The current and official versions of the course specifications are available on the web at https://www.usq.edu.au/course/specification/current.
Please consult the web for updates that may occur during the year.

# STA3301 Statistical Models

 Semester 2, 2021 Toowoomba On-campus Short Description: Statistical Models Units : 1 Faculty or Section : Faculty of Health, Engineering and Sciences School or Department : School of Sciences Student contribution band : Band 1 ASCED code : 010103 - Statistics Grading basis : Graded

## Staffing

Examiner: Enamul Kabir

## Requisites

Pre-requisite: STA3300 or approval of examiner or Students must have completed STA8170 and be enrolled in one of the following Programs: GCSC or GDSI or MSCN or MADS or MSCR or DPHD.

## Rationale

Linear Models and Generalised Linear Models are very widely used statistical tools. Linear models allow us to model data with normally distributed errors and generalised linear models extend these methods to a wider family of distributions. While students are expected to have obtained some understanding of linear regression techniques in previous courses, this course offers a more complete introduction to linear models and their application, then, building on this, extends into generalised linear models. The key functions of linear models are for describing the relationships between variables and predicting outcomes and so inference methods will be addressed in some detail. Finally, as models only give useful information when they provide an accurate reflection of the 'real world', various diagnostic tests on the appropriateness and goodness of fit of various models will be introduced. This course has relevance to all students seeking to pursue a career involving applied statistics.

## Synopsis

This course introduces and extends the student's knowledge of linear models. The mathematical development of these models will be considered, however the focus will be on practical applications. The statistical program R will be introduced and used throughout the course. The topics include developing multiple regression models, testing hypotheses for these models, selecting the 'best' model, diagnosing problems in model fit, shrinkage methods, developing generalised linear models, and a range of applications of generalised linear models including logistic, Poisson and log-linear models. Analysis of different statistical models are practised using the statistical software package through the R and RStudio.

## Objectives

On completion of this course students should be able to:

1. Recognise appropriate general and generalised linear models for analysis of different types of data sets
2. Apply a range of models and diagnostic techniques to test hypotheses and interpret the output correctly and in context.
3. Explore the capabilities of and implement R software (RStudio) as a statistical package in analysing different statistical models.
4. Interpret and communicate the results of analyses to a diverse audience.

## Topics

Description Weighting(%)
1. Review of multiple regression: specifying the model, least squares estimators of regression parameters and variance, maximum likelihood estimators of the regression parameters and variance, multiple and partial correlation, regression through the origin. 10.00
2. Inference on the normal model: interval estimation of the regression parameters and variance, prediction of future responses, analysis of variance, coefficient of determination, tests on single regression coefficients, confidence regions, tests on a subset of the regression coefficients, procedures for model selection, tests on the general linear model, test of goodness fit. 20.00
3. Model selection and checking: criteria for selecting regressors, residual analysis, data transformations, weighted least squares, detecting outliers and influential observations, multicollinearity, detecting multicollinearity, Ridge, LASSO and Elastic Net regression. 20.00
4. Generalised linear models: the exponential family of distributions, the mean and variance of the exponential family, specifying the generalised linear model, the link function, estimation of the regression parameters, adequacy of the model, the deviance, analysis of deviance and model selection. 10.00
5. Binary variables and logistic regression: probability distributions, generalised linear models, logistic regression model, deviance, Pearson's Chi-Square test, residuals and other diagnostics. 20.00
6. Count data, Poisson regression and log-linear models: Poisson regression, probability models for contingency tables, log-linear models, inference for log-linear models. 20.00

## Text and Materials

ALL textbooks and materials available to be purchased can be sourced from USQ's Online Bookshop (unless otherwise stated). (https://omnia.usq.edu.au/textbooks/?year=2021&sem=02&subject1=STA3301)

Introductory material (Current Year), Course STA3301 Statistical Models.
(Accessible from the course StudyDesk.)
Study Book (current year), Course STA3301 Statistical Models.
(Accessible from the course StudyDesk.)
All additional study material will be provided on the course StudyDesk.

