In the "Regression to the Mean" chapter of "Thinking, Fast and Slow" by Daniel Kahneman, an example is given and the reader is asked to forecast the sales of individual stores given the overall sales forecast and the sales numbers from the previous year. For instance(the book's example has 4 stores, I use 2 here for simplicity):
Store 2011 2012 1 100 ? 2 500 ? Total 600 660
The naive forecast would be 110 and 550 for stores 1 and 2, 10% increase for each. However, the author claims this naive approach is wrong. It is more likely for the poorer-performing store to increase more than 10%, and the better-performing store to increase(or even decrease) by less than 10%. So perhaps a forecast of 115(15% increase) and 535(7% increase) would be "more correct" than the naive forecast.
What I don't understand is how we can conclude that sales of 100 of store 1 is necessarily the poorer-performing store? Perhaps, due to location differences, the true time-series means of stores 1 and 2 are 10 and 550, and store 1 had a super year in 2011, and store 2 had a disastrous year in 2011. Then wouldn't it make sense to forecast a decrease for store 1 and increase for store 2?
I know that time series information was not given in the original example, but I am under the impression that "regression to the mean" refers to the cross-sectional mean and therefore time-series information does not matter. What am I misunderstanding?