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Math Help - Confidence band help please

  1. #1
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    Confidence band help please

    Can anybody explain why confidence bands are closer to the mean in the middle that at the ends?
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  2. #2
    MHF Contributor matheagle's Avatar
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    You can see that in the formulas, but it does make sense.
    We have more information near the sample mean, than at x values far from \bar X.
    For example if x is the age of a person when they can perform some task, then x=0 doesn't make any sense.
    Hence a regression line of y(x) really is usless at x=0, but we do want an intercept in our model.
    That way we are not forced to go through the origin.
    BUT analyzing y at x=0 is pointless, so having a larger variance at x at 0 than at x=\bar x makes sense.

    Look at http://www.weibull.com/DOEWeb/confid...regression.htm
    when we set x_-i=\bar x the variance term is minimized.
    Likewise in the predition intervals
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