Statistical Models

Webpage of the module 551305 T2 2024/25

General Information

Welcome to the module Statistical Models 551305 for the BSc in Mathematics at the University of Hull, academic year 2024/25. 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.

Lecturer: Dr Silvio Fanzon
Email: S.Fanzon@hull.ac.uk
Office: Room 104a, Larkin Building
Office hours: Thursday 15:00-16:00
Canvas Page: Click here

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.

Key Links

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

Slides
Lectures Diary
Homework

Lectures Calendar

We have two Lectures and one Tutorial per week:

Lecture 1: Thursday 16:00-18:00 in Wilberforce Building - Lecture Room 4
Lecture 2: Friday 12:00-14:00 in Robert Blackburn Building - Lecture Theatre C
Tutorial: Friday 15:00-16:00 in Wilberforce Building - Lecture Room 3

Assessment

This module will be assessed as follows:

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

Rules for Coursework:

Coursework available on Canvas from Week 9
Coursework must be submitted on Canvas
Deadline: 14:00 on Thursday 1st May
No Late Submission allowed

Rules for Homework:

10 Homework papers, posted weekly on Canvas
Each Homework paper is worth 14 points
Final Homework grade computation:
- Sum the top 7 scores (max score 98 points)
- Rescale to 100
Homework must be submitted on Canvas
Deadline: 14:00 on Mondays

How to submit assignments:

Submit PDFs only on Canvas
You have two options:
- Write on tablet and submit PDF Output
- Write on paper and Scan in Black and White using a Scanner or Scanner App (Tiny Scanner, Scanner Pro, …)

Important: I will not mark

Assignments submitted outside of Canvas
Assignments submitted more than 24h After the Deadline

Topics

Linear regression models with one or more explanatory variables
Least squares estimation of model coefficients and their properties
Checking the regression modelling assumptions
Analysis of variance (ANOVA)
Analysis of real-world datasets
Statistical software for testing, prediction and visualisation of data

Lectures Diary

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

Week of	Slides	Title
27 Jan	Lecture 1	An introduction to Statistics
3 Feb	Lecture 2	Multivariate distributions
10 Feb	Lecture 3	Random samples
17 Feb	Lecture 4	Hypothesis tests in R – Part 1
24 Feb	Lecture 5	Hypothesis tests in R – Part 2
3 Mar	Lecture 6	Two-sample hypothesis tests
10 Mar	Lecture 7	The chi-squared test
17 Mar	Lecture 8	The maths of regression
24 Mar	Lecture 9	General linear regression
31 Mar	Lecture 10	Practical regression
7 Apr	Lecture 11	Violation of regression assumptions and ANOVA
28 Apr	Revision Week	Coursework submission deadline
Extra	Appendix A	Probability Revision
Extra	Appendix B	More on R

Statistical tables

Available here

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 Galileo Divorces
Lecture 11	Residual graphs Autocorrelation graphic tests Multicollinearity Stepwise Regression: Longley Stepwise Regression: Divorces Anova models
Appendix B	2008 Crisis

Datasets

Homework

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

Homework #	Due date	Topics
1	3 Feb	Moment generating function. Poisson distribution. Poisson models for soccer
2	10 Feb	Computing the pdf of Student’s t distribution
3	17 Feb
4	24 Feb	t-test in R and by hand
5	3 Mar	Cancelled. Replaced by Homework 8 now worth 28 points
6	10 Mar	Chi-squared distribution and variance ratio test
7	17 Mar	Properties of chi-squared and F-distribution
8	24 Mar	Homework 8 is worth 28 points. Two-sample t-test and F-test. Chi-squared tests
9	31 Mar	Simple and general linear regression
10	7 Apr	t-test and F-test for regression

References

Slides: Available here
Main References: The slides are self-contained and based on the books
- Bingham and Fry
- Fry and Burke

Secondary References: In addition we recommend the following
- Probability & Statistics Manual: Casella and Berger
- Easier Probability & Statistics Manual: DeGroot and Schervish
- Concise Statistics with R: Dalgaard
- Comprehensive R manual: Davies