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.
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.
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.
There is a non-linear correlation when there is a relationship between variables but the relationship is not linear (straight).
There is no correlation when there is no pattern that can be detected between the variables.
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.
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.