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

y = b0 + b1x + u In getting an unbiased estimate of b1 for the above model, we are assuming E1u ƒ x2 = 0. When this assumption does not hold, we cannot expect the estimate, b n

1, to be close to the true value, b1, where E1u ƒX2 Z 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.

Application Exercises