Title: Two continuous variables
Course: UGQuants (SSPS) > Section: Data Visualisation

Two continuous variables

The relationship between two interval, or continuous, level variables is visualised using a scatterplot. Within a scatterplot, one variable is measured along the x-axis and the second on the y-axis. Each case is represented by a dot on the graph, with the position of the dot representing the value of the case on the two variables under consideration.

Where a pattern can be seen in how the values of cases on one variable are related to the values on the second variable, a correlation is said to exist. However, as with the use of all statistical measures of association (for instance Pearson’s r, Gamma, Yule’s Q etc), the existence of a correlation should not be taken as prove of causation. Correlation might be present for several reasons:-

1. It is indeed the case that values on one variable “explain” a case’s value on the second variable, i.e. causation is present.

2. Two variables reveal a correlation but to understand their exact relationship, we require a third intermediary variable. For instance, a positive relationship between age and income could be seen as too simplistic. Gaining age does not automatically lead to an increase in earnings. However, as workers grow older, they may well gain job experience and take on more senior roles, with greater pay. Hence the relationship between age and income is only fully understood when a measure of employment is also considered.

3. A spurious correlation exists. That is to say a pattern in the data in no way reflects any form of causal relationship. For instance, a correlation between the sale of ice-cream and the number of fires the emergency services are asked to attend is spurious. There is no plausible reason why selling ice-cream will cause fires to start. Instead, both ice-cream sales and fires can be “explained” by periods of hot weather.