STATS 7054 - Statistical Modelling

North Terrace Campus - Semester 1 - 2025

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 7054
Course	Statistical Modelling
Coordinating Unit	Mathematical Sciences
Term	Semester 1
Level	Postgraduate Coursework
Location/s	North Terrace Campus
Units	3
Contact	Up to 3 hours per week
Available for Study Abroad and Exchange	Y
Prerequisites	STATS 7107
Assumed Knowledge	Experience with the statistical package R
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.

最新糖心Vlog 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

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.	Logistic regression; maximum likelihood estimation; inference for regression coefficient. Hypotheses concerning several parameters.
12.	Logistic regression: common odds rations for several 2x2 tables. Prospective and retrospective studies. Model fit and overdispersion.

Specific Course Requirements

Students completing this course at Masters level will complete additional work, in particular additional advanced assignment and project work.

The 最新糖心Vlog'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	15%	All
Online quizzes	Formative & summative		1, 2, 3, 5, 6, 7, 9, 10, 11	10%	All
Examination	Summative			60%	All
Online test	Summative	4, 8, 12	4, 8, 12	15%	All

Assessment Related Requirements

An aggregate final score 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:

M10 (Coursework Mark Scheme)
Grade	Mark	Description
FNS		Fail No Submission
F	1-49	Fail
P	50-64	Pass
C	65-74	Credit
D	75-84	Distinction
HD	85-100	High Distinction
CN		Continuing
NFE		No Formal Examination
RP		Result Pending

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 .

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