England.

# Applied statistical modelling

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What do wage rates depend on? How many medals is a nation predicted to win at the next Olympics? Can we predict an OU student’s exam score based on their age and which qualification they’re studying? You can explore questions like these using the statistical modelling techniques in this module. It takes a practical approach with an emphasis on the fitting of models and the interpretation of results. Also, depending on your interests, you’ll study topics related to econometrics (statistics applied to economics) or data science.

## What you will study

Applied statistical modelling (M348) will develop your general statistical modelling skills beyond that delivered by Analysing Data (M248). In this module, simple linear regression is extended to model a wide variety of dataset types.

Book 1: Linear models
You’ll start with a revision of simple linear regression, combined with an introduction to the statistical software used, namely R. Initially, simple linear regression will be extended in two separate ways: firstly, by including more than one continuous explanatory variable, and secondly to deal with situations when the explanatory variable is categorical. You’ll then see how these two extensions can be combined to form regression models with any number of variables, continuous or categorical. You’ll then finish this book by putting the modelling techniques you’ve learned so far into practice by building a statistical model to predict success at the Olympics. In doing so, you’ll discover how fitting a model is only one part of using data to answer a question.

Book 2: Generalised linear models
All models you consider in Book 1 assume that the response variable is continuous and can be modelled, possibly after transformation, using a normal distribution. Although this is often sufficient for data analysis, there are situations where it is not. So, in Book 2, you’ll consider how linear models can be extended to cope with such situations. The resulting models are known as generalised linear models.

You’ll see that it’s possible to have models where the response distribution used is a binomial distribution instead of a normal distribution. You’ll then see that it’s possible to use other distributions as well, such as the Poisson distribution or the exponential distribution. Finally, in this book, you’ll see how a particular form of generalised linear model, the loglinear model, can be used to explore relationships between categorical variables. The loglinear model is particularly helpful when contingency tables relate to data with three or more categorical variables.

Book 3: Applications
Having extended the range of ‘regression’ tools in your data analysis toolbox, Book 3 focuses on two specialist applications of statistics: econometrics and data science. You’ll study only one of these.

In the econometrics strand, you’ll see how the assumptions associated with linear models can be problematic when applied to economic data. For example, data may represent observations made over time, so they’re not independent. In this strand, you’ll see how econometricians deal with such problems.

The data science strand focuses on a couple of topics of particular interest to data scientists. Firstly, you’ll focus on finding clusters in data: groups of observations that are similar to one another but different to observations in other groups. Next, you’ll learn suitable techniques for grouping the data when we don’t have examples of any groups – or even know how many groups there should be! You’ll then consider the challenges that ‘big data’ bring and discuss what can be done to address some of these challenges.

You’ll finish with a unit that will pull the content in the module together and help you prepare for the end-of-module assessment.

## 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 you’re ready.

## Preparatory work

We recommend you have some experience using statistical software such as Minitab or SPSS. Analysing Data (M248) and an OU level 2 mathematics module will be 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, including activities using the module software
• 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 module content, 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.

## You will need

A scientific calculator may be helpful.

### Computing requirements

You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11), or macOS (11 'Big Sur' or higher).

Any additional software will be provided or is generally freely available.

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

### Support from your tutor

Throughout your module studies, you’ll get help and support from your assigned module tutor. They’ll help you by:

• 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.

### Assessment

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

## If you have a disability

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying M348 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

Applied statistical modelling​ (M348) starts once a year – in October.

This page describes the module that will start in October 2023.

We expect it to start for the last time in October 2029.

### Course work includes:

6 Tutor-marked assignments (TMAs)
End-of-module assessment
No residential school