I'm want to show that a customer who buys paper books is more likely to buy an e-reader than a customer who does not buy paper books. Note that the number of e-readers purchased in the past is small (1,000) compared to the total set of events (1,000,000).
Here's the historical data that I have:
Customer Name | Month | Purchased Books in Last Month | Purchased Books in Last 12 Months | Purchased Books in Last 3 Years | Purchased Book this Month | Purchased e-Reader this Month Joe Smith | 1/12 | 0 | 0 | 0 | 1 | 0 Joe Smith | 2/12 | 1 | 1 | 1 | 0 | 0 Joe Smith | 3/12 | 0 | 1 | 1 | 0 | 1 ...
Using these historical data, I'd like to demonstrate that book-buyers are more likely to buy e-readers, especially if they have recently purchased a book.
When I do a linear regression on the binary events for "Purchased Books in Last 12 Months" and "Purchased e-Reader this Month", I get r < 0.1.
However, if I compare P(purchased e-reader) to P(purchased e-reader | purchased books in last 12 months), the probability of a previous-book-buyer purchasing an e-reader is 10x higher than a random customer purchasing an e-reader
How do I reconcile these two results? Am I using the right tools to answer this question with confidence?