The University of Southampton
Courses

# MATH2010 Statistical Modelling I

## Module Overview

Simple linear regression is developed for one explanatory variable using the principle of least squares. The extension to two explanatory variables raises the issue of whether both variables are needed for a well-fitting model, or whether one is sufficient and, if so, which one. These ideas are generalised to many explanatory variables (multiple regression), for which the necessary theory of linear models is developed in terms of vectors and matrices. Checking model adequacy is an important part of the data analysis throughout the module, e.g. by examining plots of the residuals. Widening the class of models that can be considered by transforming one or more of the variables is also discussed, as is the use of dummy variables for qualitative explanatory variables to assess treatment effects. The comparison of population means using t-tests is also considered and the ideas of one-way analysis of variance (ANOVA) are introduced. The usual linear model associated with one-way (ANOVA) is stated and then fitted using the principle of least squares. Practical examples are given using small and simple data sets. The methods are implemented using a suitable software and students gain experience and advice through weekly worksheets. One of the pre-requisites for MATH3012, MATH3013, MATH3014, MATH6021, MATH6025, MATH6027 and MATH6135

### Aims and Objectives

#### Module Aims

To describe the theory and methods of using linear statistical models in analysing data to understand the influence of one or more explanatory variables on a continuous response, and to make predictions about the response

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Interpret the output from such an analysis including the meaning of interactions and terms based on qualitative factors
• Make a critical appraisal of a fitted model including analysing residuals and looking for outlying and influential points
• Use the theory of linear models and matrix algebra to investigate standard and non-standard problems
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Carry out t-tests and a one-way analysis of variance by hand and by computer
##### Learning Outcomes

Having successfully completed this module you will be able to:

• Carry out simple linear regression by hand and by computer
• Fit multiple regression models using the adopted software package, including transformations of variables if needed
• Using a variety of sequential procedures for variable selection

### Syllabus

• Analysis of simple data sets, confidence intervals and t-tests; • Regression analysis, simple linear regression with one independent variable in detail, including analysis of variance, confidence intervals, plotting ideas for diagnostic assessment; • Method of least squares using matrix notation, deriving the general results from first principles; • Comparison with simple linear regression. • Multiple linear regression. Examples with two, three and many independent variables; • Diagnostics to verify assumptions and conditions; • Model selection and stepwise regression; • Indicator variables for qualitative factors and interpretation of interactions; • One-way analysis of variance

### Learning and Teaching

#### Teaching and learning methods

Lectures, coursework, problem classes, workshops, computer labs, private study.

TypeHours
Independent Study102
Teaching48
Total study time150

S. Weisberg. Applied Linear Regression.

### Assessment

#### Summative

MethodPercentage contribution
Coursework 20%
Written exam 80%

#### Referral

MethodPercentage contribution
Written exam 100%

#### Repeat Information

Repeat type: Internal & External

Pre-requisites: MATH1024 AND MATH2011

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.

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