How many factors should be retained for analysis? There is no clear answer but a couple of rules of thumb.

One rule is to consider only those with eigenvalues over 1.

Another rule of thumb is to plot all the eigenvalues in their decreasing order. The plot looks like the side of a mountain, and "scree" refers to the debris fallen from a mountain and lying at its base.

So the sree test proposes to stop analysis at the point the mountain ends and the debris (error) begins.

In this instance, that point coincides with the eigenvalue criterion.