Harvard Business School and the University of Pennsylvania collaborated on this fascinating research into human behaviour and trust.
They carried out a series of field studies and laboratory experiments to look at the relationship between the act of apologising and trust. Across all the studies they identified significant benefits to apologising. Even if you are apologising for something out of your control like the rain or a late bus you can increase the trust of those around you.
Why not take a look at the article to see how they conducted their experiments, or even try it out for yourself?