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

Two continuous variables: scatterplots

The strength of any relationship present in a scatter plot is identified by how tightly the dots representing different cases group around a specific pattern. For instance, consider a simple linear positive relationship between two variables. Where the dots for each case form a perfectly straight-line, a perfect relationship can be said to exist, i.e. the value on one variable perfectly predicts a case’s value on the other variable (Pearson r =1.0). As cases become less tightly grouped the strength of the relationship can be said to be falling, until no patterns is disenable, at which point no relationship is said to exist.

Identifying the shape of a correlation between two variables is one area where visual methods often outperform traditional numeric statistical methods. Most statistical measures of correlation assume linear relationships. Yet, at least at a descriptive level, humans can discern more complex patterns.  Consider the three relationships shown below. Pearson’s r will provide a good indication of the relationship in the first figure. While patterns are clearly identifiable in the second and third graphs, they are more complex (they deviate from the idea of linearity) and so a Pearson correlation will under-estimate the strength of the relationship, and disregard potentially interesting information about the nature of any pattern or causality.

This ability to identify relationship between variables which are linear or non-linear can make scatterplots a useful precursor to more formal statistical analyses of the relationship between variables.  Since statistical methods, like OLS regression, often involve an assumption of linear relationships between variables, inspecting scatter plots can provide a useful insight as to whether variables are suitable for this type of further analysis. Understanding the shape of a non-linear relationship between variables can also help with understanding what type of transformation data might need to undergo to exhibit a linear relationship suitable for further analysis.