STATS 3001 - Statistical Modelling III

North Terrace Campus - Semester 1 - 2022

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 3001
    Course Statistical Modelling III
    Coordinating Unit School of Mathematical Sciences
    Term Semester 1
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3 hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites STATS 2107 or (MATHS 2201 and MATHS 2202) or (MATHS 2106 and MATHS 2107)
    Assumed Knowledge Experience with the statistical package R such as would be obtained from STATS 1005 or STATS 2107.
    Course Description 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 John Maclean

    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.
    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

    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

    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.

    2
  • Learning Resources
    Required Resources
    There is no prescribed text for this course. Lecture notes are provided.
    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. 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.
    Workload

    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
    Workshops 12 12
    Assignments 3 15
    Test 3 15
    Online quizzes 9 18
    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.


  • 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 Learning
    outcomes
    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 score of at least 50% is required to pass the course.
    Assessment Detail





    Submission

    No information currently available.

    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.

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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.

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