### Types of Correlation

#### Definition

Correlation describes the relationship between variables. It can be described as either strong or weak, and as either positive or negative.

Note: 1= Correlation does not imply causation.

#### Positive Linear Correlation

There is a positive linear correlation when the variable on the $x$-axis increases as the variable on the $y$-axis increases. This is shown by an upwards sloping straight regression line.

#### Negative Linear Correlation

There is a negative linear correlation when one variable increases as the other variable decreases. This is shown by a downwards sloping straight regression line.

#### Non-linear Correlation (known as curvilinear correlation)

There is a non-linear correlation when there is a relationship between variables but the relationship is not linear (straight).

#### No Correlation

There is no correlation when there is no pattern that can be detected between the variables.

#### Worked Example

###### Worked Example

The local ice-cream shop have kept track of how much ice-cream they sell and the maximum temperature on that day. The data that they obtained during the last 15 days is as follows:

Temperature (°c)

Ice-cream Sales (£)

$12.5$

$211$

$15.8$

$230$

$22.1$

$359$

$18.9$

$284$

$17.7$

$254$

$19.3$

$287$

$15.3$

$248$

$19.2$

$303$

$13.4$

$235$

$14.1$

$209$

$16.7$

$267$

$18.6$

$295$

$11.9$

$199$

$18.4$

$274$

$18.9$

$279$

Determine the type of correlation between the number of ice-cream sales and the maximum temperature of the day.

###### Solution

Firstly draw a scatter diagram with the given data.

This shows that there is strong positive linear correlation between ice-cream sales and maximum temperature. However, it is not always as easy to tell just by looking at the scatter graph, instead we quantify it using a numeric value known as the correlation coefficient.