## STATS 7107 - Statistical Modelling and Inference

### North Terrace Campus - Semester 2 - 2021

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 Semester 2 Postgraduate Coursework North Terrace Campus 3 Up to 4 hours per week Y (MATHS 1004 or MATHS 1012) and (STATS 1000 or STATS 1004 or STATS 1005 or MATHS 2201 or MATHS 2107) and MATHS 2103. Familiarity with a programming language; R would be most beneficial. Ongoing assessment, examination
##### Course Staff

Course Coordinator: Matthew Ryan

##### Course Timetable

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

• Learning Outcomes
##### Course Learning Outcomes
1. Ability to derive the distributional results needed for statistical inference.
2. Ability to conduct appropriate hypothesis tests for comparing two or more means and for regression.
3. Demonstrate understanding that hypothesis tests, regression and analysis of variance can be seen as part of the same statistical theory of linear models.
4. Demonstrate understanding of the theory of maximum likelihood estimation for a scalar parameter.
5. Ability to analyse data and fit linear regression models using R.
6. Demonstrate skills in interpreting and communicating the results of statistical analysis, orally and in writing.

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)
all
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
all
• 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
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.

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.
• 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

 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.

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
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