What is regulation in a transformer?

One of my ELEC 342 students asked me this question on Piazza. I thought it might be good to answer that for the whole class, so here it is.
However, this answer is already in the textbook, the Stephen Chapman textbook.
The formula used RMS volts for Vnl and for Vfl, not phasors.
Of course, the regulation depends on the power factor of the load.
There is one particular value of the power factor for which the regulation is the worst. (largest value).

[@kcher]

Thank you for sharing knowledge.