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 and an introduction to R
17 Feb Lecture 4 The variance ratio and two samples t-test
24 Feb Lecture 5  
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

R codes

Lecture Material
Lecture 3 One-Sample t-test
Lecture 4 Variance ratio test
Lecture 5 Two-Sample t-test | F-test
F-test First Principles
Lecture 6 Goodness-of-fit
Goodness-of-fit First Principles
Monte Carlo pi
Monte Carlo p-value
Goodness-of-fit Contingency
Independence Test
Lecture 7 Least-squares Solution 1
Least-squares Solution 2
Lecture 8 Multiple regression
R2 multiple regression
Lecture 9 Simple regression
Longley regression
Longley selection
Galileo
Divorces
Lecture 10 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 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 Chi-squared distribution. Variance ratio test.
5 6 Mar  
6 13 Mar  
7 20 Mar Properties of chi-squared and F-distribution
8 27 Mar Homework 8 is worth 28 points. Two-sample t-test and F-test. Chi-squared tests
9 3 Apr Simple and general linear regression
10 10 Apr t-test and F-test for regression

References

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