2008/09 Undergraduate Module Catalogue

MATH3713 Regression and Smoothing

15 creditsClass Size: 100

Module manager: Dr C. Gill
Email: c.a.gill@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

Pre-requisite qualifications

MATH2735 or MATH2715.

This module is mutually exclusive with

MATH5713M

Robust Regression and Smoothing

This module is approved as an Elective

Module summary

In many areas of science and social study several measurements are taken from each member of a sample. This module will examine ways of predicting one particular aspect from the remaining measurements. The forms of relationship to be explored are either linear or a nonparametric smooth function. The general theory of linear regression models will be covered including variable selection, tests and diagnostics.

Objectives

To study the theoretical and practical aspects of building and analysing nonparametric and parametric models. 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 nonparametric and parametric regression models to data, and interpret the models; c) describe various smoothing techniques used in nonparametric regression; d) present a report on some data that the student has analysed.

Syllabus

1. Notation.
2. Matrix Algebra. Revision of appropriate matrix theory, properties and distributions of quadratic forms, discussion of Cochran's theorem.
3. Multiple linear regression model. Parameter and residual estimation, introduction to hat matrix, standard assumptions. Decomposition of sum of squares and tests.
4. Influence. Criterion for detection and evaluation of influential cases of observations - Cook's D DFBETAs and COVRATIO.
5. Selection of variables (forward and backward). Use of , adjusted and Mallows . Multicollinearity - its effect on models and identification. Variance inflation factors.
6. Kernel regression smoothing, k-NN smoothing. Bandwidth selection by Cross-validation.
7. Resistant smoothing techniques for data sets with outliers.

Teaching methods

Delivery type	Number	Length hours	Student hours
Example Class	7	1.00	7.00
Lecture	26	1.00	26.00
Practical	3	1.00	3.00
Private study hours			114.00
Total Contact hours			36.00
Total hours (100hr per 10 credits)			150.00

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	Coursework	20.00
Total percentage (Assessment Coursework)		20.00

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

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: 01/04/2009

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