# How can I set a multiple regression model to find out the correlation between store position and sales?

I need to calculate the inherent quality for every sales position inside a retail store. A sales position is a piece of furniture that holds multiple products on display for customers. Given that every product has a different inherent attractiveness, I need to set up data entry and a regression model that will enable me to calculate the inherent quality of each sales position.

I will make the simplest possible example so that it is clear what I mean by that. Let's say that we have 2 sales positions:

• A: inherent quality of 0.8 (this is the value we need to calculate and don't have a priori)
• B: inherent quality of 0.5

Let's also say we have 4 products:

• P1: inherent quality of 1000 (this is a value that we don't have a priori but we can use the proxy of total revenue of the product per week, after the season is over)
• P2: inherent quality of 2000
• P3: inherent quality of 3000
• P4: inherent quality of 4000

If we set our sales positions like this in the first week:

• A: P1 and P2
• B: P3 and P4

we expect the total revenue per position to be:

• A: 0.8 * (1000 + 2000) = 2400
• B: 0.5 * (3000 + 4000) = 3500

If we set the sales in the second week like this:

• A: P3 and P4
• B: P1 and P2

we expect the total revenue per position to be:

• A: 0.8 * (3000 + 4000) = 5600
• B: 0.5 * (1000 + 2000) = 1500

In the real world, we will have perhaps 14 to 20 weeks of data per product.

Now, I need to set a multiple regression model to determine the quality of each sales position but I am not sure how to do this. Also, I have the freedom to set the positions of the products in the store every week but bear in mind that setting them randomly will incur large costs because of foregone revenue so it would be best if I could just collect the data as is and do my calculations from there. This would be especially costly if this was done for multiple weeks.