Consider the two regression models (i) y = beta_0 + beta_1 X_1 + beta_2 X_2 + u

Question

Consider the two regression models (i) y = beta_0 + beta_1 X_1 + beta_2 X_2 + u (ii) y = gamma_0 + gamma_1 Z_1 + gamma_2 Z_2 + upsilon, where variables Z_1 and Z_2 are distinct from X_1 and X_2. Assume u ~ N(0, sigma_u^2) and upsilon ~ N(0, sigma_upsilon^2) and the models are estimated using ordinary least squares. If the true model is (i) then which of the following is true? (a) E[beta_1] = E[gamma_1] = beta_1 and E[sigma_upsilon^2] = sigma_u^2. (b) E[sigma_upsilon^2] greaterthanorequalto sigma_upsilon^2. (c) E[sigma_upsilon^2] lessthanorequalto sigma_u^2. (d) None of the above as the two models cannot be compared

Explanation / Answer

d part is correct

beacuse both models are different...

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