Statistical Models

Webpage of the module 551305 T2 2025/26

General Information

Welcome to the module Statistical Models 551305 for the BSc in Mathematics at the University of Hull, academic year 2025/26. This module focusses on both the technical and practical aspects of a range of linear statistical models. We will investigate how and why these models work, what the assumptions behind them are, and how to interpret the results. We will implement such models using the statistical computer language R.

Questions

If you have any questions please feel free to email me. We will address Homework and Coursework in class. In addition, please do not hesitate to attend office hours.

All the module information will be posted on this page, as well as on Canvas. The links to the reference material are:

Lectures Calendar

We have two Lectures and one Tutorial per week:

Topics

Lectures Diary

There are 11 Lectures in this module and 3 optional Appendices. Links to the slides and lecture titles are below. Links to the Slides and Lecture Titles are below.

Week of Slides Title
26 Jan Lecture 1 An introduction to Statistics
2 Feb Lecture 2 Random samples & The t-test
9 Feb Lecture 3 Introduction to R & The variance ratio test
16 Feb Lecture 4 Two-sample t-test & More on R
23 Feb Lecture 5 Two-sample F-test & Goodness-of-fit test
2 Mar Lecture 6 Chi-squared test & Least Squares
9 Mar Lecture 7 The Maths of Regression
16 Mar Lecture 8 Practical Regression
23 Mar Lecture 9 Model Selection & Regression Assumptions I
13 Apr Lecture 10 Regression Assumptions II & Stepwise Regression
20 Apr Lecture 11 ANOVA
27 Apr Revision Week Coursework submission deadline
Extra Appendix A Probability revision
Extra Appendix B R Style Guide
Extra Appendix C Simulation & Bootstrap

Statistical tables

R codes

Lecture Material
Lecture 3 One-Sample t-test
Variance ratio test
Lecture 4 Two-Sample t-test
Lecture 5 F-test
F-test First Principles
Goodness-of-fit
Goodness-of-fit First Principles
Goodness-of-fit Contingency
Lecture 6 Independence Test
2008 Crisis
Least-squares Solution 1
Least-squares Solution 2
Lecture 7 Multiple regression
R2 multiple regression
Lecture 8 Simple regression
Longley regression
Lecture 9 Longley selection
Galileo
Divorces
Heteroscedasticity
Lecture 10 Autocorrelation
Arima
Multicollinearity
Stepwise Regression: Longley
Stepwise Regression: Divorces
Lecture 11 Anova
Ancova
Appendix C Monte Carlo pi
Bootstrap CI
Bootstrap t-test
Bootstrap F-test

Datasets

Assessment Breakdown

This module will be assessed as follows:

Type of Assessment Percentage of final grade
Coursework Portfolio 70%
Homework 30%

Rules for Coursework:

Rules for Homework:

How to submit assignments:

Important: I will not mark

Tasks & Deadlines

The topics for the 10 Homework (HW) assignments and the Coursework (CW) are listed below.
The homework papers can be downloaded from Canvas.

Task Deadline Topics
HW1 5 Feb MGF. Poisson models for soccer
HW2 12 Feb Bivariate transformations. The t-test
HW3 19 Feb $\chi^2$ distribution. The t-test in R. Variance ratio test
HW4 26 Feb Two-sample t-test. Welch t-test. Paired t-test
HW5 5 Mar Two-sample F-test. Goodness-of-fit test
HW6 12 Mar $\chi^2$ test of independence. Least Squares
HW7 19 Mar General linear regression. Segmented models
HW8 26 Mar The t-test and F-test for regression
HW9 16 Apr Model Selection. Heteroscedasticity
HW10 23 Apr Autocorrelation. Multicollinearity
CW 30 Apr Entire Module, inc. Stepwise Selection & Anova

References

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