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Regression Analysis

PSTAT 126

Fall 2021

Catalog description

Linear and multiple regression, analysis of residuals, transformations, variable and model selection including stepwise regression, and analysis of covariance. The course will stress the use of computer packages to solve real world problems. Prerequisites: Probability and Statistics I and II (PSTAT 120A-B) and Principles of Data Science with R (PSTAT 10). Credit units: 4.

Format

The course will be conducted partly in person and partly in online asynchronous format. We will have one in person lecture per week introducing the topic for the week and covering central concepts with examples as time permits. Following the weekly lecture, a series of short videos will be released that expand on the week’s material in more detail by providing example applications, R codes, mathematical proofs, and the like. Sections will be held online; your TAs will guide you through lab activities in pre-recorded videos. Office hours will be held virtually via Zoom, and asynchronous discussion will be hosted on Nectir. All online content will be hosted or linked to on Gauchospace.

Each week, an email announcement will be sent on Monday morning summarizing students’ re-sponsibilities for that week. Reading and homework assignments will be given on a weekly basis. All assignments (with the exception of the final exam) will be distributed and submitted online; generally, these will be released on Monday and due on Friday.

Materials

Readings for the course will draw on Julian Faraway’s Linear Models with R, first or second editions, available for purchase or ebook rental here on the publisher’s website; ebook rental is the most affordable option, though you may find less expensive alternatives on other websites like Amazon.

On occasion other texts will be referenced, and in particular students may find Wickham and Grolemund’s R for Data Science to be a useful companion reference during the course.

Tentative schedule

The tentative weekly lecture schedule is indicated below and subject to change based on the progress of the class.

Learning outcomes

In this course, students will:

1. Articulate the linear model and state model assumptions in conventional statistical notation and in words.

2. Compute and interpret estimates of linear model parameters, and use them to conduct infer-ence and prediction.

3. Carry out model diagnostics to assess plausibility of model assumptions and identify and correct violations.

4. Explore data applications and practice communicating results, using .Rmd files for repro-ducible analysis, visualization, and report generation.

Assessments

Your attainment of course learning outcomes will be measured by the following assessments, with the relative weighting for final grade calculations indicated in parentheses. All assessments within each category are given equal weight.

• Homeworks (80%). Homeworks will be assigned weekly. These assignments comprise math-ematical problems that complement the lecture material, computational problems, and con-ceptual questions. The overall objective of these assignments is to provide practice in applying course material and computing tools. Collaboration is encouraged, but each student should submit their own work. Homeworks will be graded out of 50 points each.

• Final (20%). A comprehensive take-home final will be given at the end of the term. Problems will focus on applications of course material to data analysis tasks and proper interpretation of results, but may touch on mathematical material. The final will be graded out of 50 points.

Communication

There are four means of communication with the instructor, TA, and other students: Nectir, office hours, email, and (Zoom) appointments. Please use them in that order of priority; email and appointments should not be used to discuss course material.

1. Nectir. Consider Nectir as your primary communication resource for the course — this will be our virtual classroom and your way to stay connected with the instructor, the TA, and your classmates throughout the term. You can start and participate in threaded conversations in the group chat, create discussions for specific purposes as you see fit (e.g., forming a study group), and exchange direct messages with anyone in the class. The instructor and TA will monitor each page as well as their direct messages daily, so posts and messages shared and sent via Nectir are the fastest way to interact with the group and resolve questions. You are encouraged to participate actively — the instructor and TA will rely on Nectir conversations to get to know each of you and gauge how the class is doing, and your fellow students will benefit from your engagement and contributions.

2. Office hours. Office hours will be offered on a weekly basis via Zoom by both the instructor and the TA. These are opportunities to interact informally in real time and discuss course material or assignments.

3. Email. Please use email with discernment for simple communication regarding personal matters (e.g., needs for special accommodations due to medical or other emergencies). Please refrain from communicating about course material via email. A response is guaranteed within 48 weekday hours (so if you email on Friday afternoon, you may not receive a reply until Tuesday afternoon). In light of this response policy, bear in mind that you are likely to receive replies to messages or posts in Nectir much faster than replies to email. If your message is time-sensitive, please indicate so in the subject and we will do our best to respond promptly.

4. Appointment. You can schedule 20-minute Zoom appointments with the instructor via Calendly as needed. If you schedule an appointment, you will be prompted to indicate what you wish to discuss. Due to the course enrollment appointments will not be granted for private instruction; any such appointments will be cancelled.

Expected time commitment

The course is 4 credit units; each credit unit corresponds to an approximate time commitment of 3 hours per week. So, expect to allocate up to 12 hours per week, even if you find you do not need that amount of time. Bear in mind that homework assignments will be labor-intensive and may consume the majority of this time. If you find yourself spending considerably more than 12 hours on the course on a regular basis, please let the instructor or TA know so that we can help you balance the workload.

Grades

Your overall grade in the course will be calculated as the weighted average of the proportions of total possible points in each assessment category according to the weightings indicated in the Assessments section and reported as a percentage rounded to two decimal places. Tentatively, letter grades will be assigned according to the rubric below – a curve is possible, but not guaranteed.

You can keep track of your marks on individual assessments in Gradescope. Please notify the instructor or TA of any errors in grade entry or discrepancies in assessment; otherwise, please do not attempt to negotiate the grades themselves. If at the end of the course you believe your grade was unfairly assigned, you are entitled to contest it according to the procedure outlined here in the UCSB General Catalog.

Conduct

Please be especially mindful of maintaining respectful and kind communication. Bear in mind that this is much more difficult with written communication, and consider carefully how your words might be received by others. You are expected to uphold the UCSB student code of conduct; you can find the student code of conduct on the Office of Student Conduct website from this page. If you are uncomfortable with the online conduct of another participant for any reason, please notify the instructor or TA.

Academic integrity

Please maintain integrity. You are encouraged to collaborate in this course, but all submitted work must be your own. Any form of plagiarism, cheating, misrepresentation of individual effort on as-signments and assessments, falsification of information or documents, or misuse of course materials compromises your own learning experience, that of your peers, and undermines the integrity of the UCSB community. Any evidence of dishonest conduct will be discussed with the student(s) involved and reported to the Office of Student Conduct. Depending on the nature of the evidence and the violation, penalty in the course may range from loss of credit to automatic failure. For a definition and examples of dishonesty, a discussion of what constitutes an appropriate response from faculty, and an explanation of the reporting and investigation process, see the OSC page on academic integrity.

Late work

There is a one-hour grace period on all submission deadlines. After that, work may be submitted late within 48 hours of the deadline.

Every student can submit two late assignments without penalty. Thereafter, late submissions will be evaluated for 75% of assessed credit.

Extensions due to personal circumstances will be considered but should be arranged in advance of relevant deadlines. Without an extension, late work will not be accepted beyond 48 hours after the deadline.

Accommodations

Reasonable accommodations will be made for any student with a qualifying disability. Such requests should be made through the Disabled Students Program (DSP). More information, instructions on how to access accommodations, and information on related resources can be found on DSP website. Semi-remote learning may present unique accommodation needs requiring additional flexibility; students receiving accommodation via DSP are invited to discuss this with the instructor if desired.

Student evaluation of teaching

Toward the end of the term you will be given an opportunity to provide feedback about the course via ESCI. Your suggestions and assessments are essential to improving the course, so please take the time to fill out the evaluations thoughtfully.