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Statistics, prediction

  1. May 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Given a simple linear model y = B1 + B2*x + e and the least square estimators, we can estimate E(y) for any value of x = x0 as Y0 = b1 + b2*x0

    Describe the difference between predicting y0 and estimating E(y0)
    2. Relevant equations



    3. The attempt at a solution

    I am not sure what the difference is.

    Prediction:
    Y= b1 + b2*x0

    f = y0 - Y0 = (B1 +B2*x0 + e0) - (b1 + b2*x0)

    E(f) = 0

    and var(f) = sigma2*(1 + 1/N + (x0 - [tex]\bar{x}[/tex])2/sum(xi - [tex]\bar{}x[/tex])2

    where [tex]\bar{}x[/tex] is the average.

    the prediction interval is Y0 +- tc*se(f)

    where se is the standard error of the forcast.

    Can anyone help me with estimating E(y0)?
     
  2. jcsd
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