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Unit of study_

STAT3022: Applied Linear Models

Linear models are core to a wide range of real-world data analyses, for example in agriculture, health, sport and business. This unit provides an in-depth exploration of various linear models outlining when they can be applied, and how to assess if they are appropriate. The unit will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical linear methods, together with concepts of collection of data and design of experiments. You will consider linear models and robust regression methods with diagnostics for checking appropriateness of models and strategies for performing feature selection. You will learn to design and analyse experiments considering notions of replication, randomisation and ideas of factorial designs. You will apply, construct and interpret multi-way ANOVA models and make inferences, including post-hoc tests and making corrections for multiple comparisons. Throughout the unit you will use the R statistical package to perform analyses and generate statistical graphics. By completing this unit you will learn how to generate, interpret, visualise and critique linear models.

Code STAT3022
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
STAT2X11 and (DATA2X02 or STAT2X12)
STAT3912 or STAT3012 or STAT3922 or STAT4022
Assumed knowledge:
Introductory knowledge to linear algebra (MATH1X02 or equivalent)

At the completion of this unit, you should be able to:

  • LO1. apply, formulate, interpret and compare multiple linear regression including evaluation of model diagnostics and outlier detection
  • LO2. apply, construct and interpret multi-way ANOVA models and make inference on all parameters
  • LO3. conduct and master correction for multiple pairwise comparisons by applying the Tukey, Scheffe and Bonferroni correction
  • LO4. perfectly calculate and interpret confidence intervals for all parameters in linear regression and distinguish the difference between confidence intervals and prediction intervals
  • LO5. implement the R function lmer for the fitting of mixed models and explain these complicated models
  • LO6. design of an appropriate scheme for treatment allocation and data collection as well as the correct analysis for complete randomised designs (CBD), randomised CBD (RCBD), Latin square designs (LSD), incomplete block designs (IBD) and balanced IBD (BIBD), ANCOVAs, and nested designs
  • LO7. identify and explain blocks, nested factors, interactions terms, experimental units, observational units, confounding and pseudo-replication in experimental designs.