We want to construct a "constant quality" housing index. Suppose that we have a (sample from a) set of housing units at time A. We have a measure of housing quality: for us, separately, rent per month for rental units and price for condos; we do two separate analyses for rents and condos. In addition to quality we observe a set of characteristics for each unit: floor space, availability of air conditioning, etc. We look at the relationship between quality and characteristics.