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Regression Model Estimator

  1. Feb 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Assume regression model [itex]y_i = \alpha + \beta x_i + \epsilon_i[/itex] with [itex]E[\epsilon_i] = 0, E[\epsilon^2] = \sigma^2, E[\epsilon_i \epsilon_j] = 0[/itex] where [itex]i \ne j[/itex]. Suppose that we are given data in deviations from sample means.

    If we regress [itex](y_i-\bar{y})[/itex] on [itex](x_i-\bar{x})[/itex] without a constant term, what is the expected value of the least squares estimator of the slope coefficient?

    2. Relevant equations

    3. The attempt at a solution
    I was thinking I could start with [itex]S(\beta)=\Sigma (y_i-x_i \beta)^2[/itex] and replace y and x with [itex](y_i-\bar{y})[/itex] and [itex](x_i-\bar{x})[/itex] and then take FOC to get the estimator.
  2. jcsd
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