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I am working on a project to try understand Linear Regression a bit deeper (they say experimenting is key and getting lost is part of the process) :(

In this project, let's assume I have a watch shop. I want to calculate price elasticity of demand for my watches but how do I setup the data as in my mind there are two options:

  1. I have 100 watch styles and each have their own prices and quantity sold for a period of time, so the first setup looks like:
Watch Styles Price Quantity
Style 1 900 10
Style 2 1500 20
Style 3 1000 30
... ... ...
Style 100 2000 50
  1. Alternatively, I can set my data as a transactional time series (monthly for 2 years worth of data). Now the 'price' variable will be the average unit price of watches sold per month and 'quantity' will be the aggregated monthly figure.
Month Avg Price per Month Quantity
April 2019 1225 110
May 2019 1135 150
June 2019 1575 75
... ... ...
April 2021 2050 15

Which data setup is appropriate to run the regression analysis and why?

$$ ln(Quantity) = c + \beta\ ln(Price) + Error $$

After reading some marketing research papers, it looks like the setup using (2) is favored for elasticity calculation. So how do we interpret the regression results if we use (1) instead?

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  • $\begingroup$ What do you mean by "price elasticity of demand"? $\endgroup$
    – Harry
    May 12, 2021 at 10:11
  • $\begingroup$ Hi @Harry, Price elasticity of demand as in the measurement of the change in consumption of a product in relation to a change in its price $\endgroup$
    – umm
    May 12, 2021 at 13:24
  • $\begingroup$ Ok, that makes sense. In your first table you sold 10 "Style 1" for 900 each. Did you sell all of the "style 1" watches for 900? If so I don't see how you could calculate price elasticity. They all sold for the same price... In table 1 the variation in the number sold could have just as much to do with the style as the as the price. In your example should each style actually have multiple price points at which it is being sold, or if not, are you assuming that the style of watch has no influence on the price (seems a rather big assumption)? $\endgroup$
    – Harry
    May 12, 2021 at 21:33
  • $\begingroup$ Right.. so to your point, I could run regression with (1), however i need to incorporate a change in price (and quantity) into the data. Would it work if I change the data table in (1) to the following? Watch Styles | Price difference between Year 1 and 2 | Quantity Difference between Year 1 and 2 $\endgroup$
    – umm
    May 13, 2021 at 1:49
  • $\begingroup$ So now the regression equation using (1) becomes ln(Quantity difference between year 1 and 2) = c + beta * ln (price difference between yr 1 and 2) + error $\endgroup$
    – umm
    May 13, 2021 at 1:51

1 Answer 1

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I think you should be working out the price elasticity of one style of watch. If you look at multiple styles of watches you wouldn't be using linear regression.

I would set my data up to look something like this (but obviously include more weeks/months/years):

enter image description here

There's more information on this here:

https://www.statworx.com/de/blog/food-for-regression-using-sales-data-to-identify-price-elasticity/

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  • $\begingroup$ this is a great resource, thank you. Just a small observation, looks like a randomized price is used in the blog so i think i can follow suit and use model (2) with average price of all watches in that month as the 2nd column and sum of monthly quantity in 3rd column. Although im still unclear why we can't use (1) with price difference between year (1) and (2) in 2nd column and quantity difference between year (1) and (2) in 3rd column :( $\endgroup$
    – umm
    May 14, 2021 at 19:27

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