MTH5120 - Statistical Modelling I - 2023/24

v3 May 2024 p35 updated for MLE of normal with betas instead of mu

module intro and the simple linear regression model

Typed notes to accompany the week 1 lecture material. At the end of the module we will add a single PDF document with full notes for the module.

principles of statistical modelling 1 of 2

principles of statistical modelling 2 of 2

simple linear regression model 1 of 2

simple linear regression model 2 of 2

least squares estimation 1 of 2

least squares estimation 2 of 2

How to install R and R Studio available at https://www.youtube.com/watch?v=d-u_7vdag-0&feature=youtu.be

Lecture Example data for use in R 

Example of simple linear regression model for climate change data

based on the Global_Temperature_NASA_Data.csv data file

Exercise Sheet 1 data 

typed notes covering the theoretical material from week 2 - assessing the simple linear regression model

assessing the model plus details of the task you will need to complete this week

Our World in Data’s mission is to publish the “research and data to make progress against the world’s largest problems”

properties of the estimators 1 of 2

properties of the parameters 2 of 2

Assessing the model, fitted values and residuals, sums of squares

introducing ANOVA

using the ANOVA table

working with residuals

document updated 6/2/2024 revised sections 4.4, 4.5

inference about the parameters

last year's inflation and current 10 year government bond yields by country

inference, confidence interval for beta1

inference about the parameters continued

confidence intervals and prediction intervals

Data for use in Introduction to R_3 Labs

further model checks based on issues with the observation data

matrix approach, maximum likelihood

poorly fitting model diagnostics - pure error and lack of fit, expanded anova

jankaNEW.csv (same file as that used in week 4 copied here for convenience)

training data size and "knowledge" test results for different AI systems up to chatGPT4

outliers

influential observations

transforming the response variable

pure error and lack of fit

for week 6 labs

why do we want to use matrix approaches to regression modelling?

matrix approaches 1 of 2

matrix approaches 2 of 2

maximum likelihood estimation introduction

MLE in the normal distribution

Multiple Linear Regression Models

for multiple linear regression example in R

multiple linear regression ANOVA and inference

for the IT labs in week 8

note that this week the Thursday labs are moved to Monday and Friday by central timetabling. Please check your timetable

liver.csv for use in the week 8 labs

data needed for exercise sheet 6 Q2

introduction to multiple linear regression models and model building using F tests

event this week organised by QM Careers team should be helpful for anyone considering career as maths teacher

multiple linear regression models; matrix form

multiple regression ANOVA, overall F test

inference about betas; confidence intervals

All Subsets Regression

For use in R Labs

For use in Week 9 Labs

slides used by Hugo Maruri-Aguilar in Thursday lecture and includes link to QM Plus page with more details on module selection for the third year

The "Swiss" data set needed for this exercise is already found in R (no separate CSV file). To get the data use the command data(swiss) and then to check the data is loaded use the command head(swiss) to display the first 6 rows. The data is then ready for the rest of the exercise sheet.

problems fitting models, variance inflation factor plus a re-cap of automated methods of model building

What is a linear model?

week 11 and 12 Exercise sheets Bridge data saved as .csv file (easier to import into R)

revision lecture 1 of 2

exam information and revision on topics requested last week

This link will take you to all the past papers for this module. However the 2023 papers above are a better guide for the 2024 exam as earlier years were either online or before the module used R programming.