# 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