In this course the fundamental principles and techniques underlying modern statistical and data analysis will be introduced. The course will cover the core foundations of statistical theory consisting of:

  • probability distributions and techniques;
  • statistical concepts and methods;
  • linear models.

The course highlights the importance of computers, and in particular, statistical packages, in performing modern statistical analysis. Students will be introduced to the statistical package R as a statistical and programming tool and will gain experience in interpreting and communicating its output.

Learning Outcomes

A student who completes this module successfully will be able to:

  • derive and explain properties of basic statistical inference; linear regression models and probability techniques;
  • perform exploratory data analysis; summarising their analysis and proposing further investigations;
  • derive point and interval estimators, and perform hypothesis tests for a variety of situations;
  • apply the theory and methods for statistical inference, linear regression models and probability techniques to a wide range of practical examples;
  • use the statistical package R to derive results concerning statistical inference;
  • communicate their statistical analysis in a written report.

Syllabus Overview

  • Summary statistics and visualising data
  • Probability, random variables and expectation
  • Joint distributions, conditional distribution, covariance and correlation
  • Central limit theorem
  • Parameter estimation - Method of Moments and Maximum Likelihood Estimation
  • Transformations of random variables
  • Multivariate normal distribution
  • Linear Models
  • Least squares estimation
  • Interval estimation
  • Hypothesis testing and goodness-of-fit


At the end of most Chapters there are Tasks to complete. These tasks will typically be either computer lab sessions using the statistical package R or statistical exercises or both to reinforce the material covered in the chapter (or last couple of chapters).