Olympics - does population influence medal prospects?

Some statistics from the London 2012 Olympics. Data taken from www.medalspercapita.com

 There seems to be a pretty strong relationship between GDP and total medals won, with a few exceptions.

There is not a very strong relationship between total medals won and total population. However, if you take out India and China, the odd ones out, then this relationship is slightly stronger, but not as strong as the GDP-Medals comparison.