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Unbiased Slope Estimate

  1. Mar 8, 2013 #1
    1. The problem statement, all variables and given/known data

    There is the suggestion to use an alternative estimate for the slope $$\beta$$ in the linear regression $$y_i=\alpha+\beta x_i+\epsilon_i$$which is formulated as $$B=(y_{max} -y_{min})/(x_{max} - x_{min})$$

    Prove that such a formulation of $$B$$ is unbiased.

    2. Relevant equations



    3. The attempt at a solution

    I'm actually having a very hard time with this problem and would appreciate the slightest nudge in the right direction. Can anyone assist me with this problem?
     
  2. jcsd
  3. Mar 8, 2013 #2

    Ray Vickson

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    When you write ##y_{\min}##, etc., do you mean the ##y## value that accompanies ##x_{\min}## (that is, ##y_{\min} = f(x_{\min})##) or are ##x_{\min}## and ##y_{\min}## unrelated, each being the min in its own data set?
     
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