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.

Lecturer: Dr Silvio Fanzon
Email: S.Fanzon@hull.ac.uk
Office: Room 104a, Larkin Building
Office hours: Wednesday 12:00-13:00
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 course 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: Wednesday 10:00-12:00 in Wilberforce Building - Lecture Room 22
Lecture 2: Thursday 15:00-17:00 in Wilberforce Building - Lecture Room 10
Tutorial: Thursday 11:00-12:00 in Wilberforce Building - Lecture Room 7

Assessment

This course 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 3
We will discuss coursework exercises in class
Coursework must be submitted on Canvas by 14:00 on Thursday 2nd May 2024

Rules for Homework:

There will be 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)
- Bonus 2 points will be added to the final score
Homework papers must be submitted on Canvas by 14:00 on Mondays. Due dates are listed below

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 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
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

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	2008 Crisis

Datasets

Homework

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

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