# Introduction to Statistical Modelling

Queensland University of Technology

## Course Description

• ### Course Name

Introduction to Statistical Modelling

• ### Host University

Queensland University of Technology

• ### Location

Brisbane, Australia

Statistics

• ### Language Level

Taught In English

• ### Prerequisites

Sound Achievement in Senior Mathematics C (or equivalent) or MXB100 or MAB120 or MAB125 or MXB101 or MXB102 or MXB103 is assumed knowledge.

• ### Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Credit Points

12
• Recommended U.S. Semester Credits
3 - 4
• Recommended U.S. Quarter Units
4 - 6
• ### Overview

Describing and understanding relationships in data is important in both scientific exploration and understanding.  Building on methodology from prior studies in probability and stochastic modelling, this unit focuses on the statistical modelling of data with an emphasis on relationships and effects for purposes of statistical inference, prediction and validation.  Attention is also given to the challenges that analysing real-world datasets pose with alternative statistical techniques which yield the valid inference.  This unit provides an introduction to some of the advanced material covered in the latter parts of the Statistical Science major.

Learning Outcomes
On successful completion of this unit you should be able to:

1. Apply elementary statistical modelling techniques in an appropriate way.
2. Apply Monte Carlo based techniques for appropriate statistical inference.
3. Draw inferences using the likelihood function, resampling, simulation and Bayesian statistics.
4. Use statistical software packages such as R commander to model and analyse data.

Content
The mathematical/statistical content of this unit includes:

1. Data Structures and Measurement Types
2. Data Gathering Issues: Design, Representativeness and Bias, Accuracy and Confounding
3. Data Summarisation: Graphical and Numerical Methods, Location/Spread/Shape/Correlation
4. Introduction to Distribution Theory: Normal, Gamma, Binomial, Poisson, Negative Binomial distributions, the Central Limit Theorem and Moment Generating Functions
5. Introduction to Likelihood models
6. The Confidence Interval: Univariate intervals for means and proportions, Tolerance Intervals
7. The Hypothesis Test: Normal and t-tests for univariate means and proportions and chi-squared tests for univariate discrete distributions
8. Contingency Tables: Tests of Independence, Odds Ratios, Difference in Proportions, Chi-Squared Residual Analysis
9. ANOVA: Differences in Means, F-tests, Confidence Intervals for Contrasts, Diagnostics and Heteroskedasticity
10. Simple Linear Regression: Coefficient of Determination, Transformations, Prediction Intervals, Diagnostics and Residual Analysis, the Geometry of Regression and Projection Matrices
11. Analysis of Covariance: Sum of Squares breakdowns, Testing for Interaction
12. Simple Logistic Regression: Via weighted least-squares for grouped data, Via Likelihood and GLM approach.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.