## Reference Materials

Reference materials are materials that, if accessed by students, may improve their knowledge and understanding of the material in the course and enrich their learning experience.
Crawley, MJ 2012, The R Book, 2nd edn, Wiley, India.
Dobson, AJ and Barnett, AG 2018, An Introduction to Generalized Linear Models, 4th edn, CRC Press, Boca Raton, FL.
McCullagh, P & Nelder, JA 1989, Generalized linear models, 2nd edn, Chapman and Hall, London: New York.
Myers, RH 1990, Classical and modern regression with applications, 2nd edn, Duxbury Press, Belmont.

Activity Hours
Assessments 32.00
Online Lectures 26.00
Private Study 88.00
Tutorials 26.00

## Assessment Details

Description Marks out of Wtg (%) Due Date Objectives Assessed Notes
ANALYSIS ASSIGNMENT 1 20 20 02 Sep 2021 1,2,3,4
ANALYSIS ASSIGNMENT 2 30 30 07 Oct 2021 1,2,3,4
OPEN EXAMINATION - TAKE HOME 50 50 End S2 1,2,4 (see note 1)

Notes
1. This will be a take home exam. Students will be provided further instruction regarding the exam by their examiner via StudyDesk. The examination date will be available via UConnect when the Alternate Assessment Schedule has been released.

## Important assessment information

1. Attendance requirements:
It is the students' responsibility to participate appropriately in all activities and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.

2. Requirements for students to complete each assessment item satisfactorily:
To complete an assessment item satisfactorily, students must obtain at least 50% of the marks available for that assessment item.

3. Penalties for late submission of required work:
Students should refer to the Assessment Procedure http://policy.usq.edu.au/documents.php?id=14749PL (point 4.2.4)

4. Requirements for student to be awarded a passing grade in the course:
To be assured of receiving a passing grade a student must obtain at least 50% of the total weighted marks available for the course (i.e. the Primary Hurdle), and have satisfied the Secondary Hurdle (Supervised), i.e. the end of semester examination by achieving at least 40% of the weighted marks available for that assessment item.

Supplementary assessment may be offered where a student has undertaken all of the required summative assessment items and has passed the Primary Hurdle but failed to satisfy the Secondary Hurdle (Supervised), or has satisfied the Secondary Hurdle (Supervised) but failed to achieve a passing Final Grade by 5% or less of the total weighted Marks.

To be awarded a passing grade for a supplementary assessment item (if applicable), a student must achieve at least 50% of the available marks for the supplementary assessment item as per the Assessment Procedure http://policy.usq.edu.au/documents/14749PL (point 4.4.2).

5. Method used to combine assessment results to attain final grade:
The final grades for students will be assigned on the basis of the aggregate of the weighted marks obtained for each of the summative assessment items in the course.

6. Examination information:
A Take Home Examination is one in which candidates may have access to any printed, written, or online material as well as a calculator.

7. Examination period when Deferred/Supplementary examinations will be held:
Deferred and Supplementary examinations will be held in accordance with the Assessment Procedure https://policy.usq.edu.au/documents/14749PL.

8. University Student Policies:
Students should read the USQ policies: Definitions, Assessment and Student Academic Misconduct to avoid actions which might contravene University policies and practices. These policies can be found at http://policy.usq.edu.au.

## Other Requirements

1. Computer, e-mail and Internet access:
Students are required to have access to a personal computer, e-mail capabilities and Internet access to UConnect. Current details of computer requirements can be found at http://www.usq.edu.au/current-students/support/computing/hardware .

2. Students can expect that questions in assessment items in this course may draw upon knowledge and skills that they can reasonably be expected to have acquired before enrolling in this course. This includes knowledge contained in pre-requisite courses and appropriate communication, information literacy, analytical, critical thinking, problem solving or numeracy skills. Students who do not possess such knowledge and skills should not expect the same grades as those students who do possess them.

Date printed 8 November 2021