Statistical Models

Webpage of the Course 551305 T2 2023/24

General Information

Welcome to the Course Statistical Models 551305 for the BSc in Mathematics at the University of Hull, academic year 2023/24. 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 also implement such models using the programming language R.


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 course 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:


This course 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


Lectures Diary

There are 11 lectures in this module. Links to the slides and lecture titles are below

Week of Slides Title
29 Jan Lecture 1 An introduction to Statistics
5 Feb Lecture 2 Multivariate distributions
12 Feb Lecture 3 Random samples
19 Feb Lecture 4 Hypothesis tests in R – Part 1
26 Feb Lecture 5 Hypothesis tests in R – Part 2
4 Mar Lecture 6 Two-sample hypothesis tests
11 Mar Lecture 7 The chi-squared test
18 Mar Lecture 8 The maths of regression
8 Apr Lecture 9 General linear regression
15 Apr Lecture 10 Practical regression
22 Apr Lecture 11 Violation of regression assumptions and ANOVA
29 Apr Revision Week Coursework submission deadline
Extra Appendix More on R

Statistical tables

R codes

Lecture Material
Lecture 4 One-Sample t-test
Lecture 5 Variance ratio test
Lecture 6 Two-Sample t-test | F-test
F-test First Principles
Lecture 7 Goodness-of-fit
Goodness-of-fit First Principles
Monte Carlo pi
Monte Carlo p-value
Goodness-of-fit Contingency
Independence Test
Lecture 8 Least-squares Solution 1
Least-squares Solution 2
Lecture 9 Multiple regression
R2 multiple regression
Lecture 10 Simple regression
Longley regression
Longley selection
Lecture 11 Residual graphs
Autocorrelation graphic tests
Stepwise Regression: Longley
Stepwise Regression: Divorces
Anova models
Appendix 2008 Crisis



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

Homework # Due date Topics
1 5 Feb Moment generating function. Poisson distribution.
2 12 Feb Poisson models for soccer
3 19 Feb Computing the pdf of Student’s t distribution
4 26 Feb t-test in R and by hand
5 4 Mar Cancelled. Replaced by Homework 8 now worth 28 points
6 11 Mar Chi-squared distribution and variance ratio test
7 18 Mar Properties of chi-squared and F-distribution
8 8 Apr Homework 8 is worth 28 points. Two-sample t-test and F-test. Chi-squared tests
9 15 Apr Simple and general linear regression
10 22 Apr t-test and F-test for regression


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