Suppose that a population model of a simple linear regression is given by the following In getting an unbiased estimate of 1 for the above model, we are assuming E(u x) 0 When this assumption does not hold, we cannot expect the estimate, 1 , to be close to the true value, 1 , where E(u X) 0 and cal...

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Suppose that a population model of a simple linear regression is given by the following: In getting

Question:

Suppose that a population model of a simple linear regression is given by the following:

In getting an unbiased estimate of β₁ for the above model, we are assuming E(u Ι ƒ x) = 0. When this assumption does not hold, we cannot expect the estimate, β̂₁, to be close to the true value, β₁, where E(u Ι X) ≠ 0 and called this problem omitted variable bias.
a. Define a population regression model with two independent variables in which the estimates are unbiased.
b. Use the ordinary least squares formula to show how the coefficient estimates become bias for the model in part a.