- **Math**
(*https://www.mersenneforum.org/forumdisplay.php?f=8*)

- - **Normalising rent levels**
(*https://www.mersenneforum.org/showthread.php?t=22601*)

Normalising rent levelsHi all,
I work in social housing. We have 13,000 properties. Over several decades for various reasons rents for properties have moved giving slightly different values for properties in some cases by a few pence to a few pounds. Across the properties this means there are hundreds of variations. My goal is to normalise rents based on number of bedrooms with the least possible movement. Is there a mathematical way to solve this? Are there any formulas or methodologies that are geared towards this problem? I can write VBA so do the work once I know where to start (I think!). As this is social (low income) housing the least possible change to a single figure is the ideal outcome. While doing this I would need to ensure that the total weekly rent collected changes very little (no more than +3%) so we could achieve this during a rent increase period. Moving rent downwards would have less of a limitation. Thank you in advance for any help you can give. |

Can you supply some (fake) data and a small sample of what the outcome of the adjustments might look like? Are there other considerations other than rooms designed for sleeping (like total floor space, appliances provided, income levels of the occupants, number and type of bodies dwelling within, etc.)?
I suspect that you can define the variables and then seek to cluster those that share the same factors, then proceed to the adjustments. I would use looking at median and mean functions along with standard deviations to examine the groups and set the numbers. This might be an iterative process over 2 or 3 rent increase periods. Edit: Does the local or national "poverty level" of income or "living wage" play into this? Taking that into consideration might also be worthwhile. |

Yes I can even post real rent values with anonymised identifiers. To answer your questions:
No the size of the actual rooms is not counted. Just the number of bedrooms (1,2,3,4 bedrooms. At this stage I don't think type of property would be a factor although if I can get a handle on an approach then I might factor in whether a property is flat / detached.. etc. Local or customer incomes would not be relevant as the maximum rents are still within the scope of benefits designed for the most disadvantaged. Should be able to post data in the next hour or two. |

1 Attachment(s)
So I have isolated the set of 2 bedroom properties which is the largest at 5697 properties. All of the data has been stripped to the bare minimum and anonymised.
So in this set there are 696 unique rent values with a minimum of £55.96 and a max of £89.14 |

What if you follow the following basic idea?
If the rent is >1σ below the mean you exercise the max allowable increase. For rents 1σ to 0.5σ below the mean, 1/2 of the max increase. For rents 0.5σ above and below the mean, 1/3 or 1/4 max. For rents >2σ above the mean, lower them to 2σ above the mean. (Drop this step for all following iterations.) Those bottom few will take 10-15 periods to catch up. You can tune the values as you go. Start all new rentals (for a while) at 1σ above the mean. By using σ you will draw the lower ones along. Every period you can run the values and make adjustments to the zones and the proportion of the max allowable increase. Later on, it might just be that if they are below the average, they get moved up to the current average or a set figure. At some point they will all be close enough that you can just set them all to the same value. |

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