"If interest rates rise this year, it could make a home purchase too expensive for some buyers, analysts have said."
Prices rise & fall on "affordability". You cannot price people out of homes, especially now that so much of the market is underwater already. The only thing pushing people to buy at a higher price will be higher rents, and of course the buy-vs-rent ratio is still somewhat out of whack (though thanks to 4% interest rates, not too bad in most places).
Also note the zero mention of new construction, or the 2010-2011 peak Alt-A reset wave coming upon us.