The "scientific method" is called Dead Reckoning or Heading Hold; the other is a track crawl.
It depends on whether the examiner has asked you to fly a leg as a heading hold or a track crawl; in which case, you do as asked!
On your map, draw 5 and 10 degree fan lines either side of your heading and draw the half-way and quarter-way points. These will give you an idea of the correction you need to make. For example, if at half way, you estimate yourself to be 7 degrees off course, then you'll need to make a correction of 14 degrees in your heading. And yes, much of it is based on guess-timations but they do become more educated with practice and experience.
Track Crawl though is what most people sorry, helicopter pilots do in real life!!!
Cheers
Whirls