## Statistics 3L: Linear Models STATS3016

• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 3 (SCQF level 9)
• Typically Offered: Semester 1
• Available to Visiting Students: Yes

### Short Description

This course revises and extends previous work on the Normal Linear Model under standard assumptions and describes some of the main tools required for the construction, evaluation and verification of Normal Linear Models

### Timetable

Two lectures per week for 10 weeks, fortnightly tutorials and two two-hour laboratory sessions.

### Requirements of Entry

The normal requirement is that students should have been admitted to the third year of the Designated Degree programme in Statistics.

### Excluded Courses

Linear Models 3 [STATS4015]

Regression Models (Level M) [STATS5025]

### Co-requisites

The courses prescribed in the Designated Degree programme to which the student has been admitted.

### Assessment

90-minute, end-of-course examination (100%)

Main Assessment In: April/May

### Course Aims

The aims of this course are:

■ to revise and extend previous work on the Normal Linear Model under standard assumptions;

■ to describe some of the main tools required for the construction, evaluation and verification of Normal Linear Models;

■ to explain how one- and two-way analysis of variance, the analysis of covariance, and multiple and polynomial regression can be seen as a special case of the Normal Linear Model;

■ to provide methods for detecting and dealing with breakdowns in the standard assumptions for the Normal Linear Model.

### Intended Learning Outcomes of Course

By the end of this course students will be able to:

■ formulate Normal Linear Models in vector-matrix notation and, in simple cases, manipulate these formulations algebraically in order to produce estimates of functions of model parameters;

■ explain the underlying theory of the linear model, sketch the corresponding derivations and explain the practical relevance.

■ state the assumptions underlying a specified model and conduct appropriate diagnostic tests;

■ sketch how different variable selection procedures work implement these rules for model building in particular cases;

■ construct and interpret analysis of variance tables appropriate for model comparisons;

■ sketch potential problems caused by multicollinearity and heteroscedasticity (unequal variances) and present strategies to detect and address these problems ,

■ use suitable variable transformations;

■ define and interpret measures of influence of individual observations;

■ interpret the output of R procedures for Normal Linear Models.

### Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.