Correlation

In a nutshell

Bivariate data can be shown on a scatter graph. This helps you understand whether or not data is correlated.

Bivariate data

Bivariate data is the result of observing two variables from the same sample.

Example 1

Regarding a certain population, when registering the height and the weight of each person, you are creating bivariate data: you are relating each person's height with their weight.

Scatter graphs

Bivariate data can be shown on a scatter graph.

The horizontal axis shows the independent variable (the one you control) and the vertical axis shows the dependent variable (the one being measured).

The two variables in a scatter graph are often correlated:

Scatter diagram	Correlation	meaning
	Strong positive correlation.	On average, when one variable increases, the other also increases.
	Strong negative correlation.	On average, when one variable increases, the other decreases.
​	No correlation.	There is no clear relation between the two variables.

Causality

Two variables will have a causal relationship if the change in one variable induces a change in the second.

However, just because two variables are correlated, it doesn't necessarily mean they have a causal relationship. Causation can only be deduced in the context of the data.

Example 2

Describe the correlation between the data shown on the graph. Is there a causal relationship between them?

You can see that when the $$x$$ values increase, $$y$$ values also increase. This can be shown by drawing a line of best fit:

Therefore, the two variables have a strong positive correlation.

However, you cannot state that there's a causal relationship between the variables. You don't know what the axes represent and so the context is not known.