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I'm trying to build a model to understand units purchased over time for a product whose price changes frequently. Would it be possible to use a multivariate regression where short term week over week elasticity is the dependent variable and seasons and holidays are the independent, to see change in price elasticity given certain periods of the year?

Further, if there were multiple products that I wanted to group together, would I need a separate regression model per product, or would the average week over week elasticity work as dependent?

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