davelj makes some excellent points, as to the other factors involved (namely rents).

People tend to look at how interest rates relate to payments. They correctly see that an increase in rates lowers the amount of property they might qualify for. However, people often make the mistake of extraolating this to the macroeconomy.

The mistake is assume that other factors remain constant (rent, income, inflation, etc).
Interest rates do not move in a vacuum.

If prices were inversely proportional to interest rates, we should have seen significant increases in prices as rates fell from about 6% to near 3% over the past 6 years.

In fact, history tells us that interest rates and housing prices over long-term periods (e.g. 5 year periods) tend to move in the same direction.

The lay person might ask, “How can this happen if the amount of the loan I can afford decreases when rates go up ?” The answer is that over the long run rates tend to move up with inflation and down with disinflation (or outright deflation). Rates are low now because the economy is sluggish, joblessness is high. Rates historically increase when either the economy is on the upswing or inflation is present. In both cases (historically) home prices tend to move up.

Look at what prices did in the late 1960’s to the early 1980s as interest rates moved from 5 or 6 % to the teens.

An inverse relationship of home prices to interest rates is a fallacy.