DOC: Modernize and fix example script

[taldcroft]

Description

This example script was no longer running so it has been fixed and somewhat modernized.

Interface impacts

Testing

Unit tests

• No unit tests (Change does not impact package code, documentation only)

Independent check of unit tests by [REVIEWER NAME]

• [PLATFORM]:

Functional tests

The script runs as expected and creates a reasonable looking plot.

$ cd examples/dpa
$ ipython --matplotlib --classic
>>> run plot_dpa_resid.py