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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.

## Entry requirements

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

## 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

• a week-by-week study planner
• course-specific module materials
• audio and video content
• assessment details, instructions and guidance
• online tutorial access

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

You'll need a desktop or laptop computer with an up-to-date version of 64-bit Windows 10 (note that Windows 7 is no longer supported) and broadband internet access.

To join in spoken conversations in tutorials we recommend a wired headset (headphones/earphones with a built-in microphone).

Our module websites comply with web standards and any modern browser is suitable for most activities.

Our OU Study mobile App will operate on all current, supported, versions of Android and iOS. It's not available on Kindle.

It's also possible to access some module materials on a mobile phone, tablet device or Chromebook, however, as you may be asked to install additional software or use certain applications, you'll also require a desktop or laptop as described above.

## Teaching and assessment

• Marking your assignments (TMAs) and providing detailed feedback for you to improve.
• Guiding you to additional learning resources.
• Providing individual guidance, whether that’s for general study skills or specific module content.
• Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part. If you want to participate, you’ll likely need a headset with a microphone.

### 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.

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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