# Introduction to Statistics

Paul Hewson of Plymouth University
gave us an introduction to statistics and R.

The following notes are based on this session.

## Introduction

- Data and summaries thereof are not considered “statistics”
- “Statistics” are rather mathematical models of what generated the observed
data (explanation) and which can be used to predict more data points
- Generally, regard observed data as a sample from a population that we try
and make a statement about
- Models are hardly every correct exactly and are usually just a starting point

## Bayesian Inference

- Bayes theorem is provable and solid
- Where it gets interesting is the choice of the prior distribution

## Exercises

## Random Notes

`logit`

is a link function
- Least squares parameters describe a hyperplane that minimizes the
$L_2$ error
- Normal QQ plots
- Leverage:
- is a property of each observed data point
- is the change in the predicted value for a given observation of
the independent value caused by moving the corresponding observed
dependent value up or down
- lecture notes on this

- Residuals
- p-value is a measure of the evidence against the Null hypothesis
- Statistical testing has not been confirmed well for large
`N`

(i.e. a great number of data points)
- use a computer to generate data from the assumed model and compare
model data with your sample to decide whether the model makes sense