STATS 7107 - Statistical Modelling and Inference

North Terrace Campus - Semester 2 - 2024

Course Content: Statistical methods underpin disciplines which draw inference from data and this includes just about everything: for example, the sciences, humanities, technology, education, engineering, government, industry and medicine. Analysis of the complex problems arising in practice requires an understanding of fundamental statistical principles together with knowledge of how to use suitable modelling techniques. Computing using high-level software is also an essential element of modern statistical practice. This course provides you with these skills by giving an introduction to the principles of statistical inference and linear statistical models using the freely available statistical package R. Topics covered are: point estimates, unbiasedness, mean-squared error, confidence intervals, tests of hypotheses, power calculations, derivation of one and two-sample procedures: simple linear regression, regression diagnostics, and prediction: linear models, analysis of variance (ANOVA), multiple linear regression, factorial experiments, analysis of covariance models including parallel and separate regressions, and model building; maximum likelihood methods for estimation and testing, and goodness-of-fit tests.

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Course Details

Course Code	STATS 7107
Course	Statistical Modelling and Inference
Coordinating Unit	Mathematical Sciences
Term	Semester 2
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	MATHS 7027
Assumed Knowledge	MATHS 7103. Experience with the statistical package R such as would be obtained from MATHS 7107
Assessment	Ongoing assessment, examination

Course Staff

Course Coordinator: Angus Lewis

Course Timetable

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

Course Learning Outcomes

Upon successful completion of this course you will be able to:

1	Explore the statistical theory of modelling and analysis.
2	Derive the key results needed for statistical modelling and inference.
3	Identify statistical techniques for parameter estimation.
4	Analyse data using the theory of statistical modelling and inference to solve real-world problems.
5	Discuss the principles and results of statistical modelling and analysis using clear language and appropriate terminology.

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, 4, 5
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, 4
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.	1, 2, 3, 4, 5
Attribute 7: Digital capabilities Graduates are well prepared for living, learning and working in a digital society.	1, 2, 3, 5
Attribute 8: Self-awareness and emotional intelligence Graduates are self-aware and reflective; they are flexible and resilient and have the capacity to accept and give constructive feedback; they act with integrity and take responsibility for their actions.	4, 5

Learning Resources
Required Resources

None.

Recommended Resources
1. J.A. Rice: Mathematical Statistics and Data Analysis, 3rd edition (2007).
2. D.D. Wackerly, W. Mendelhall and R.L. Scheaffer: Mathematical Statistics with Applications, 7th edition (2008).
3. R.J. Larsen, M.L. Marx: An Introduction to Mathematical Statistics and its Applications, 5th edition (2012).
Online Learning

This course uses MyUni for providing electronic resources, such as lecture notes, assignments, tutorial, and computer exercises. It is recommended that students make appropriate use of these resources.
Learning & Teaching Activities

Learning & Teaching Modes

The lecturer guides the students through the course material in 35 lectures. Students are expected to prepare for lectures by reading the printed notes in advance of the lecture, and to engage with the material in the lectures. Interaction with the lecturer and discussion of any difficulties that arise during the lecture is encouraged. Students are expected to watch the lecture videos and study the lecture notes. In the fortnightly tutorials, students are encouraged to discuss their solutions with each other. 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 computing skills using R. Homework assignments build on the tutorial and practical materials and help students strengthen their understanding of the theory and practical work, and gives them 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 35 90

Assignments 4 30

Quizzes 10 16

Tests 2 3

Tutorials 5 5

Practicals 6 12

TOTALS 156

Learning Activities Summary

Lecture Outline

1. Introduction to statistical inference: notation, mean squared error (Week 1)
2. Best Linear Unbiased Estimation (BLUE) (Week 1)
3. Confidence intervals, tests of hypotheses and power calculations (Week 2)
4. Inference for a single sample, unknown variance; pivotal quantities (Week 3)
5. Inference for two independent samples (Week 4)
6. Regression modelling and least squares estimation (Week 5)
7. Prediction for regression and residuals (Week 6)
8. Multiple linear regression and least squares estimation (Week 7)
9. BLUE and tests of hypotheses (Week 8)
10. Applications to prediction, polynomial regression and one-way analysis of variance (Week 8)
11. Analysis of covariance and two-way analysis of variance (Week 9)
12. Maximum likelihood (ML) estimation (Week 10)
13. Inference for ML estimators and tests based on the likelihood (Week 10)
14. Practical issues: randomization, imputation, multiple testing, non-parameteric tests (Week 11)

Tutorial Outline
1. MSE, BLUE, expectation and MGFs
2. Chi-squared distribution, inference for two independent samples
3. Regression and properties of estimators, Multiple regression
4. Parallel regression, ANOVA, ANCOVA, and other applications
5. Maximum likelihood estimation and hypothesis tests

Practical Outline
1. Introduction to R, reading data into R.
2. Summary statistics and cleaning data.
3. Using ggplot to visualise data.
4. Modelling data part 1.
5. Modelling data part 2.
6. Using Rmarkdown to write statistical reports.

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

Assessment task	Weighting	Due	Task type	Learning outcomes
Quizzes	10%	Weeks 1-7, 9-11	Formative	All
Assignments	20%	Weeks 3,5,7,11	Summative	All
Theoretical Test	15%	Week 8	Summative	All
Practical Test	15%	Week 12	Summative	All
Examination	40%	Examination period	Summative	All

Assessment Related Requirements

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

Assessment Detail

Assessment Item	Distributed	Due Date	Weighting
Assignment 1	Week 2	Week 3	5%
Assignment 2	Week 4	Week 5	5%
Assignment 3	Week 6	Week 7	5%
Assignment 4	Week 10	Week 11	5%

Submission

All written assignments are to be submitted online via MyUni.

Late assignments will not be accepted unless with permission by the lecturer.

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 Access Adelaide.

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