# 2019/20 Taught Postgraduate Module Catalogue

## MATH5714M Linear Regression, Robustness and Smoothing

### 20 creditsClass Size: 35

Module manager: Professor Charles Taylor
Email: C.C.Taylor@leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2019/20

### 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