## STATS 4101 - Statistical Modelling - Honours

### North Terrace Campus - Semester 1 - 2021

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.

• General Course Information
##### Course Details
Course Code STATS 4101 Statistical Modelling - Honours School of Mathematical Sciences Semester 1 Undergraduate North Terrace Campus 3 Up to 3 hours per week STATS 2107 or (MATHS 2201 and MATHS 2202) or (MATHS 2106 and MATHS 2107) Experience with the statistical package R such as would be obtained from STATS 1005 or STATS 2107 Honours students only 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.
##### Course Staff

Course Coordinator: Dr Jono Tuke

##### Course Timetable

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

• Learning Outcomes
##### 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.

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

University Graduate Attribute Course Learning Outcome(s)
Deep discipline knowledge
• informed and infused by cutting edge research, scaffolded throughout their program of studies
• acquired from personal interaction with research active educators, from year 1
• accredited or validated against national or international standards (for relevant programs)
1,2,3
Critical thinking and problem solving
• steeped in research methods and rigor
• based on empirical evidence and the scientific approach to knowledge development
• demonstrated through appropriate and relevant assessment
1,2,3
• technology savvy
• professional and, where relevant, fully accredited
• forward thinking and well informed
• tested and validated by work based experiences
2
• 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 Activities
##### 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.

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.
• Assessment

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

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

##### Assessment Summary
 Component Assessment mode Week Set Week Due Weighting Learningoutcomes 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.

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

M11 (Honours Mark Scheme)
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 Access Adelaide.

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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
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