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I work for a company that sells a small portfolio of products - we'll call them toasters. These toasters vary in quality and price, but all of them will toast your food.

We have historic data on our toaster prices, quality, and sales. We had some periods where we were selling only 1 toaster, and other periods where we were selling up to 4 at a time. We'd like to see if there's a way to model the underlying demand for price/quality of toasters.

We want to answer questions like: if we launch a new toaster that's a 7/10 on the quality scale, and priced at $26.99, how many sales can we expect? What will that do to sales of our other toasters?

Obviously, this is somewhat related to a marketing mix model, but not really the same. We've also thought about simply creating some summary variables about our products and our product portfolio (e.g., ratio of device A's price to average price, current size of portfolio, etc) to get at this. Is there a better way?

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Not sure if this question is still relevant to you or not, but luckily, I think there's a simple solution which involves the use of a technique called panel regression which is used when the question involves modeling data for various products across time. It takes into account the time variant effects (things that change over time, such as trends and seasonality, price, etc.), and at the same time, it takes care of time independent effects (things not influenced by the passing of time, such as different SKUs).

Do you have experience with statistical modeling techniques? If so, I would first build a table with your data that looks something like this (we'll keep it simple to start):

Column names: SKU#, time, sales, price, quality

There's likely other variables influencing your toaster sales, so you'll want to build in variables which control for those factors too, eventually.

Time should be something like a trend or something countable which increments up by 1 each period (if you think there's a linear trend to your sales growth). If it's something related to seasons, try adding monthly average weather to the model.

I'm not sure what statistical software your company uses, but mine uses STATA. An application most analysts I've encountered have never heard of, unfortunately. Before you run your model, you just have to set what your panels are (time independent variable). In your case, it would be SKU#.

But when we run our model used to answer a question very similar to this (predict sales), based on time influenced factors, and other factors unaffected by time, the output (coefficient) for our price variable, which has been cleansed of any influence from other factors included in the model, would state something like: "For every 1 dollar change in price, sales increase by x dollars"; likewise for the quality variable.

Essentially, what this model does is this case is produce clean estimates of the variables included in the model, while controlling for the effect of the product (think of it as controlling for the naturally high/low baseline sales levels of each of the SKUs in your data so that you don't end up with messy results in the case that a certain popular SKU has really high sales, but is around the same price as another less popular brand (with equal quality)).

We're also doing something similar at my company, which I find very exciting/interesting.

Hope this helps.

Cheers.

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