2024/25 Taught Postgraduate Module Catalogue

MATH5714M Linear Regression, Robustness and Smoothing

20 creditsClass Size: 70

Module manager: Dr Jochen Voss
Email: J.Voss@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

Pre-requisite qualifications

MATH2715 or MATH2735, or equivalent.

This module is mutually exclusive with

MATH3714

Linear Regression and Robustness

This module is approved as an Elective

Module summary

In many areas of science and social study, several variables or measurements are taken from each member of a sample. This module will examine ways of predicting one particular variable from the remaining measurements using the linear regression model.The general theory of linear regression models will be covered, including variable selection, tests and diagnostics. Robust methods will be introduced to deal with the presence of outliers. Nonparametric models will be introduced to relax the assumption of a linear relationship.

Objectives

By the end of this module, students should be able to:
a) prove basic linear model theory using matrix algebra;
b) use a computer package to fit parametric and nonparametric regression models to data, and interpret the models;
c) apply methods of robust regression;
d) describe various smoothing techniques used in density estimation and nonparametric regression;
e) present a report on some data that the student has analyzed.

Syllabus

1. Notation.
2. Revision of appropriate matrix theory; discussion of Cochran's theorem.
3. Multiple linear regression model. Parameter and residual estimation, introduction to the hat matrix, standard assumptions. Decomposition of sums of squares. Tests.
4. Influence. Criteria for detection and evaluation of influential cases of observations.
5. Selection of variables (forward and backward).
6. Multicollinearity - its effect on models and identification. Variance inflation factors.
7. Resistant fitting techniques for data sets with outliers. Breakdown point.
8. Kernel density estimation and regression smoothing, k-NN smoothing. Bandwidth selection by cross-validation.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	44	1.00	44.00
Practical	1	2.00	2.00
Private study hours			154.00
Total Contact hours			46.00
Total hours (100hr per 10 credits)			200.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular problem solving assignments

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
Assignment	.	20.00
Total percentage (Assessment Coursework)		20.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	3 hr 00 mins	80.00
Total percentage (Assessment Exams)		80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 29/04/2024 16:16:34

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