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Statistics, regression model, unbiased estimator help

  1. Oct 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Professor E.Z.Stuff has decided that the least squares estimator is too much trouble. Noting that two points determine a line, Dr. Stuff chooses two points from a sample of size N and draws a line between them, calling the slope of this line the E.Z. estimator of beta1 in the simple regression model. Algebraically, if the two points are (x1, y1) and (x2, y2 ) , the E.Z. estimation rule is beta1=(y2-y1)/(x2-x1)

    I need to show:
    (1) Show that beta1
    EZ is an unbiased estimator.
    To show this the lecturer said we need to calculate the mean: E(( beta0+beta1*xN+ epsilonN-(beta0 +beta1*x1+epsilon1))/(xN-x1), and this should be equal to beta1. How to do it?

    (2) Find the probability distribution of beta1
    EZ .
    To show this we need to show that a*epsilonN + b*epsilon1~N(..,..) Normal distribution and calculate the mean value and the dispersion. But i don't know how.
    Can someone help me?
     
  2. jcsd
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