## STATS 7107 - Statistical Modelling and Inference

### North Terrace Campus - Trimester 3 - 2022

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.

• General Course Information
##### Course Details
Course Code STATS 7107 Statistical Modelling and Inference Mathematical Sciences Trimester 3 Postgraduate Coursework North Terrace Campus 3 Up to 4 hours per week Y MATHS 7027 and MATHS 7103. Familiarity with a programming language; R would be most beneficial. Ongoing assessment, examination
##### Course Staff

Course Coordinator: Mr Max Glonek

##### Course Timetable

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

• Learning Outcomes
##### 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.

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

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
None.
##### Recommended Resources
J. A. Rice: Mathematical Statistics and Data Analysis, 3rd edition (2007).
D.D. Wackerly, W. Mendelhall and R.L. Scheaffer: Mathematical Statistics with Applications, 7th edition (2008).
##### Online Learning
This course uses MyUni for providing electronic resources, such as lecture notes, assignments, tutorial and practicals. It is recommended that students make appropriate use of these resources.

• Learning & Teaching Activities
##### Learning & Teaching Modes
This course is delivered in a semester, trimester and intensive format, although enrolment options may be limited by availability.

This course offers opportunities for you to learn through blended learning approaches, meaning some of the learning is done autonomously online and some of the learning is done through face-to-face engagement. This blended approach is used to create a rich scaffolded and supportive learning experience.

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

This is a 3-unit course. In the semester or trimester format, you are expected to allocate the following study time to fully meet the Course Learning Outcomes (CLOs) for this course. Please note that students work at different paces, so this indicates the approximate time required to complete this course.

 Learning Activity Hours/Week Duration Total Online learning activities 1 hour 12 weeks 12 hours Face-to-face learning activities 3 hours 12 weeks 36 hours Independent study 4 hours 12 weeks 48 hours Assessment tasks 5 hours 12 weeks 60 hours Expected total student workload 156 hours
##### 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.
• 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
 Assessmenttask Weighting Due Task type Learningoutcomes 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
Full descriptions of the assessment tasks and associated grading rubrics are in the Assignments space on the MyUni course site. You will have opportunities to get further clarification on assessment tasks as needed.
##### Submission
Unless otherwise specified, submit all of your assessments to the Assignments space in the MyUni course site for this course. For written assessments, your submissions will go through Turnitin to check for originality. Make sure your submissions adhere to the University of Adelaide Academic Integrity policies.

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

M10 (Coursework Mark Scheme)
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
• Fraud Awareness

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 studentâ€™s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.

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