I own a software business that follows a common pattern: Interested people can download the software and try it free for 30 days, and if they like it, they can buy it at any time during those 30 days (or after). I'd like to calculate my "conversion rate," which I will define as the percentage of downloads that lead to sales within 30 days.
I don't track individual users, so I have no way of knowing whether downloader X ever ended up buying. I do, however, have time series data for the number of downloads each day and the number of sales each day. I have this data going back several years.
I would like to be able to do any of a few things with this information: 1. Compare this rate to a similar time period last year. 2. Determine whether the rate is generally increasing or decreasing. 3. Predict what the next X days sales might look like based on the last X days downloads.
Given that information and those goals, is it possible to determine (or at least approximate), a useful conversion rate? If so, how is it done?
(I'm a programmer who had one intro stats class in college, which was mostly about the probability of rolling dice. Answers that explain it like I'm 5 would be greatly appreciated)