Module: Statistics II

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Statistics II
Module Code	MTH1082 (ITS: MS228)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	7.5

Description

MS228 aims to provide a strong foundation in the fundamental statistical method of regression modelling. Simple and multiple linear regression models will be presented. The fitting and interpretation of regression models will be explained and practical examples given. The linear model will be extended to model non normal data using generalised linear models (GLMs). The regression models will be applied to practical datasets using R. Students will also be introduced to Bayesian statistical methods and their use in credibility theory.

Learning Outcomes

1. Perform exploratory data analysis techniques on a sample of data.
2. Describe and interpret linear regression models and estimate the parameters of a simple linear regression model.
3. Describe and interpret generalised linear models (GLMs).
4. Fit linear and generalised linear models to datasets using R and apply appropriate model checks.
5. Understand the Bayesian approach to statistical modelling.
6. Apply the Bayesian and empirical Bayesian approaches to credibility theory.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	30	Classes
Tutorial	10	Classes
Laboratory	10	Computer labs
Independent Study	138	Individual
Total Workload: 188

Section Breakdown
CRN	21077	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Vladimir Krylov	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
Assignment	lab assignment	30%	n/a
Formal Examination	n/a	70%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Exploratory Data Analysis
Data visualisation – histograms, box plots, scatter plots, heatmaps. Use of R visualisation packages. Correlation measures. Introduction to Principal Components Analysis. Use of R to implement analysis techniques.

Linear Regression
Exploratory data analysis; correlation; least squares estimation; model fitting in R; goodness of fit measures; residual checking; predication; confidence intervals.

Multiple Linear Regression
Model definition; modelling fitting and checking in R.

Generalised Linear Models (GLM)
Exponential family - binomial, Poisson, exponential, gamma and normal; link function and canonical link function; deviance and scaled deviance; model fitting in R; Pearson Chi-square test and the Likelihood ratio test; model interpretation.

Bayesian Statistics
Bayes theorem; prior and posterior distributions; loss functions.

Credibility Theory
Credibility premium; Bayesian approach to credibility theory; empirical Bayes approach to credibility theory.

Indicative Reading List

Books:
None

Articles:
None

Other Resources

None