The latest Famitsu says that Yakuza 3 needs a 5120MB installation on the HDD. The slow speed of the BluRay-Drive is to blame.
I do not have a direct source to famitsu or an English website. I read it on a German website, which won't help here, I guess.
IMO mandatory Installations on a console is the worst thing this generation brought to us.
*edit* found a source! http://www.n4g.com/ps3/News-267725.aspx
Imagine not having GamePass on your console...