Outline

Overview

Classical linear models are widely used in science, business, economics and technology. This unit will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using linear methods, together with concepts of collection of data and design of experiments. You will first consider linear models and regression methods with diagnostics for checking appropriateness of models, looking briefly at robust regression methods. Then you will consider the design and analysis of experiments considering notions of replication, randomisation and ideas of factorial designs. Throughout the course you will use the R statistical package to give analyses and graphical displays. This unit includes material in STAT3022 Applied Linear Models, but has an additional component on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	An average mark of 65 or above in 12 credit points from (STAT2X11 or DATA2X02 or STAT3X23 or STAT3X21 or STAT3925 or STAT3888 or DATA3888)
Corequisites ?	None
Prohibitions ?	STAT3012 or STAT3912 or STAT3022 or STAT3922 or STAT3004 or STAT3904
Assumed knowledge ?	Material in DATA2X02 or equivalent and MATH1002 or MATH1X61 or equivalent; that is, a knowledge of applied statistics and an introductory knowledge to linear algebra, including eigenvalues and eigenvectors
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Linh Nghiem, linh.nghiem@sydney.edu.au

Assessment

The census date for this unit availability is 31 March 2026

Details
Criteria

Type	Description	Weight	Due	Length	Use of AI
Written exam	Final Exam Final examination	50%	Formal exam period	2 hours	AI prohibited
Outcomes assessed:
Written work	Biweekly homework Biweekly homework on the advanced proof. only handwritten answers are accepted	5%	Multiple weeks	Variable	AI allowed
Outcomes assessed:
In-person written or creative task	Quiz 1 Quiz 1	10%	Week 05 Due date: 27 Mar 2026 at 23:59 Closing date: 27 Mar 2026	50 minutes	AI prohibited
Outcomes assessed:
Written work	Assignment 1 Answers with calculations. Submitted through Canvas	5%	Week 07 Due date: 19 Apr 2026 at 23:59 Closing date: 29 Apr 2026	Variable	AI allowed
Outcomes assessed:
In-person written or creative task	Quiz 2 Quiz 2	10%	Week 11 Due date: 15 May 2026 at 23:59 Closing date: 15 May 2026	50 minutes	AI prohibited
Outcomes assessed:
In-person written or creative task	Advanced quiz Advanced quiz during advanced lectures	10%	Week 13 Due date: 29 May 2026 at 23:59 Closing date: 29 May 2026	50 minutes	AI prohibited
Outcomes assessed:
Written work	Assignment 2 Answers with calculations. Submitted through Canvas	5%	Week 13 Due date: 31 May 2026 at 23:59 Closing date: 09 Jun 2026	Variable	AI allowed
Outcomes assessed:
Contribution	Workshop participation Participation in workshop	5%	Weekly	1 hour per week	AI allowed
Outcomes assessed:
= hurdle task ?

Assessment summary

Detailed information for each assessment can be found on Canvas.

Assignments: There are two assignments (shared with STAT3022), which must be submitted electronically via Canvas by the deadline. There will be no simple extension for these two assignments.
Quiz 1 and Quiz 2: Two regular quizzes (shared with STAT3022) will be held in-person on campus during Week 5 and Week 11. You must sit the quiz at the time and location that appears as Assessment on your timetable. If you are unable to sit the quiz at that time for a valid reason, then you have the option to apply for Special Consideration or Special Arrangements. No "better mark" principle is used for this unit.
Advanced quiz: The advanced quiz will be held during the Advanced Lecture Week 13 and cover all the contents of advanced lectures + homework. The advanced quiz must be attempted to pass the unit; if you are unable to sit the quiz at that time for a valid reason, then you have the option to apply for Special Consideration or Special Arrangements. If it is approved, you will sit on a Replacement Advanced quiz.
Homework: There will be 5 homework for advanced lecture's content. Only the highest marks of 4 homework are counted. Only handwritten answers are acceptable.
Workshop contribution: Every week you are expected to attend one hour of workshop. There will be up to 3 marks available for each week, note that attendance alone may not be sufficient to get the full marks.
Final exam: The final exam will be shared with STAT3022 and will not cover any content in Advanced lectures. It is a hurdle task and student has to pass the final exam to pass the unit.

If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

Assessment criteria

Resultname	Markrange	Description
High distinction	85 -100	Representing complete or close to complete mastery of the material.
Distinction	75-84	Representing excellence, but substantially less than complete mastery.
Credit	65-74	Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.
Pass	50-64	Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.
Fail	0-49	When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Use of generative artificial intelligence (AI)

You can use generative AI tools for open assessments. Restrictions on AI use apply to secure, supervised assessments used to confirm if students have met specific learning outcomes.

Refer to the assessment table above to see if AI is allowed, for assessments in this unit and check Canvas for full instructions on assessment tasks and AI use.

If you use AI, you must always acknowledge it. Misusing AI may lead to a breach of the Academic Integrity Policy.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The University expects students to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

Our website provides information on academic integrity and the resources available to all students. This includes advice on how to avoid common breaches of academic integrity. Ensure that you have completed the Academic Honesty Education Module (AHEM) which is mandatory for all commencing coursework students

Penalties for serious breaches can significantly impact your studies and your career after graduation. It is important that you speak with your unit coordinator if you need help with completing assessments.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Support for students

The Support for Students Policy reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

Weekly schedule

WK	Topic	Learning activity
Week 01	Introduction, simple linear regression	Lecture (3 hr)
Week 02	Simple linear regression (continued)	Lecture (4 hr)
Week 03	Review of linear algebra, multiple linear regression models: formulation and model fitting	Lecture (4 hr)
Week 04	Multiple linear regression models: inference and prediction	Lecture (4 hr)
Week 05	Multiple linear regression model: diagnostics and analysis of unusual observations	Lecture (4 hr)
Week 06	Multicollinearity, special linear regression models	Lecture (4 hr)
Week 07	ANOVA models for design with one factor	Lecture (4 hr)
Week 08	ANOVA models for design with two factors	Lecture (4 hr)
Week 09	ANOVA models with two factors (continued)	Lecture (4 hr)
Week 10	ANOVA models with two factors (continued)	Lecture (4 hr)
Week 11	Linear mixed effect models: formulation and estimation	Lecture (4 hr)
Week 12	Linear mixed effects models: inference and prediction	Lecture (4 hr)
Week 13	Linear mixed effects models; revision	Lecture (4 hr)
Weekly	Computer lab on weekly topic	Lecture (1 hr)

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

At the completion of this unit, you should be able to:

LO1. Apply and formulate appropriate linear models to analyse data from diverse settings, including cross-sectional studies, experiments, panel studies
LO2. Apply, analyse, and implement least square estimators for parameters in linear models
LO3. Calculate and interpret interval estimators, including confidence intervals and prediction intervals, for appropriate quantities in linear models
LO4. Conduct appropriate hypothesis testings for parameters in linear models
LO5. Conduct appropriate diagnostics to check model assumptions and detect unusual observations
LO6. Apply, implement, and interpret the results from likelihood-based methods to fit linear mixed effects models
LO7. Derive and re-create proofs of theoretical aspects of linear models.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

Reweighting the assignments to reflect the impact of AI

Disclaimer

Important: the University of Sydney regularly reviews units of study and reserves the right to change the units of study available annually. To stay up to date on available study options, including unit of study details and availability, refer to the relevant handbook.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links

STAT4022: Linear and Mixed Models

Semester 1, 2026 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links