[coldtea]

>The proportion is different, because different areas have different borrowing costs, risks, regulatory environments, etc. The proportionality is always there

That holds for everything. Only if they necessarily also move in the same way does this have any meaning, else it's like saying two points connect to a line.

[AnthonyMouse]

There is an anthill in Brazil. If you pour honey near it, the ants will make more ants. The number of ants in the anthill is proportional to the amount of honey. If you pour pesticide near it, some of the ants will die. The number of ants in the anthill is inversely proportional to the amount of pesticide. If you pour honey and pesticide near the anthill, and the number of ants stays the same, you haven't disproven either of these things, they're both still true, you're just adding the lines together.

If you kill all the bears in Montana, or add a thousand more, the number of ants in Brazil doesn't change. They are not proportional, they're completely unrelated.

[coldtea]

You keep using this word, proportional. I don't think it means what you think it means.

"having a constant ratio to another quantity"

Inversely proportional too is a mathematic relationship with specific meaning (for one the product must be a constant). It doesn't just mean "more pesticide, less ants" (that's a more general statement than inversely proportional).

Perhaps you merely meant correlated with respect to the rent. But even so, in this thread there were so many provisos added, that the relationship is nebulous at least.

[AnthonyMouse]

The relationship we're actually talking about is proportional using your definition. Rent is proportional to housing prices, all else equal.

If all else isn't equal, i.e. you change interest rates or tax rates, then you're changing the constant. But they're still proportional with the new constant. You're only changing the ratio, not the nature of the relationship.