Questions 8

  1. Show that estimator {$s^2$} is unbiased
  2. Prove that {$s^2(X'X)^{-1}$} is unbiased estimator of {$Var(b)$}
  3. Give the form o estimator of linear combination of parameters {$\delta'\beta$} and show that it is unbiased
  4. What do we mean by prediction? Show that prediction {$x_f b$} is unbiased
  5. Explain what are two sources of prediction error and give the formula for the variance of prediction error.
  6. (*) Derive the formula for the variance of prediction error
  7. Derive the distribution of the OLS estimator. What additional assumption do we have to make over assumptions of CLRM to make this derivation?