STATS 2107 - Statistical Modelling and Inference II

North Terrace Campus - Semester 2 - 2024

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, including maximum likelihood methods for estimation and testing.

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Course Details

Course Code	STATS 2107
Course	Statistical Modelling and Inference II
Coordinating Unit	Mathematical Sciences
Term	Semester 2
Level	Undergraduate
Location/s	North Terrace Campus
Units	3
Contact	Up to 3 hours per week
Available for Study Abroad and Exchange	Y
Prerequisites	(MATHS 1004 or MATHS 1012) and (STATS 1000 or STATS 1004 or STATS 1005 or MATHS 2201 or MATHS 2107)
Assumed Knowledge	MATHS 2103. Familiarity with a programming language; R would be most beneficial.
Assessment	Ongoing assessment, exam

Course Staff

Course Coordinator: Angus Lewis

Course Timetable

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

Course Learning Outcomes

On successful completion of this course, students will be able to

1. demonstrate their understanding of the mathematics of statistical inference;
2. derive the distributional results needed for statistical inference;
3. conduct appropriate hypothesis tests for comparing two means and for regression;
4. recognise that hypothesis tests, regression and analysis of variance belong to the same theory of linear models;
5. demonstrate their understanding of the theory of maximum likelihood estimation for a scalar parameter;
6. analyse a variety of datasets and fit linear regression models using R; and
7. interpret and communicate the results of statistical analyses, orally and in writing.

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.	all
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.	all
Attribute 3: Teamwork and communication skills Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.	all
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.	all
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.	all

Learning Resources

Required Resources

There are no required resources for this course. Lecture notes are provided and R and RStudio are freely available.

Recommended Resources

We will refer to the following two text books throughout the course. Both books contain material directly relevant to the content and objectives of the course, and are available in the Barr Smith library:

J. A. Rice: Mathematical Statistics and Data Analysis. Third edition (2007).
D.D. Wackerly, W. Mendelhall and R.L. Scheaffer: Mathematical Statistics with Applications. Seventh edition (2008).

Online Learning

This course uses MyUni for providing electronic resources, such as lecture notes, assignments, tutorial and practicals. It is recommended that the students make appropriate use of these resources.

Link to MyUni login page:
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. Four 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 .

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.
Fraud Awareness

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

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