Unbiased Slope Estimate in Linear Regression

[TranscendArcu]

Homework Statement

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.

Homework Equations

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?

 

[Ray Vickson]

Homework Statement

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.

Homework Equations

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?

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?