STATS 4101 - Statistical Modelling - Honours

North Terrace Campus - Semester 1 - 2024

One of the key requirements of an applied statistician is the ability to formulate appropriate statistical models and then apply them to data in order to answer the questions of interest. Most often, such models can be seen as relating a response variable to one or more explanatory variables. For example, in a medical experiment we may seek to evaluate a new treatment by relating patient outcome to treatment received while allowing for background variables such as age, sex and disease severity. In this course, a rigorous discussion of the linear model is given and various extensions are developed. There is a strong practical emphasis and the statistical package R is used extensively. Topics covered are: the linear model, least squares estimation, generalised least squares estimation, properties of estimators, the Gauss-Markov theorem; geometry of least squares, subspace formulation of linear models, orthogonal projections; regression models, factorial experiments, analysis of covariance and model formulae; regression diagnostics, residuals, influence diagnostics, transformations, Box-Cox models, model selection and model building strategies; logistic regression models; Poisson regression models.

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Course Details

Course Code	STATS 4101
Course	Statistical Modelling - Honours
Coordinating Unit	Mathematical Sciences
Term	Semester 1
Level	Undergraduate
Location/s	North Terrace Campus
Units	3
Contact	Up to 3 hours per week
Available for Study Abroad and Exchange	Y
Prerequisites	STATS 2107 or (MATHS 2201 and MATHS 2202) or (MATHS 2106 and MATHS 2107)
Incompatible	STATS 3001
Assumed Knowledge	Experience with the statistical package R such as would be obtained from STATS 1005 or STATS 2107
Restrictions	Honours students only
Assessment	ongoing assessment, exam

Course Staff

Course Coordinator: Dr John Maclean

Course Timetable

The full timetable of all activities for this course can be accessed from .

Course Learning Outcomes

1. Explain the mathematical basis of the general linear model and its extensions to multilevel models and logistic regression.

2. Use the open source programming language R for the analysis of data arising from both observational studies and designed experiments.

3. Explain the role of statistical modelling in discovering information, making predictions and decision making in a range of applications including medicine, engineering, science and social science.

University Graduate Attributes

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute	Course Learning Outcome(s)
Attribute 1: Deep discipline knowledge and intellectual breadth Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.	1,2,3
Attribute 2: Creative and critical thinking, and problem solving Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.	1,2,3
Attribute 4: Professionalism and leadership readiness Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.	2

University Graduate Attribute

Course Learning Outcome(s)

Attribute 1: Deep discipline knowledge and intellectual breadth

Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.

1,2,3

Attribute 2: Creative and critical thinking, and problem solving

Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.

1,2,3

Attribute 4: Professionalism and leadership readiness

Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.

Learning Resources

Required Resources

There is no prescribed text for this course.

Recommended Resources

The following references are recommended reading:

1. A. Agresti. Foundations of linear and generalized linear models. Wiley, 2015.
2. A. Dobson and A. Barnett. An introduction to generalised linear models. Third Edition, Chapman & Hall/CRC, 2008.
3. P. McCullagh and J. Nelder. Generalised linear models. Second Edition, Chapman & Hall/CRC, 1989.
4. W. Venables and B. Ripley. Modern Applied Statistics with S. Fourth Edition, Springer, 2002.

Online Learning

This course uses MyUni-Canvas for providing course materials and resources, including lecture notes, assignment papers, tutorial and computing worksheets, solutions, project materials and so on. Students should check their email and MyUni announcements for this course regularly for any notices or correspondence from the Course Coordinator and tutors.

Learning & Teaching Modes

The lecturer guides the students through the course material in 24 lectures. Students are expected to prepare for lectures by reading the printed notes in advance of the lecture, and by engaging with the material in the lectures. Students are expected to attend all lectures, but lectures will be recorded (where appropriate facilities are available) to help with occasional absences and for revision purposes.

In the fortnightly tutorials, students will work on and discuss their solutions in groups, and seek help from the tutors as needed. These exercises will be further supplemented by the fortnightly computing practical sessions during which students will work under guidance on practical data analysis and develop more advanced computing skills using R. A series of three homework assignments and a group project build on the tutorial and practical material, and provides students with the opportunity to gauge their progress and understanding of the course material.

Workload

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

Activity	Quantity	Workload Hours
Lectures	24	72
Tutorials	6	12
Practicals	6	12
Assignments	3	15
Test	3	15
Online quizzes	9	30
Total		156

Learning Activities Summary

Week:	Topics covered
1.	Introduction, matrix notation, multiple regression. The linear regression model.
2.	Estimable functions and best linear unbiased estimates. The Gauss-Markov Theorem. Inference for multiple regression. Prediction. Symbolic specification of linear models.
3.	Factors and contrasts. The marginality principle.
4.	Regression diagnostics; influence diagnostics. Leverage and Cook's distance.
5.	Model building: variance reduction in randomised experiments; observational studies and quasi-experiments. The role of predictor variables.
6.	Model selection algorithms: forwards, backwards and stepwise selection procedures. Box-Cox transformation and the profile likelihood.
7.	Generalised least squares (GLS). The geometry of least squares; orthogonal projections.
8.	The geometry of least squares (cont.). Estimation of the residual variance; estimable functions; hypothesis tests; expected mean squares.
9.	Orthogonality of hypotheses. Extension to generalised least squares. Multistratum experiments and random effects models.
10.	Expected mean squares for the split plot experiment. Least squares estimates for balanced factorial experiments. Averaging operators.
11.	Logisitic regression; maximum likelihood estimation; inference for regression coefficient. Hypotheses concerning several parameters.
12.	Logisitic regression: common odds rations for several 2x2 tables. Prospective and retrospective studies. Model fit and overdispersion.

Specific Course Requirements

Students completing this course as an Honours course will complete additional work, in particular additional advanced assignment and project work.

The University's policy on Assessment for Coursework Programs is based on the following four principles:

Assessment must encourage and reinforce learning.
Assessment must enable robust and fair judgements about student performance.
Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
Assessment must maintain academic standards.

Assessment Summary

Component	Assessment mode	Week Set	Week Due	Weighting	Learning outcomes
Assignments	Formative & summative	1, 4, 8	2, 6, 10	30%	All
Online quizzes	Formative & summative		1, 2, 3, 5, 6, 7, 9, 10, 11	10%	All
Examination	Summative			30%	All
Online test	Summative	4, 8, 12	4, 8, 12	30%	All

Assessment Related Requirements

An aggregate final mark of at least 50% is required to pass the course.

Assessment Detail

No information currently available.

Submission

No information currently available.

Course Grading

Grades for your performance in this course will be awarded in accordance with the following scheme:

M11 (Honours Mark Scheme)
Grade	Grade reflects following criteria for allocation of grade	Reported on Official Transcript
Fail	A mark between 1-49	F
Third Class	A mark between 50-59	3
Second Class Div B	A mark between 60-69	2B
Second Class Div A	A mark between 70-79	2A
First Class	A mark between 80-100	1
Result Pending	An interim result	RP
Continuing	Continuing	CN

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through .

Student Feedback

The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
Student Support
Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
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Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student鈥檚 disciplinary procedures.

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Authorised by:	Deputy Vice-Chancellor and Vice-President (Academic)
Maintained by:	Course Outlines Administrator

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