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:

Assessment

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

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  
13 Apr Lecture 10 Model Selection & Regression Assumptions
20 Apr Lecture 11 Stepwise Regression & 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  
Lecture 10 Longley selection
Galileo
Divorces
Heteroscedasticity
Autocorrelation
Lecture 11 Multicollinearity
Stepwise Regression: Longley
Stepwise Regression: Divorces
Anova
Ancova
Appendix C Monte Carlo pi
Bootstrap CI
Bootstrap t-test
Bootstrap F-test

Datasets

Homework

Homework papers must be submitted on Canvas by 14:00 on Thursday

Homework # Due date Topics
1 5 Feb Moment generating function. Poisson distribution. Poisson models for soccer.
2 12 Feb Bivariate transformations. Deriving the distribution of the t-statistic. The t-test.
3 19 Feb Chi-squared distribution. The t-test in R. Variance ratio test in R and by hand.
4 26 Feb Two-sample t-test. Welch t-test. Paired t-test.
5 5 Mar Two-sample F-test. Goodness-of-fit test.
6 12 Mar Chi-squared test of independence / no association. Least Squares.
7 19 Mar General linear regression. Segmented models.
8 26 Mar  
9 16 Apr The t-test and F-test for regression
10 23 Apr Model Selection and testing Regression Assumptions

References

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