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 Thursdays

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	Random samples
10 Feb	Lecture 3	The t-test & Introduction to R
17 Feb	Lecture 4	The variance ratio & Two-samples t-test
24 Feb	Lecture 5	The two-sample F-test & Goodness-of-fit test
3 Mar	Lecture 6	Contingency tables & Simulation
10 Mar	Lecture 7	Bootstrap & Least Squares
17 Mar	Lecture 8	The maths of Regression
24 Mar	Lecture 9	Practical regression
31 Mar	Lecture 10	Model Selection & Regression Assumptions
7 Apr	Lecture 11	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 3	One-Sample t-test
Lecture 4	Variance ratio test Two-Sample t-test
Lecture 5	F-test F-test First Principles Goodness-of-fit Goodness-of-fit First Principles
Lecture 6	Goodness-of-fit Contingency Independence Test Monte Carlo pi
Lecture 7	Bootstrap CI Bootstrap t-test Bootstrap F-test 2008 Crisis Least-squares Solution 1 Least-squares Solution 2
Lecture 8	Multiple regression R2 multiple regression
Lecture 9	Simple regression Longley regression
Lecture 10	Longley selection Galileo Divorces Residual graphs Autocorrelation graphic tests Multicollinearity Stepwise Regression: Longley Stepwise Regression: Divorces Anova models

Datasets

• Stock-Gold prices
• Longley
• Fridge Sales
• 2008 Crisis
• Family Guy

Homework

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

Homework #	Due date	Topics
1	6 Feb	Moment generating function. Poisson distribution. Poisson models for soccer.
2	13 Feb	Bivariate transformations. Deriving the distribution of the t-statistic. Conditional expectation and variance.
3	20 Feb	Vectors in R. The t-test: in R and by hand.
4	27 Feb	Variance ratio test. Two-sample t-test.
5	6 Mar	The two-sample F-test and t-tests.
6	13 Mar	The goodness-of-fit test. The chi-squared test of independence / no association
7	20 Mar	Bootstrap Confidence Intervals. Bootstrap t-test and F-test.
8	27 Mar	Simple and general linear regression
9	3 Apr	The t-test and F-test for regression
10	10 Apr

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