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I am working on an price optimization problem for a Real Estate company. Basically, we'd like to optimize their rental price to maximize revenue on their properties.

I have submarket level data such as rental price, occupancy rate, comparable units, operating expenses (fixed cost) in the market, etc.

So for a given set of prices p = {40....60}, the objective is to find the optimal price point i.e the point where marginal revenue => marginal cost.

The first answer on this question is one of way of doing it, however, I may not always have probability distribution and the relationship between price and predicted occupancy is non linear:

enter image description here

Simple Linear: ()=+×() where is a scaling constant. Implies that price and probability are linearly related. 2

I have attempted to use log-log regression to calculate elasticities:

import statsmodels.formula.api as sm

mod = sm.ols(formula = 'np.log(Occupancy) ~ np.log(Rent) + np.log(Income) + np.log(unemp) + np.log(comparable)', data=df).fit()

mod.summary()

enter image description here

The regression above fits price and economic control variables on occupancy rates.

With R-Square of 0.94, I am suspicious of this model and there is likely an endogeneity problem. What non-linear methods can I fit to find the optimal rental price. Open to any other ideas/suggestions as well.

kms
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  • I found following links: https://scipy-cookbook.readthedocs.io/items/robust_regression.html https://stackoverflow.com/questions/51972637/nonlinear-regression-with-python-whats-a-simple-method-to-fit-this-data-bette https://stackoverflow.com/questions/39895369/how-to-run-non-linear-regression-in-python https://stackoverflow.com/questions/52930401/how-to-get-a-robust-nonlinear-regression-fit-using-scipy-optimize-least-squares https://stackoverflow.com/questions/52943720/how-to-do-exponential-nonlinear-regression-in-python regards, shibamouli – Shibamouli Lahiri Sep 27 '20 at 09:19
  • You need to supply different information and a clearer focus before the question "I would like a non-linear model" can be answerable. Little about this summary of a linear model can help anyone determine what, if anything, might be done. – whuber Sep 27 '20 at 13:28
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    @whuber got it. I have edited the question and added more details. I hope that helps clarify the ask. – kms Sep 27 '20 at 13:42

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