As a work assignment, I've been asked to determine the optimal SKU count for a product group. I've decided to tackle this Q using a simple linear regression with sales as my dependent variable and the # of SKUs and the # of SKUs squared as my independent variables. My data set is a cross section of store sales and SKU counts for each store.

Trouble arises when I run the regression and get positive coefficients for both # of SKUs and # of SKUs squared (I think diminishing returns are identified by a negative coefficient for the squared variable). I suspect that sales for larger stores are proportionally higher than # of SKUs compared to smaller stores and maybe this is why my coefficient doesn't make sense.

I'm looking for suggestions on either model specification or ways to standardize stores (if that's the solution). My data set has about 600 stores and I thought about restricting the group by store size but similarly sized stores also generally have the same number of SKUs.

I also thought about using a time series, but my yearly data only goes back a decade or so. I'm also inexperienced in this area, and would be concerned I wouldn't model it properly.

Thanks for any advice.


  • $\begingroup$ Have you considered running a Poisson model for sales with a robust variance-covariance matrix, with store size as an offset? $\endgroup$ – Dimitriy V. Masterov Jun 24 '14 at 0:42
  • $\begingroup$ If I were doing this, I would use a different tool. I would have as inputs the store, each sku, the price for each sku, and the quantity of sales for each sku (yes this might be 10's or hundreds of thousands of columns. I would have as output the total sales for the store. I would use a random forest to fit the inputs to the outputs. When I got a fair fit, then I would deconstruct the random forest to get importance rating for the variables. This would allow me to nuke 99.5% of the columns, and to make a much cleaner non-CART model. $\endgroup$ – EngrStudent Jun 24 '14 at 0:46

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