Types of Correlation


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.

|225px|text-top|Positive Correlation

|225px|text-top|Positive Correlation

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.

|225px|text-top|Negative Correlation

|225px|text-top|Negative Correlation

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).

|225px|text-top|Non-linear Correlation

|225px|text-top|Non-linear Correlation

No Correlation

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

|225px|text-top|No Correlation

|225px|text-top|No Correlation

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 (£)































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.

|300x350px|texttop|Ice-cream Sales vs Maximum Temperature.

|300x350px|texttop|Ice-cream Sales vs Maximum Temperature.

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.

Test Yourself

External Resources

See Also