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# Linear statistical modelling

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This module covers statistical modelling where a response variable depends on one or several explanatory variables: such as how well patients respond to a treatment, given their age and disease severity; or how different strains of wheat compare when grown in various conditions. Taking a practical approach, you’ll use real problems and data to stimulate analyses and their interpretation. Statistical tools are introduced, and use of the statistical software package, Genstat (supplied) is taught. You need a reasonable understanding of basic statistical ideas, as developed by Analysing data (M248). You’ll learn to use the most important methods of analysing data – a skill that too few people have.

## What you will study

This module is about the statistical modelling of situations in which a response variable depends on at least one explanatory variable. It offers a practical treatment of an important area of statistical methodology, applicable in a wide variety of situations. For example, it enables us to deal with questions such as how cavity wall insulation will affect the total energy consumption of a house; or how the probability of a successful bone marrow transplant is influenced by the ages of the donor and recipient, and other factors; or how loss due to abrasion might depend on the hardness and tensile strength of samples of rubber.

Linear statistical modelling uses real problems and data to stimulate analyses and their interpretation. Technical background is not ignored, but the main emphasis is on the knowledge needed to analyse data effectively.

The module begins with a general introductory unit, including a review of the general statistical methods and concepts that will be used later. The next unit gives a complete introduction to using the statistics package Genstat for Windows (which is supplied). We then move on to the basic linear regression model, extensions of which are the core of this module.

Subsequent units introduce a wide variety of linear statistical modelling tools: one-way analysis of variance, multiple regression, more general analysis of variance and designed experiments. All these are widely applicable cases of the normal linear model.

Further units develop linear modelling in the more general framework of the generalised linear model: binary regression; the full generalised linear model; diagnostic checking; and log-linear modelling.

A closing unit applies the methods you have learnt to the analysis of further data sets.

The Genstat package is extensively used throughout the module to perform the necessary calculations and analyses.

Read the full content list here.

### You will learn

Successful study of this module should enhance your skills in analysing and interpreting data.

### Professional recognition

This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.

This module may also help you to apply for the professional award of Graduate Statistician conferred by The Royal Statistical Society (RSS).

## Entry requirements

There is no formal pre-requisite study, but you must have the required mathematical and statistical skills.

Talk to an advisor if you’re not sure if you’re ready.

## Preparatory work

You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz here, and follow the advice in the quiz.

The key topics to revise include:

• algebra
• logarithmic and exponential functions
• histograms, boxplots and scatterplots
• normal, Poisson and binomial distributions
• the central limit theorem
• confidence intervals
• hypothesis testing
• simple linear regression
• correlation.

We also recommend you have some experience using a statistical software package.

Analysing data (M248), together with an OU level 2 module in mathematics is ideal preparation.

## What's included

You'll have access to a module website, which includes:

• a week-by-week study planner
• course-specific module materials
• audio and video content
• assessment details, instructions and guidance
• online tutorial access
• access to student and tutor group forums.

You'll be provided with printed books covering the content of the module, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques. You'll also receive a printed module handbook and software guide.

## You will need

Calculator (basic mathematical functions would be useful).

### Computing requirements

A computing device with a browser and broadband internet access is required for this module. Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.

Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.

• A desktop or laptop computer with an up-to-date version of Windows
• The screen must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.

To join in the spoken conversation in our online rooms we recommend a headset (headphones or earphones with an integrated microphone).

Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students.

## Teaching and assessment

### Support from your tutor

You'll have a tutor who will help you with the study material and mark and comment on your written work, and who you can ask for advice and guidance. Your tutor can also provide additional assistance with your study skills, especially if you're new to OU study.

Tutorials are designed to aid student success by providing help and guidance with your studies, including hints and tips to improve your understanding. You are encouraged to attend as many as you can – whether face-to-face or online they are an informal way to ask questions and to feel part of a student community.

We aim to provide face-to-face tutorials in a range of locations students can travel to, though we cannot guarantee availability close to where you live. An online alternative, covering similar content, is usually provided, typically with a recording of at least one such online tutorial being made available.

Student numbers on the module, and where tutors are based, will affect which tutor may lead a particular tutorial, the locations of face-to-face tutorials, and what online alternatives are offered.

Contact us if you want to know more about study with The Open University before you register.

### Assessment

The assessment details for this module can be found in the facts box above.

You can choose whether to submit your tutor-marked assignments (TMAs) on paper or online through the eTMA system. You may want to use the eTMA system for some of your assignments but submit on paper for others. This is entirely your choice.

## If you have a disability

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying M346 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.

## Future availability

Linear statistical modelling (M346) starts once a year – in October.

This page describes the module that will start in October 2020.

We expect it to start for the last time in October 2021.

### Course work includes:

6 Tutor-marked assignments (TMAs)
Examination
No residential school

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