1. Combining Prediction Intervals

I'm having trouble finding how to combine a number of prediction intervals. The best way to explain the problem is:

Imagine a race with 4 relay runners running a 4x100m. I have different bits of information on how fast each runner can complete various distances which I use to predict how quickly they can run 100m. Each runner has a regression model which predicts their expected finish time and an interval in which I am 95% confident they will finish (the predcition interval). How would I calculate the prediction interval for the finish time of the whole race (ie all 4 runners together)? I have the Standard error of the regression for each runner's model and the standard error of the prediction (so I can calculate each individual prediction interval).

Any help greatly appreciated!

2. You;re looking for a simultaneous CI.Bonferroni's CI's is a simple thing to do

> http://www.itl.nist.gov/div898/handb...on4/prc473.htm

3. Thanks MP83.

I know CIs and PIs are calculated in a very similar way so the Bonferonni test would give a combined PI that was wider than just adding up all the prediction intervals - you're calculating an interval that ensures each separate range is wide enough so that there is only a 5% chance that any of the separate predictions you make from the model are outside your interval.

But - I'm not so interested in the separate predictions, only in the overall prediction, so I want only a 5% chance that my overall prediction is wrong (if some of the separe predictions are outside the 95% range, that doesn't matter).

Intuitively to me I would have thought a combined PI would have a narrower interval than just adding up all the separate intervals - variation in each runner's time would act to 'soften' the impact of any one runner's extremely low (or high) time.

I might have got the logic completely wrong here and happy to be shown the right path!

4. [In short coz my post got lost!]

If you are looking for a CI for a linear combination [average(mu1+mu2+mu3+mu4) for an estimate of the overall time] then you should use the Scheffe method.

You could use one model instead of 4,simply use indicators variables,then say using R,the Scheffe CI is right in front of you...

5. Hi,

I have a similar problem. I predicted a bunch of values using a regression equation and calculated the 95% prediction interval for each observation. Now I want to aggregate/average all of them and calculate the combined prediction interval. I am not sure if the methods mentioned above apply to my problem. Any suggestions?

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