# Statistical tests on the revenue data of a small business

I have daily revenue data from a small business with 6 locations. The business sells food products that range from roughly \$2.00 to \$9.00, mainly to professionals. They do over a million dollars a year in sales and are located in a major North American city (scattered around the downtown core / business district). The revenue data contains what is sold at each location on any given day. The daily revenue data spans the duration that a given location has been in operation. The longest being five years and the shortest being two years.

There are some questions I wish to answer, for example:

1. How sensitive are sales to macroeconomic events?
2. Do sales have seasonal patterns?
3. What factors/characteristics influence a given location's sales?
4. Do different locations exhibit the same patterns of sales growth?
5. What are the demand elasticities of different products?
6. What endogenously determined "events" have occurred that have resulted in an increase in sales? (A promotion, for example)

Here are some ideas of how to answer the above questions:

1. See if positive or negative macroeconomic demand shocks show up in the daily revenue time-series. Or, define some macroeconomic "event" (like a sharp decline in the stock market) and check for abnormal changes (decreases) in revenues.
2. Look for seasonal fluctuations around some trend line of sales.
3. Identify differences in characteristics between locations and run multiple variable regressions on the sales data. For instance, have a dummy variable for the presence of a government office within 100m of a given location, or a similarly branded competitor within 100m, et cetera. Then test the hypothesis that each variable has a coefficient of zero. (Note: possibly use this to predict the future revenue of a potential location)
4. Compare the "shape" of the growth in sales between different locations.
5. Determine if the sales of a given product change after a price increase. Do this for each increase in price, being careful to identify if other factors may have contributed to the change in demand.
6. Define some "event" and look for changes in revenue around this event.

Further, I suppose it would be helpful to "clean" the data depending on what I am using it for. I might find that one location had an initial rate of growth in income that was far higher than other locations, but that it opened just prior to a typically high-sales season and also a positive macroeconomic event. The same goes for an increase in sales after a promotion. I would not want to mix up endogenous and exogenous changes in revenue.

I am hoping for some input on what meaningful conclusions I can actually draw given the data set. I've arrived at my ideas from brainstorming and I'm sure they are very flawed. I've just finished third year economics with some extra math and stats thrown in. I'm doing this because the data is available to me and I want to (try and) use some of the tools I've learned.

Questions:

• In terms of identifying differences between locations, is six locations too few?
• In general, what statistical pitfalls will I run into?
• Should I not do this because there is nothing meaningful to be found in this data?
• Are there any statistical tests I should do that will yield meaningful results (i.e any questions I can actually answer given the data set)?
• Six locations isn't too few if you're interested in those six locations. – Scortchi - Reinstate Monica May 6 '13 at 2:55
• Because I'm not worried about a sample size, I am looking at a population? – nervous_student May 6 '13 at 3:02
• Yes, it's only a consideration for things like point #3. – Scortchi - Reinstate Monica May 6 '13 at 3:07