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## MATH2735 Statistical Modelling

### 10 creditsClass Size: 120

Module manager: Dr Leonid Bogachev
Email: L.V.Bogachev@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2019/20

### Pre-requisite qualifications

(MATH1712 or MATH2700), or equivalent.

This module is not approved as a discovery module

### Module summary

Statistical modelling is concerned with building a model which attempts to explain how measurements are related in the presence of random variation. In this course, we are interested in modelling the average value of a response variable given the values of one or more explanatory variables. In this module, we consider linear models which are subject to normally distributed variation. We look at various different ways of estimating model parameters, see how to check that the models we fit are adequate, and discuss how to interpret the models.Throughout this module, many practical examples are solved and illustrated using the R statistical computing package.

### Objectives

On completion of this module, students should be able to:

a) use the normal distribution to construct other probability distributions;
b) use alternative methods to estimate parameters in a statistical model and derive distributions of the estimators in simple cases;
c) construct a variety of linear models and select the appropriate model to analyse given data sets;
d) be able to conduct and interpret analyses of real data using linear models;
e) assess whether linear modelling assumptions are met;
f) use sub-hypotheses to determine which treatment groups differ;
g) use a statistical package to carry out data analysis.

### Syllabus

1. Random variables - density functions, expectation, variance, covariance; the normal distribution and its relation to chi-squared, and F distributions.
2. Simple linear regression - matrix formulation; parameter estimation by least squares, maximum likelihood, method of moments; hypothesis tests; confidence and prediction intervals.
3. One- and two- way fixed effects ANOVA; parameter estimation by least squares, maximum likelihood, and the method of moments; use of residuals in diagnostic plots.
4. One-way random effects model.
5. Post-hoc testing - orthogonal contrasts; multiple comparisons.

### Teaching methods

 Delivery type Number Length hours Student hours Workshop 10 1.00 10.00 Lecture 22 1.00 22.00 Private study hours 68.00 Total Contact hours 32.00 Total hours (100hr per 10 credits) 100.00

### Private study

- 5 exercise sheets, 2 hours per sheet: 10 hours
- Exam revision: 26 hours
- Consolidating lecture material: 22 hours

### Opportunities for Formative Feedback

Regular exercise sheets.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 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) 2 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