Upgrade from Home Basic to Home Premium question.

Hello. I have a new eMachines computer that I bought a few months ago. It
was a floor model and did not come with a disc but I made a "restore" DVD.
The Windows Vista Home Basic on it is legit. I bought 1 gig of RAM to add to
the PC the day I bought it so I have 1.5 gig of RAM.

Since I have enough RAM I'd like to upgrade to the Home Premium version of
Vista, I like the Aero look and feel (though the non-Aero Vist is still very
spiffy!).

I qualify for academic pricing, therefore the "Home Premium" upgrade is less
expensive to me than the "Anytime Upgrade" since I need to buy the "Anytime
Upgrade" disc.

Can the "Home Premium" academic version upgrade a "Home Basic" installation?