Rates do not directly effect prices. However, under current economic understanding, raising the prime rate should lower demand for housing, thus LOWERING home prices.
This is what Greenspan has been trying to accomplish for a few years now. Raise the fed funds rate, driving up the cost structure for commercial banks. Banks pass this on in the form of higher interest rates. This raises the cost of investment to companies and individual investors, in turn decreasing investment. Less individuals looking to invest is represented by a decrease in the demand for housing (a shift downward or to the left for those familiar with a basic Supply and Demand graph). This results in a lower price.
Greenspan, and anyone with any sense, knows that there is a bubble in the housing market. He doesn't want to retire having left a bubble about to pop on his watch. So for years now he has been trying to control housing prices by upping the fed funds rate. It sure isn't fear of inflation that's been driving it up.
What he and many others can't figure out is why it hasn't been working. And personally, I am holding off on buying a home because the last thing I want to be sitting on is a 300K house with a 750K mortgage. And in So. Cal, I believe that the bubble is large enough that those numbers could end up in reality.