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Math Help - Confidence and prediction intervals

  1. #1
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    Confidence and prediction intervals

    If we have an extremely large sample, 95% and 99% confidence
    intervals for the mean response will be very narrow indeed. Discuss
    whether, in the same situation, it also becomes possible to do very
    accurate predictions of individual values that is, to obtain very
    narrow prediction intervals.

    (Hint: the amount of random variation associated with individual
    values does not change as information on other individuals becomes
    available.)

    Please can anyone help me answer this??
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  2. #2
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    Re: Confidence and prediction intervals

    In order for larger sample populations to reduce the variance of the sample mean you have to make the assumption that members of the population are independent. Thus the conditional distribution of any parameters you might be interested in about the individual is equal to their unconditional distribution. Information about the rest of the sample population provides no information about that individual.
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  3. #3
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    Re: Confidence and prediction intervals

    Thanks for replying! But I still don't know if it's possible to obtain very narrow prediction intervals? Please help!
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  4. #4
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    Re: Confidence and prediction intervals

    After reading up on this some I see I didn't understand the question.

    Ok. How tight your prediction interval can be is dependent on the population distribution.

    As N increases you can get very tight estimates of say the mean and variance of your population distribution but that won't help you get tight prediction intervals if the underlying population variance is large.
    Last edited by romsek; March 7th 2014 at 01:40 AM.
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