Unit of study_

# STAT3922: Applied Linear Models (Advanced)

This 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 first consider linear models and regression methods with diagnostics for checking appropriateness of models, looking briefly at robust regression methods. Then you will consider the design and analysis of experiments considering notions of replication, randomisation and ideas of factorial designs. Throughout the course you will use the R statistical package to give analyses and graphical displays. This unit is essentially an Advanced version of STAT3012, with additional emphasis on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods.

Code STAT3922 Mathematics and Statistics Academic Operations 6
 Prerequisites: ? STAT2X11 and [a mark of 65 or greater in (STAT2X12 or DATA2X02)] None STAT3912 or STAT3012 or STAT3022 or STAT4022

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
• LO8. derive and re-create proofs of theoretical aspects of regression methods.

## Unit outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.