It is a Ratio variable.
And is well known in the literature that the correct interpretation of a correlation between ratio variables is debatable.
See User's guide to ratio variables and A note on using ratio variables in regression analysis for more details.
What you are proposing is an unusual application of hedonic regression in respect of house prices. The method is most commonly used for one of two purposes:
a) To explain and perhaps predict relative house prices.
b) To estimate the value of characteristics of houses and their neighbourhoods, especially those which are hard to value in other ways such as ...
If you watch closely, you will find out that the slope of the lines is -1. I.e. the values of y along every one of the lines are exactly equal. That is you get this lines only because you have great many cases for which the left hand side variable is equal. The lines are visible because relative to the number of observations there are not that many different ...