37252 Regression and Linear Models
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Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 35151c Introduction to Statistics OR 33116 Design, Data, and Decisions OR 33230 Mathematics 2 OR 33290 Statistics and Mathematics for Science OR 26134 Responsible Evidence-Based Decisions OR 37151c Introduction to Statistics OR 68103 Mathematics for Secondary Education Statistics
The lower case 'c' after the subject code indicates that the subject is a corequisite. See definitions for details.
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 35353 Regression Analysis
Description
Regression analysis provides a way to model the relations among a set of quantitative variables. This subject focuses on the most common situation of one response variable and several explanatory variables, a situation encountered in many areas in science, engineering, medicine and business. Models for several explanatory variables are developed and tested, and ways for deciding which of a set of variables give the best model are developed.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Fit a model to obtain estimates together with their standard errors in regression problems, analyse the adequacy and reasonableness of a particular regression model. |
|---|---|
| 2. | Define relevant terminology, describe the main concepts of regression analysis, and formulate problems for simple linear regression. |
| 3. | Formulate applied problems in regression analysis and solve them using a variety of approaches. |
| 4. | Contribute effectively and professionally in a team context. |
| 5. | Use the statistical package (R) to conduct regression analysis and interpret the results of the analysis. |
| 6. | Independently source a suitable data set and apply simple linear regression techniques to the data set. |
| 7. | Communicate clearly the results of a statistical analysis. |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Demonstrate theoretical and technical knowledge of mathematical sciences including calculus, discrete mathematics, linear algebra, probability, statistics and quantitative management. (1.1)
- Evaluate mathematical and statistical approaches to problem solving, analysis, application, and critical thinking to make mathematical arguments, and conduct experiments based on analytical, numerical, statistical, algorithms to solve new problems. (2.1)
- Work autonomously or in teams to demonstrate professional and responsible analysis of real-life problems that require application of mathematics and statistics. (3.1)
- Design creative solutions to contemporary mathematical sciences-related issues by incorporating innovative methods, reflective practices and self-directed learning. (4.1)
- Use succinct and accurate presentation of reasoning and conclusions to communicate mathematical solutions, and their implications, to a variety of audiences, using a variety of approaches. (5.1)
Contribution to the development of graduate attributes
The Faculty of Science has determined that our courses will aim to have developed the following attributes in students at the completion of their course of study. Each subject will contribute to the development of these attributes in ways appropriate to the subject and the stage of progression, thus not all attributes are expected to be addressed in all subjects. This subject contributes to the development of the following graduate attributes:
1. Disciplinary knowledge
The lectures, PC laboratories, and R assignment impart skills necessary in a number of mathematical disciplines and demonstrate how to apply these skills to a variety of problems. This is further assessed by the final exam.
2. Research, inquiry and critical thinking
A major component of the PC laboratories is the consideration of how best to apply regression techniques to a particular data set. Statisticians who work in the industry are often required to use their own judgement in model building using regression analysis and this subject imparts the necessary skills. This is reinforced by the R assignment and the requirement of students to understand and interpret model outputs in the final exam.
3. Professional, ethical, and social responsibility
The PC laboratories help students learn to manage their own work and to accept responsibility for their own learning and, together with the assignment, they give practice in computing skills, data handling and quantitative and graphical literacy skills. The group element of the R assignment allows students to work collaboratively and includes independent research by the group to source suitable data for simple linear regression.
4. Reflection, innovation, creativity
The requirement to source own data allows students to demonstrate initiative to find additional information to support their learning.
5. Communication
The PC laboratories, R assignment and final exam allow students to present written solutions to statistical problems using appropriate professional language.
Teaching and learning strategies
Materials are available on Canvas to help you prepare for the subject. These include an introduction to R, as well as short video clips to help reinforce your prerequisite statistical knowledge.
During session, the subject is four hours of classes each session (weekly for Autumn/Spring, daily for Summer), consisting of lectures, laboratory work, tutorials and discussions. Students are expected to support each hour of class time with an hour of private study, be it in groups or as individuals.
Each lecture will be two hours that will involve review of the previous session's content and the presentation of new material. The practical application of this material will then occur in that session's computer lab. After completing the two-hour computer lab, full solutions will be made available and students are encouraged to review the lab output prior to attending the following lab session.
The subject makes extensive use of Canvas. Lecture materials are posted prior to the lectures and students are encouraged to review prior to the lecture as interaction during the lectures is encouraged. All lab solutions, discussion of the R assignment, and solutions to a previous exam will also be available as the course progresses.
The main R assignment MUST be undertaken as a group assignment. To support this, students will complete a SPARKPlus review of the contribution by each group member to ensure equity with respect to student engagement in the assignment. General feedback covering the solutions to the assignment will be given during the review lecture and made available online. Marks will be available prior to the final exam.
Content (topics)
This subject will cover simple linear and multiple linear regression, regression diagnostics, variable selection methods, logistic regression and selected other topics in regression analysis.
Assessment
Assessment task 1: Lab worksheets
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, inquiry and critical thinking 5. Communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3, 5 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1 and 5.1 |
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 20% |
| Criteria: | Accuracy of analysis, clarity of communication. |
Assessment task 2: Assignment (Group Work)
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, inquiry and critical thinking 3. Professional, ethical and social responsibility 4. Reflection, Innovation, Creativity 5. Communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3, 4, 5, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 3.1, 4.1 and 5.1 |
| Type: | Report |
| Groupwork: | Group, group assessed |
| Weight: | 30% |
| Criteria: | Evidence of correct use of R, accuracy of interpretation, appropriate choice model, clarity of communication appropriate group contribution. |
Assessment task 3: Examination
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, inquiry and critical thinking 5. Communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 5 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1 and 5.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 50% |
| Length: | TBA |
| Criteria: | Accuracy of interpretation, appropriate choice of model, clarity of communication. |
Minimum requirements
Students must obtain an overall mark of at least 50 to pass this subject.
Recommended texts
Draper, N.R., Smith, H. (1998) Applied Regression Analysis, 3rd edition, Wiley.
Hosmer, D.W., Lemeshow, S., Sturdivant, R.X. (2013) Applied Logistic Regression, 3rd edition, Wiley.
(Both of these texts are available online from UTS library.)
Other resources
-
Mendenhall, W. & Sincich, T. (2012) A Second Course in Statistics: Regression Analysis. 7th Edition Pearson.
- Dielman, T.E. (2005) Applied Regression Analysis: A Second Course in Business and Economic Statistics, 4th edition. Thomson.
- Kleinbaum, D. G., Kupper, L. L., Muller, K. E. & Nizham, A. (2008) Applied Regression Analysis and Other Multivariable Methods. 4th edition. Thomson/Duxbury.
- Kutner, M.H., Neter, J., Nachtsheim, C.J. (2004) Applied Linear Regression Models, 4th edition, McGraw-Hill/Irwin