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.

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.

All the module 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:

Assessment

This module 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

Topics

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 Stepwise Regression & ANOVA
28 Apr Revision Week Coursework submission deadline
Extra Appendix A Probability revision
Extra Appendix B More on R

Statistical tables

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
Heteroscedasticity
Autocorrelation
Lecture 11 Multicollinearity
Stepwise Regression: Longley
Stepwise Regression: Divorces
Anova
Ancova

Datasets

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 Model Selection and testing Regression Assumptions

References

drawing drawing