Unit of study_

# STAT3922: Applied Linear Models (Advanced)

## Overview

This unit will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical 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 is essentially an Advanced version of STAT3012, with additional emphasis on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods.

### Unit details and rules

Unit code STAT3922 Mathematics and Statistics Academic Operations 6 STAT3912 or STAT3012 or STAT3022 or STAT4022 STAT2X11 and [a mark of 65 or greater in (STAT2X12 or DATA2X02)] None None Yes

### Teaching staff

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

## Assessment

Type Description Weight Due Length
Supervised exam

Final examination
Final examination
50% Formal exam period 2 hours
Outcomes assessed:
Small continuous assessment Biweekly homework
Biweekly homework on the advanced proof.
5% Multiple weeks
Due date: 28 May 2023 at 23:59
Variable
Outcomes assessed:
Tutorial quiz Quiz 1
Tutorial Quiz 1
5% Week 05
Due date: 22 Mar 2024 at 18:00
50 minutes
Outcomes assessed:
Assignment Assignment 1
Answers with calculations. Submitted through Turnitin
10% Week 07
Due date: 13 Apr 2024 at 23:59
Variable
Outcomes assessed:
Tutorial quiz Quiz 2
Tutorial Quiz 2
10% Week 11
Due date: 10 May 2024 at 18:00
50 minutes
Outcomes assessed:
10% Week 13
Due date: 24 May 2024 at 18:00
50 minutes
Outcomes assessed:
Assignment Assignment 2
Answers with calculations. Submitted through Turnitin
10% Week 13
Due date: 25 May 2024 at 23:59
Variable
Outcomes assessed:

### Assessment summary

Detailed information for each assessment can be found on Canvas.

Final exam: 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

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range

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.

### 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.

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

## 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 2023 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 2023. 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)

## Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 Introduction, simple linear regression Lecture (3 hr)
Week 02 Simple linear regression, review of linear algebra Lecture and tutorial (4 hr)
Week 03 Multiple linear regression models: formulation, model fitting, and inference Lecture and tutorial (4 hr)
Week 04 Multiple linear regression models: F-test, model diagnostics, leverage, outliers and influential analysis Lecture and tutorial (4 hr)
Week 05 Polynomial regression, additive and interaction models, models with qualitative variables Lecture and tutorial (4 hr)
Week 06 Model evaluation, variable selection, automated search procedure Lecture and tutorial (4 hr)
Week 07 ANOVA models Lecture and tutorial (4 hr)
Week 08 ANOVA models, multiple comparison Lecture and tutorial (4 hr)
Week 09 Experimental designs: completely randomized designs, block designs Lecture and tutorial (4 hr)
Week 10 Incomplete block designs, nested designs Lecture and tutorial (4 hr)
Week 11 Fixed and random effects, variance component estimation Lecture and tutorial (4 hr)
Week 12 Mixed effects models Lecture and tutorial (4 hr)
Week 13 Mixed effects models Lecture and tutorial (4 hr)
Weekly Computer lab on weekly topic Computer laboratory (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.

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

• LO1. formulate and compare linear models, including evaluation of model diagnostics and outlier detection in various settings, including regression, experiments designs, and longitudinal (panel) data
• LO2. apply, construct and interpret multi-way ANOVA models and make inference on all parameters
• LO3. conduct and recognize different methods of multiple comparisons
• LO4. calculate and interpret confidence intervals for all parameters in linear regression and distinguish the difference between confidence intervals and prediction intervals
• LO5. formulate mixed models, including recognizing the difference between fixed and random effects, and implementing likelihood-based model fitting methods in R
• LO6. derive and re-create proofs of theoretical aspects of regression methods.

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

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Responding to student feedback

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

- Replacing two online quizzes by closed-book tutorial quizzes will help student get used to closed-book final exams. - Advanced quiz (10%) is added back to make other quizzes and final exam the same as those for STAT3022.

### Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General Laboratory Safety Rules

• No eating or drinking is allowed in any laboratory under any circumstances
• A laboratory coat and closed-toe shoes are mandatory