Syllabus

Course description

STATS 413 is an introduction to applied regression analysis. The course covers

1. model estimation: ordinary least squares (OLS) estimation, including finite-sample & asymptotic properties of OLS
2. statistical inference: hypothesis testing, confidence and prediction intervals
3. analysis of variance (ANOVA), model diagnosis, model selection,
4. generalized linear models (GLMs): logistic regression
5. shrinkage methods (eg, ridge regression, lasso, etc).

If we have time at the end of the semester, we may cover some advanced topics (eg, causal inference, time series etc).

Prerequisites (in no particular order):

• linear algebra at the level of MATH 214/217/417,
• probability at the level of STATS 412/425,
• statistics at the level of STATS 250/412

You should have a good grasp of the following topics:

• matrix arithmetic (addition, multiplication, inversion, transposition, rank, trace, etc),
• random variables: expecation, variance, covariance & correlation
• joint distributions, independence, conditional expectations
• common distributions (such as normal, Bernoulli, binomial, etc)
• estimation, (statistical) hypothesis testing, confidence intervals

We shall review some relevant topics, but this should not be the first time you see them. Here are some references that cover the prerequisite topics:

• Linear Algebra Review and Reference
• Probability Theory Review and Reference

Course staff

Ethan Schubert M 1–2:30 PM, Zoom	Gabriel Durham M 10–11:30 AM, Zoom	Jacob Trauger
Luke Francisco Tu 10:30-12 PM, Zoom	Xinhe Wang W 10–11:30 AM, Zoom	Yuekai Sun W 1–2:30 PM, 271 WH

References and textbooks

There is no textbook for the course; we will provide lecture materials on the course website. Although not required, you may find the following references useful:

• Hayashi’s Econometrics: the first two chapters are good references (albeit at a more advanced level) for linear regression;
• An Introduction to Statistical Learning and Elements of Statistical Learning: ESL is the more advanced version of ISL; both are good references for the more modern methods presented in the course.

In the past, other STATS 413 instructors have recommended the following references:

• Weisberg’s Applied Linear Regression,
• Faraway’s Practical Regression and ANOVA using R.

Problem sets

Problem sets are assigned weekly on Fridays and due at noon ET the following Friday. If you need an extension on a problem set, you must request an extension from the GSI leading your tutorial at least 24 hours before the due date. We want you to complete the problem sets because they are an integral part of the course, so we are generous with extensions. On the other hand, if you submit a problem set late, 1 pt will be deducted from your overall score on the late problem set.

You must typeset your solutions with LaTeX. If you submit handwritten solutions to a problem set, 1 pt will be deducted from your overall score on the problem set. If you are new to LaTeX, we recommend editing LaTeX documents on Overleaf. The Overleaf documentation is also a great place to learn LaTeX. In fact, when you search for LaTeX related searches, the Overleaf documentation is often one of the first results that come up!

Grading: Problem sets are graded on a scale of 0 to 2. Each problem in a problem set is graded according to the following scale:

• 2 pts = essentially correct
• 1 pt = incorrect but you made some progress towards the correct solution
• 0 pt = no progress towards the correct solution

Your score on a problem set is the sum of your scores on the all the problems divided by the number of non-extra credit problems (if there are no extra credit problems on a problem set, then your grade on the problem set is simply the average of your scores on all the problems).

Tutorials (labs)

The “lab” component of STATS 413 consists of a weekly, 50-min, in-person Oxbridge-style tutorial/supervision with 4 other students. The tutorial is the lab component of the course; there are no other labs. In a tutorial, the GSI will lead a socratic round-table discussion of the problems on the problem set due the previous week. If you are not familiar with Oxbridge-style tutorial/supervisions, I suggest you watch a recording of an Oxford tutorial on YouTube.

During the 1st (half) week of the semester, you will sign up for a weekly, 50-min in-person tutorial with 4 other students led by a GSI. Tutorials start the 3rd week (2nd full week) of the semester (the week of MLK), and occur at the same times every week for the rest of the semester. Please check the Canvas for tutorial assignments.

You must go to the tutorial you are assigned to. If you cannot attend your (assigned) tutorial, please make arrangements with the course staff to attend an alternative tutorial at least 24 hrs in advance. To find an alternative tutorial,

1. look for tutorials groups with <5 students on Canvas;,
2. once you find a potential alternative tutorial, contact the GSI leading the alternative tutorial to confirm you can attend their tutorial.
3. if the GSI leading the alternative tutorial confirms you can attend their tutorial, then contact the GSI leading your regular tutorial to let them know you will be attending the alternative tutorial.

Grading: Your participation in each tutorial is graded on a scale of 1 to 2. Your participation in the discussion of each problem is graded according to the following scale:

• 2 pts = full participation, and you knew how to solve the problem
• 1 pt = full participation but you didn’t know how to solve the problem
• 0 pt = no participation

Your score for a tutorial is the average of your participation scores for the problems discussed in the tutorial.

Exams

There are 2 midterm exams:

• midterm I: Wed, Feb 25 in class.
• midterm II: Mon, Apr 20 in class. Midterm II is not cumulative; it assesses topics not covered on midterm I.

Please keep the preceding dates in mind when making plans for spring and summer break. If you cannot make an exam, you must make arrangements with the course staff at least 1 week in advance.

The exams are closed book and closed notes except for a single (letter-sized) handwritten sheet of notes (front and back). Most of the exam problems are easier versions of problem sets problems, so you are well-prepared for the exams if can do the problem sets unassisted.

Grading

Your overall grade is determined by your overall score:

• 20% problem sets,
• 20% tutorials,
• 5% midterm I + 55% midterm II or 55% midterm I + 5% midterm II, whichever is higher.

We want you to complete all problem sets and attend all tutorials, so we do not drop any problem set/tutorial grades. Students who obtain an average of at least 90%, 80%, and 70% will receive grades of at least A-, B-, and C- respectively. We may lower the cutoffs at the end of the semester, but we will not raise them.

Academic misconduct

The College of LSA prohibits all forms of academic dishonesty and misconduct. Minor infractions usually result in a zero on the assignment and a one letter overall grade reduction; more serious or repeated infractions will result in a failing overall grade and additional sanctions imposed by the Office of the Assistant Dean. For more information, including examples of behaviors that are considered academic misconduct and potential sanctions, please see LSA’s Community Standards of Academic Integrity.

Accommodations for students with disabilities

We work with Office of Services for Students with Disabilities to determine appropriate accommodations on an individual basis. Please follow the instructions in their website to request accommodations.