I'm attempting to build a model that will fit a trend line/slope to a gradually increasing count of events. I would like to use this model to predict the date at which n events will have occured.
For example:
Day 1 = Total events: 1
Day 2 = Total events: 2
Day 3 = Total events: 5
Day 4 = Total events: 6
Day is the total number of days that have elapsed and Total events is the sum of events that have happened up to that date.
From there I would Eureqa to model the trend or slope of the event accrual line so I can see where it will interesct an arbitrary number of events. In other words, I want to be able to say: "How long will it take for 60 events to have occured?" and I can just look at the slope to see on what day 60 events will take place.
Currently, I've only figured out how to build a target expression with a static prediction interval. For example: y = f(delay(y, 60), days) will tell me the count of events (y) 60 days into the future from the current observation. But I don't need a point prediction on a specific day. Rather, I need a prediction for each day into the future until a certain number of events have transpired. For one project that might be 60 events, for another it might be 10,000