Scatterplot with semi-transparent data points in gnuplot

In my "Improving Diagrams" post I showed you a scatterplot with semi-transparent data points that was made with Excel. You can produce similar diagrams with gnuplot if you use a little trick. Unfortunately, you can not set normal points semi-transparent in gnuplot, but you can plot circles instead.

The plot generated by gnuplot

Let's take a look at how this diagram was produced.