I have a problem right now at work. For certain business segments, some sales target are established each year. These targets are established based on the managers feelings. It's like this:
Manager: "so we grew 10% last year"
Employee: "yes, economic conditions where good"
Manager: "ok I feel this year we can grow 8%"
I'm currently analysing if this forecast tends to be too low and if that is one of the reason why managers tend to grow a lot more than initial target.
But when I showed that we are getting marks 130% over target on average. Managers just says it was because those years economic conditions where much more favorable than what they expected when the target was set. Which is kind of true, but that doesn't necessarily mean over performance is strictly cause favorable economic conditions. How could prove if this is true, what model could I use to try to isolate the effect of economic growth on sales target? I already try to explain variability on target growth using time series (ARIMA model). And economic inputs tend to be significant and tend to have positive significant parameters but what does this tell me?
How can I explain variability in target result in one year based on economic variability? If I can say that only a small part of target variability is explained by variability on economic growth I could argue that target might be too low. But how do I implement this analysis. It sound like I'm looking for some kind of R squared but I'm not sure how to make it from time series data.