Statistical Problem MV Analysis

[Ender]

To elaborate a bit more on the subject. Yes, this is not a hypothetical case but a real life experiment. The experimental design is as follows:
The price of a product is sampled in 2 regions based on its UPC and from the same chain store operating in both regions to eliminate store differences. Other product prices are sampled in a similar fashion. There are no multiple samples of the same product, meaning that for any product, there are only 2 prices.
The hypothesis is that the price differential is a function of the price of the product, store pricing policy, origin of distribution of the product, the product type (consumable or non-consumable), and the product classification (i.e., food and beverages, clothing and apparel, etc.).
I guess the simplest way would be to undertake a uni-variate analysis of each variable independently. I am wondering whether there is a better approach that is more succinct and illustrative at the same time, capturing the effects of all the variables in one go. Thanks again.