## What is R?

The **basic reproduction number **is not to be confused with the **effective reproduction number** (expected number of cases).

The **R** number is an **average**. A complex, **statistical calculation**. R refers to single person who will go on to pass on the infection.

The **number is not fixed** it changes according to behavioural changes, or as* immunity develops*.

## How is R calcluated?

To calculate R you require data. Obviously to acquire data people need to be infected. In other words, historical data is a necessitate to calculate R.

Data is acquired by the *number of people diagnosed* as either *infected* by the virus or *died* from the illness.

As data is historical calculations of the **spread is an estimate**.

## Why a number above one suggests concern.

A number above one implies exponential Covid 19 infection rate.

**Below one** suggests the illness is in **decline** and **may disappear**.

R squared, also called coefficient of determination, is a statistical calculation that measures the degree of interrelation and dependence between two variables. In other words, it is a formula that determines how much a variable’s behaviour can explain the behaviour of another variable.

The Pearson correlation coefficient is used to measure the strength of a linear association between two variables, where the value r = 1 means a perfect positive correlation *(virus Infection growing)* and the value r = -1 means a perfect negative correlation *(virus growth declining or eradicated)*.

A scatterplot diagram is used to graphically illustrate correlation r values.

## Look at the scatterplot diagram below.

**Figure (a) a correlation of nearly +1** - *A perfect evolution (virus growing)***Figure (b) a correlation of -0.50** - *declining but the points are somewhat scattered in a wider band, showing a linear relationship is present, but not as great as in figures (a) and (c)***Figure (c) a correlation of +0.85** - *a very strong uphill linear pattern (not as strong as (a). ***Figure (d) a correlation of +0.15** - *does not indicate much is happening and it shouldn’t, its correlation is very close to 0, (would suggest Covid 19 is dying out).*

**–0.70.***A strong downhill (negative) linear relationship***–0.50.**A*moderate downhill (negative) relationship***–0.30.***A weak downhill (negative) linear relationship*- No linear relationship

**+0.30.***A weak evolution (positive) linear relationship***+0.50.***A moderate evolution (positive) relationship***+0.70.***A strong evolution (positive) linear relationship***Exactly +1.***A perfect evolution (positive) linear relationship*

## Warning

If a scatterplot does not show at least a bit of a linear relationship, the correlation does not mean much.

### So why measure a linear relationship if there appears to not be one?

*Think of no linear relationship in two ways:*

- If no relationship exists at all, calculating the correlation
*does not make sense*because correlation only applies to linear relationships. - If a strong relationship exists but it is
**not linear**, the correlation*may be misleading*. The reason in some cases a strong curved relationship exists. That is why it is critical to examine the scatterplot first.

### Summary

**Many mistakenly think a correlation of –1 indicates no relationship.**

In fact, a correlation of **–1** means the **data is aligned** in a perfect straight line.

**In other words, the strongest negative linear relationship you can get.**

The **“–”** (minus) sign indicates a **negative relationship**, a *downward line*.

**In Covid 19 terms the virus may disappear. **

#### Key points to remember.

- Data is historical.
- The data may be incomplete or incorrectly defined or collected.
- Such analysis is subjective i.e. the answer may or may not be true. It’s open to interpretation.
- At best a guideline.