Root causes of error in a forecast consisting of two multiplicative factors I have a warehouse that packages units and ships them. Any number of units can go into the same package, including only 1 unit. I have a forecast for number of units and units per package (UPP). From it, I calculate the total number of expected packages I will ship. 
As the forecast and actuals vary each week, when the expected number of packages differs from actual packages shipped, how do I determine how much blame to put on each of the two forecasts? Obviously, if one forecast has 0% error, then the other forecast is 100% to blame. But when they both have error, then I get stuck. 
Sample data:
150 = Units Forecast
100 = Units Actual
2 = UPP Forecast
2.5 = UPP Actual
75 = Packages Forecast (calcuated, Units Forecast / UPP Forecast)
40 = Packages Actual (calculated, Units Actual / UPP Actual)

Here's a google sheet with the sample data. Please feel free to add answers to it.

 A: One simple way would be to look it like this:


*

*Your current absolute forecast error is $|100-150| = 50$.

*If your UPP forecast had been perfect (but not the packages forecast), then your absolute error would have been $|100-2.5\times 75| = 87.5$.

*If your packages forecast had been perfect (but not the UPP forecast), then your absolute error would have been $|100-2\times 40| = 20$.


Thus, improving the packages forecast would improve your total forecast, whereas improving the UPP forecast (and leaving the packages forecast unchanged) would actually make the forecast worse. This suggests to me that the packages forecast should be worked on to be improved, which could also be formulated as "the packages forecast is more to be blamed".

Alternatively, you could look at each component's absolute percentage error, which is $\frac{|2-2.5|}{2.5}=20\%$ for the UPP and $\frac{|40-75|}{40}=87.5\%$ for the packages forecast, so the UPP forecast is more precise. So both ways of looking at this yield the same answer in this case, although this is probably not guaranteed to hold in general.
(However, percentage errors have the effect of penalizing overforecasts more strongly than underforecasts, so use with caution. The MAPE tag wiki has more information.)
