Biplot

The biplot (Gabriel, 1971) is a graph that represents both variables and cases together in two dimensions. Information about the variables is provided by the variable projections or axes. The orientation of the axes displays the relationship between the variables and the components. For instance, a variable that lines up with a component axis will load heavily on that component and a variable axis that is almost perpendicular to a component axis will not load heavily on that component. In addition variable axes in close proximity indicate a high correlation among the variables. For example in the biplot below, the variables Var1 and Var2 are almost line up completely with the t1 axis thus indicating that they both load heavily on t1. The closeness in proximity also indicates that they are highly correlated.

Information about the cases can also be obtained. Distances between points, clusters of points, outliers, etc. can be quickly visualized with this graph as they would be with a regular scatterplot. For example, in the biplot above we can clearly discern the presence of two groups. Also, by looking at the variable axes you can see that the two variables responsible for this separation are Var1 and Var2.

There are two different types of biplots available. The first type of biplot is based upon the raw or unstandardized components. This graph is good at representing distances between the data points while the standardized graph is better at representing the relationships among the variables.