Circulation: Use Regression Analysis to Optimize Catalog Circ and Sales Data

¥ The standard error of coefficient shows how close the prediction will be.

¥ The T-statistic tells you if the error is large or small. Any number greater than 2 is a good indication of a reliable predictor.

Back to our regression analysis of the discount coupons offered over the course of a year: R-squared on the East Coast is greater than 0.7, so we can assume there’s a good relationship between discounts and new sales. The West Coast comes in at less than 0.7, so we know there’s no correlation; for whatever reason, discounts offered have less impact on generating new sales.

The T-statistic is more than 2 for the East Coast but not for the West Coast, which means any information gathered from coupons from the West Coast can’t be used to determine potential sales increases with future discounts offered. Unknown forces are driving West Coast customers to spend money differently, and discounts have a smaller impact on their purchases.

So the East Coast regression analysis predicts a 5.9 percent increase in sales for every 8 percent discount offered. But on the West Coast, there will be only a 2.1 percent increase in sales for the same amount of discount, which doesn’t make sense at all. Remember, the sales increase averages are almost the same -- 8.89 percent vs. 9.17 percent. What’s wrong?

We’re not optimizing sales on the West Coast. We can’t predict with certainty how customers there will spend. On the other hand, since the increases were fairly similar in both regions (even though the West Coast has no statistical match with the discounts), if we could find out how to improve sales there, then double-digit sales increases should be easily reachable even with minimal discount offerings.

The differences in spending between the two regions could be explained by, for example, customers’ ages, gender, wage brackets, ethnicity or number of catalog mailings by direct competitors. Upon further study, we can determine if we would want to do the following to increase sales on the West Coast: