Preliminaries

Overview

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
• ANOVA