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So I am new to regression and I have a basic doubt:

Let's say I have 100 unique products(product id) which have a lot of other features that contribute in calculating the product_price(dependent variable). Some of the features worth mentioning are Quantity_sold, Region, Supplier etc.

My aim is to calculate the price of each of the product at a

"Product_id, Quantity_sold,Region,Supplier" level

i.e. the ideal output of the predicted price should be as follows:

Product_id Quantity_sold Region Supplier Product_price
1023       25        Texas      AMC      20

Now my question is should i first filter the data for specific product_id, quantity, region,supplier and then run linear regression or should i run the linear regression on the whole data set containing all the product id, quantity,region, supplier.

In case I should run the regression on the entire data set, then should i convert the region(more than 100 unique values), supplier(more than 300 unique values) etc into dummy variables or remove them all together.

This question may sound very novice to you, but I would really appreciate some explanation as to how do we usually go about solving such problems in regression.

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Using a mixed model might be a solution to your problem. It avoids having 400+ dummy variables. A mixed model might also be preferable to dropping the variables Region and Supplier completely, because they probably contain information relevant to the price and therefore create dependencies between observations.

I don't know the size of your dataset and the amount of time you have, but doing individual regressions for every combination of region and supplier seems like overkill to me. However, I don't think you can really avoid having individual models for every product. I imagine their prices behave quite differently. Quantity_sold (or a monotonic transformation) can be modeled as a fixed effect in such a mixed model.

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