# Statistics BSc/MSci

## Linear Models 3 STATS4015

• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 4 (SCQF level 10)
• Typically Offered: Semester 1
• Available to Visiting Students: Yes

### Short Description

This course extends previous work on the Normal Linear Model under standard assumptions and describes 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.

### Excluded Courses

Regression Models (Level M) [STATS5025]

Statistics 3L: Linear Models

### Co-requisites

Courses prescribed in the Honours or Master's programme to which the student has been admitted.

### Assessment

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

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? Not applicable

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below.

### Course Aims

The aims of this course are:

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

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

■ to show how this methodology may be applied to special cases of the Normal Linear Model, such as the one- and two-way analysis of variance, the analysis of covariance, and multiple and polynomial regression;

■ 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 student will be able to:

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

■ establish relevant probabilistic properties of parameter estimators and linear functions thereof;

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

■ state the Gauss-Markov Theorem and describe the implications and restrictions of this result;

■ define and briefly explain the relative advantages and disadvantages of certain variable selection procedures and implement these rules for model building in particular cases;

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

■ describe the problems created by multicollinearity, to formulate a strategy for the detection and elimination of multicollinearity and to implement this strategy in particular cases;

■ describe the problems created by heteroscedasticity (unequal variances), formulate a weighted least squares approach in order to overcome these problems and demonstrate algebraically that the weighted least squares method does lead to a linear model under standard assumptions;

■ describe the circumstances under which variable transformation might be required, and analyse and interpret models involving transformed variables;

■ 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.