Statistical Models

Lecture Slides

Authors

Affiliation

Dr Silvio Fanzon

University of Hull

Dr John Fry

University of Hull

Welcome

These are the Slides of the module Statistical Models 551305 for T2 2025/26 at the University of Hull. If you have any question or find any typo, please email me at

S.Fanzon@hull.ac.uk

Up to date information about the module will be published on the University of Hull Canvas Webpage

canvas.hull.ac.uk/courses/77772

and on the Course Webpage hosted on my website

silviofanzon.com/blog/2026/Statistical-Models/

Slides

There are 11 Lectures in this module and 3 optional Appendices. Links to the Slides and Lecture Titles are below.

Slides	Title
Lecture 1	An introduction to Statistics
Lecture 2	Random samples & The t-test
Lecture 3	Introduction to R & The variance ratio test
Lecture 4	Two-sample t-test & More on R
Lecture 5	Two-sample F-test & Goodness-of-fit test
Lecture 6	Chi-squared test & Least Squares
Lecture 7	The Maths of Regression
Lecture 8	Practical Regression
Lecture 9	Model Selection & Regression Assumptions I
Lecture 10	Regression Assumptions II & Stepwise Regression
Lecture 11	ANOVA
Appendix A	Probability revision
Appendix B	R Style Guide
Appendix C	Simulation & Bootstrap

Statistical tables

• Download here

R Codes

Lecture	Codes
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	Longley selection Galileo Divorces Heteroscedasticity
Lecture 10	Autocorrelation Arima Multicollinearity Stepwise regression: Longley Stepwise regression: Divorces
Lecture 11	Anova Ancova
Appendix C	Monte Carlo \(\pi\) Bootstrap CI Bootstrap t-test Bootstrap F-test

Datsets

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

Assessment Breakdown

This module is assessed as follows. Further details are available on Canvas.

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

Tasks & Deadlines

The topics for the 10 Homework (HW) assignments and the Coursework (CW) are listed below.
The homework papers can be downloaded from Canvas.

Task	Deadline	Topics
HW1	5 Feb	MGF. Poisson models for soccer
HW2	12 Feb	Bivariate transformations. The t-test
HW3	19 Feb	\(\chi^2\) distribution. The t-test in R. Variance ratio test
HW4	26 Feb	Two-sample t-test. Welch t-test. Paired t-test
HW5	5 Mar	Two-sample F-test. Goodness-of-fit test
HW6	12 Mar	\(\chi^2\) test of independence. Least Squares
HW7	19 Mar	General linear regression. Segmented models
HW8	26 Mar	The t-test and F-test for regression
HW9	16 Apr	Model Selection. Heteroscedasticity
HW10	23 Apr	Autocorrelation. Multicollinearity
CW	30 Apr	Entire Module, inc. Stepwise Selection & Anova

References

Main textbooks: These slides are self-contained and largely based on the books

• Bingham and Fry [1]
• Fry and Burke [2]

Secondary References: In addition we reccomend the following

• Probability & Statistics Manual: Casella and Berger [3]
• Easier Probability & Statistics Manual: DeGroot and Schervish [4]
• Concise Statistics with R: Dalgaard [5]
• Comprehensive R manual: Davies [6]

References

[1]

Bingham, Nicholas H., Fry, John M., Regression, linear models in statistics, Springer, 2010.

[2]

Fry, John M., Burke, Matt, Quantitative methods in finance using R, Open University Press, 2022.

[3]

Casella, George, Berger, Roger L., Statistical inference, second edition, Brooks/Cole, 2002.

[4]

DeGroot, Morris H., Schervish, Mark J., Probability and statistics, Fourth Edition, Addison-Wesley, 2012.

[5]

Dalgaard, Peter, Introductory statistics with R, Second Edition, Springer, 2008.

[6]

Davies, Tilman M., The book of R, No Starch Press, 2016.