follow along with statistical computing topics. A tablet may also be useful, but likely will not be able to run R.
Out of courtesy to your class-mates, please keep all screen use relevant to the class. Bear in mind that those beside or behind you may be distracted by your screen.
Attendance in class will not be checked, but is a good predictor of success.
The first half of this course has a fair amount of computing and learning to work with matrices. Keep engaged with this, and you’ll see why this material is useful for the statistical data analysis applications emerging in the second half.
We will work to comply with all individual accommodations requested by the office of Services for Students with Disabilities (SSD).
Accommodations for a small-group environment and additional time will be met for the midterm and final by additional exam sessions starting at the same time as the main session.
To help with the logistics, please give the instructor a copy of your SSD accommodation form within the first two weeks of class.
University of Michigan is committed to advancing the mental health and wellbeing of its students. If you or someone you know is feeling overwhelmed, depressed, and/or in need of support, services are available.
For help, contact Counseling and Psychological Services (CAPS) at (734)764-8312 and https://caps.umich.edu/ during and after hours, on weekends and holidays, or through its counselors physically located in schools on both North and Central Campus. You may also consult University Health Service (UHS) at (734) 764-8320 and https://www.uhs.umich.edu/mentalhealthsvcs, or for alcohol or drug concerns, see www.uhs.umich.edu/aodresources.