I have around 20 products with 30 monthly observations for each that I need to analyze.

I have data on demand, normal price, discount in percent, as well as some categorical variables but we can disregard these categorical variables for now.

I want to understand for example how much a discount effect sales, per product, and find the products with the highest beta for this so that I know which products are suitable to discount and which ones that are not. The problem is however the low sample size. 30 observations, and discount is 0 for around 20 of the 30 weeks.

In order to solve this a friend of mine told me that i could just run a regression with all products at the same time, and separate them by using a dummy variable for each one. But, after reading up on this method, I realized that these dummies will then only change the Y intercept for each product, and not the slopes for the % discount. This is a major issue as I am certain that the slopes are very different for each product..

So, anyone out there that can help me and tell me if there is a way to solve my problem?

THANKS!