That's correct. But the price an investor can charge to renters scales with the opportunity cost of buying, so (house prices x interest rates). Or equivalently

That's correct. But the price an investor can charge to renters scales with the opportunity cost of buying, so (house prices x interest rates). Or equivalently, the price an investor will pay for a house scales with (rent - interest payments). If interest rates go up and housing prices don't fall, then market rents must be rising.