Topic outline

  • Announcements

    Collapse all Expand all

  • Week 1 : Module intro and the Simple Linear Regression Model

    Welcome to Statistical Modelling 1

    This week there are two lectures on campus both in the Peoples Palace Great Hall. These are Monday at 2pm and Thursday at 11am. In the first lecture we will explain in full how the module teaching will run. This will be a bit different from the 3 lectures + 1 tutorial you have been used to in other modules. To access all you need for this course you will need 3 types of teaching. It will be very important to keep up with the material as we go along as each week builds upon the previous ones. 

    1. the two hours of in person lectures

    2. watching a number of short videos each week - these will be clearly signposted on QM Plus. Each video will be up to 15 minutes long. All of the videos will combine to cover the mathematics and methods of statistical modelling covered in this course. It is very important you watch these videos as well as come to timetabled activities. This is a new way of sharing the material which should both give you all you need in accessible, short video format and provide the foundation for a more interactive style of lecture and IT lab.

    3. [from week 2] a one hour IT lab focused on modelling in R

    This week we will introduce statistical modelling and cover the Simple Linear Regression Model which we will spend the first four weeks of the module constructing and analysing.



  • Week 2 : Properties of estimators and assessing the model

  • Week 3: Inference about the model parameters

  • Module Description

    A mathematical model is an imitation of a real-world system or process. Models are used in almost every field of business, economics, science and industry where quantitative data are collected, the most fundamental type being Linear models. Despite their simplicity these models are very useful and also form the basis for more advanced statistical techniques covered in Level 6 modules. This module is concerned with both the theory and applications of linear models and covers problems of estimation, inference and interpretation. Graphical methods for model checking will be discussed and various model selection techniques introduced. You will also have gain hands on experience of developing and testing models with the R statistical package in the computer practical sessions.

  • Week 4: Further model checks

  • Assessed Coursework 1 due in week 5

    This coursework, to be completed in R programming, counts for 15% of your total module mark. Below you will find the coursework question and instructions (released at the end of week 4) and a submission point where you should upload your answer in a MS Word document. You will need the data set you found in week 2 to complete this coursework. The deadline for submission is 5pm UK time on Thursday 22 February (week 5). Late submissions will not be accepted. 

    • Coursework instructions and Question File
      128.5 KB
    • Assessed Coursework 1 Assignment

      You should submit your answer to the question in a single MS Word document that contains your R code and output copied from R-Studio as well as your own typed answers to the question above. The deadline is 5pm UK time on 22 February and late submissions or email submissions will not be accepted. You must only submit your own work using your own analysis in R.

    • Coursework 1 Solution File
      329.0 KB

  • Week 5: Poorly Fitting Models and introducing Matrix approaches

  • Week 6: Matrix approach & Maximum likelihood estimation

  • Week 7: Reading Week (note lecture Tuesday 9-10

    This week there is just one timetabled class - a lecture on Tuesday 5th March at 9:00am in the Peoples Palace Great Hall. This is because the university will be closed on Monday of week 11 for a bank holiday. 

  • Week 8: Multiple Linear Regression models

  • Assessed Coursework 2 due in week 9

    This coursework which counts for 15% of the module mark will be released below at the end of week 8 and requires an understanding of how to analyse linear regression models using R programming.

    • Assessed Coursework 2 Quiz

      This handwritten assessment is available for a period of 3 hours from the time you start the quiz, within which you must submit your solutions. You may log out and in again during that time, but the countdown timer will not stop. If your attempt is still in progress at the end of your 3 hours, any file you have uploaded will be automatically submitted. All submissions must be completed by the deadline for this assessment which is 5pm UK time on Wednesday 20th March (week 9). Late submissions and submissions by email will not be accepted. Please ensure that you leave sufficient time to upload your scanned pdf file to QM Plus within the time allowed.

      This assessment is intended to be completed within 1 hour.

    • Coursework2data.csv File
      7.1 KB
    • Coursework 2 Solution File
      77.2 KB

  • Week 9: Model building

  • Week 10: Automated approaches and issues of Multicollinearity

  • Week 11: What is a linear model?

  • Syllabus 

    • The course will cover the following topics:
        • Relations among variables and basic concepts of statistical modeling;
        • Normal linear regression model: Definition of simple, multiple and polynomial regression models;
        • Matrix algebra: Matrix form and multivariate linear regression models;
        • Least square estimation: properties of estimators, predicting mean responses;
        • Assessing fitted models: analysis of variance, $R^2$, lack of fit, residuals and outliers;
        • Model selection: transformation of response variables, variable selection and criterion for selection (AIC);
        • Inference: Confidence intervals for parameters and testing for parameters;
        • Problems: leverage and influence, multicollinearity;
        • Apply theory to practical analysis using R.

  • Module aims and learning outcomes 

    • At the end of this course, students will be able to:
        • express regression models as linear equations or in matrix form; 
        • estimate parameters of simple linear regression models by least squares; 
        • calculate confidence intervals and predictive intervals for predictions;
        • explain methods for selecting variables in multiple regression models;
        • explain the effects of outliers and collinearity and how to detect them;
        • interpret computer output of the above methods.

  • Assessment information

    • Assessment Pattern - 70% final exam in May 2024, 30% in-term assessments

      Format and dates for the in-term assessments - There will be two in-term assessments each contributing 15% to your overall module mark. The first will be set in week 4 for submission in week 5 (and will require a little pre-work in week 2). The second will be set in week 8 for submission in week 9. Both will involve R programming and will require submission via QM Plus.

      Format of final assessment - The final assessment will be a 3 hour handwritten exam on campus. You will need a non-programmable calculator.

      Link to past papers - past papers and solutions will be added to the week 12 (revision) section of the module content page.

      Description of Feedback - In term assessment will be marked with written feedback provided. In addition there will be weekly exercises both in the form of R programming problems (like the in term assessment) and exam style questions (like the final exam) with solutions available the following week on QM Plus.

       

  • Teaching team

    • Both lectures and IT labs will be divided between

      Chris Sutton, Senior Lecturer in Actuarial Science, Head of the Centre for Mathematical Education

      Dr Lubna Shaheen, Lecturer in Mathematics

  • Hints and tips

    • Add information here.

  • Where to get help

    • Add information here.

  • General course materials

    • Add information here.

  • Coursework

    • Add information here.

  • Exam papers

    • Add information here.

  • Week 12: Revision

  • Sample Exam Papers and Solutions

    In this section you will find the exam papers and solutions from 2023 (both May and LSR). These two papers are a good guide to the type and level of questions that will be asked in the 2024 exams. The syllabus and lecturers are the same as last year and the 2023 exams were on campus (2020 - 22 were online). Whilst in 2023 students were permitted 3 pages of notes and this will not be the case in 2024, the 2023 papers were deliberately written in such a way that notes were not needed to answer questions (assuming of course that the course material had been revised).

  • Q-Review

  • Online Reading List