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I'm trying to create a regression model for a dynamic pricing system that looks to maximize revenue. The problem that I'm having is that the system in place before (which is the source of my data) involved the owner deciding where to price things based on his own personal expectations of demand. Thus, when trying to tease out any sort of relationship between price and demand, I end up getting that a higher price = more demand, which is obviously not the case. Is there any way to correct for this, or is the data essentially useless to me?

So far I've looked into instrumental variables, but I'm not sure that I have anything that would work for my situation.

EDIT: Here's a link to some data

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  • $\begingroup$ perhaps you are not teasing it out correctly. Please post your data and I will try and tease it out using comprehensive time series methods/software. $\endgroup$
    – IrishStat
    Aug 2, 2014 at 14:21
  • $\begingroup$ Your data is as I suspected time series data. Time series analysis requires that data be available every day. If price didn't change that's ok just include price and demand for every day. If holidays caused no demand simply report 0 demand and the prior day's price. Please correct your data and let me know. $\endgroup$
    – IrishStat
    Aug 3, 2014 at 19:42
  • $\begingroup$ There actually isn't data for every day, those are the only days that the item in question was available to be purchased. $\endgroup$ Aug 3, 2014 at 20:53

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The short answer is that a thorough analysis of your data suggests a positive impact due to price. enter image description here where for every $ increase in price demand is expected to increase by 17.5 units. This result could reflect an omitted variable e.g. a competing product's price became much higher thus shifting demand to your product even though the price was "high". A simple OLS solution for your data which ignores day effects and night\day effects and increased changes in demand (around 6/2/13 ) would suggest a coefficient of 31.2 enter image description here . We normally see demand/price data where sales are made every day save some holidays thus we can tease out specific-day-of-the=week,week-of=the-month, patterns around known events, level shifts , weekly effects, monthly effects etc. and lagged responses to price changes and even lead responses to future price changes. Your data is of course intermittent and is not totally amenable to all of the high-powered functionality of AUTOBOX a piece of software that I have helped develop.

In closing you delivered 217 observations with one blank day (7/4/13). Using 216 days AUTOBOX detected a level shift at 6/2/13 and a number of very unusual days

4/3/13,4/2/14,7/22/14,4/25/12,5/4/12,5/5/12,5/6/12 in addition to a day/night effect and a day type effect.

I hope this helps you. IF you wish to communicate specifically about the anything you can either respond here or contact me .

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  • $\begingroup$ The product is ticket sales, so it's essentially a monopoly. There is also a ceiling on how much can be sold. The issue of course is that in the summer months and on weekends the demand shifts upward dramatically. Because the owner knew this, he would move the price up in accordance with the shift in demand, and the tickets would still sell out much like they would on less attractive days with lower prices. $\endgroup$ Aug 3, 2014 at 23:34

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