## STATS 2107 - Statistical Modelling and Inference II

### North Terrace Campus - Semester 2 - 2015

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 2107 Statistical Modelling and Inference II Statistics Semester 2 Undergraduate North Terrace Campus 3 Up to 4 hours per week Y MATHS 1012 (STATS 1000 or STATS 1004 or STATS 1005 or MATHS 2201) and MATHS 2103. Experience with the statistical package R such as would be obtained from STATS 1005 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.
##### Course Staff

Course Coordinator: Professor Patricia Solomon

##### Course Timetable

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

• Learning Outcomes
##### Course Learning Outcomes
1. Demonstrate understanding of the mathematical basis of statistical inference.
2. Ability to derive the distributional results needed for statistical inference.
3. Ability to conduct appropriate hypothesis tests for comparing two means and for regression.
4. Demonstrate understanding that hypothesis tests, regression and analysis of variance can be seen as part of the same statistical theory of linear models.
5. Demonstrate understanding of the theory of maximum likelihood estimation for a scalar parameter.
6. Ability to analyse data and fit linear regression models using R.
7. 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)
Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all
An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 4,5,6,7
Skills of a high order in interpersonal understanding, teamwork and communication. 7
A proficiency in the appropriate use of contemporary technologies. 3,6,7
A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all
An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. 6,7
• Learning Resources
None.
##### Recommended Resources
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.

• Learning & Teaching Activities
##### Learning & Teaching Modes
The lecturer guides the students through the course material in 30 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 to help with occasional absences and for revision purposes. In the fortnightly tutorials, students will discuss their solutions in groups and present them to the class on the board. 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.  A series of five homework assignments builds on the tutorial and practical material and provides students 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 30 90 Tutorials 6 18 Assignments 5 30 Practicals 6 18 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 2)
3. Confidence intervals, tests of hypotheses and power calculations (Week 3)
4. Inference for a single sample, unknown variance; pivotal quantities (Week 4)
5. Inference for two independent samples (Week 5)
6. Regression modelling and least squares estimation (Week 6)
7. Prediction for regression and residuals (Week 7)
8. Multiple linear regression and least squares estimation (Week 8)
9. BLUE and tests of hypotheses (Week 9)
10. Applications to prediction, polynomial regression and one-way analysis of variance (Week 10)
11. Analysis of covariance and two-way analysis of variance (Week 11)
12. Maximum likelihood (ML) estimation (Week 11)
13. Inference for ML estimators and tests based on the likelihood (Week 12)

Tutorial Outline

1. MSE, BLUE, expectation and MGFs
2. Chi-squared distribution, inference for two independent samples
3. Regression and properties of estimators
4. Multiple regression, matrix formulation
5. Parallel regression and other applications
6. Maximum likelihood estimation and hypothesis tests

Practical Outline

1. Introduction to R, one and two sample t-tests, simple linear regression
2. Confidence intervals and prediction intervals for linear regression
3. Using residuals for model checking
4. Matrix calculations for regression in R
5. Polynomial regression and model selection
6. Analysis of covariance models
• 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 Weighting Outcomes Assessed Tutorials 5% All Practicals 5% All Assignments 20% All Exam 70% All
##### Assessment Related Requirements
An aggregate final score of at least 50% is required to pass the course.
##### Assessment Detail

Attendance at five out of six tutorials will contribute 5% to the assessment for this course, and attendance at five out of six computing practicals will contribute 5% to the assessment for this course, for a total of 10%. Tutorials will be in the even weeks, commencing in Week 2. Computing practicals will be in the odd weeks, commencing in Week 1. If students are unable to attend classes owing to illness or compassionate reasons, please let the lecturer know.

 Assessment Item Distributed Due Date Weighting Assignment 1 Week 1 Week 3 4% Assignment 2 Week 3 Week 5 4% Assignment 3 Week 5 Week 7 4% Assignment 4 Week 7 Week 9 4% Assignment 5 Week 9 Week 11 4%
##### Submission

All written assignments are to be submitted to the designated hand in box within the School of Mathematical Sciences with a signed cover sheet attached.

Late assignments will not be accepted unless with permission by the lecturer.

Assignments will have a two week turn-around time for feedback to students.

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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