Assume that the regression model Yi = b0 + b1Xi + ui satisfi
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Assume that the regression model Yi = b0 + b1Xi + ui satisfies the least squares assumptions in Key Concept 4.3 in Secti
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Assume that the regression model Yi = b0 + b1Xi + ui satisfies the least squares assumptions in Key Concept 4.3 in Section 4.4. You and a friend collect a random sample of 300 observations on Y and X. a. Your friend reports the he inadvertently scrambled the X observations for 20% of the sample. For these scrambled observations, the value of X does not correspond to Xi for the i th observation; rather, it corresponds to the value of X for some other observation. In the notation of Section 9.2, the measured value of the regressor, X ? i, is equal to Xi for 80% of the observations, but it is equal to a randomly selected Xj for the remaining 20% of the observations. You regress Yi on X ? i. Show that E(bn 1) = 0.8b1. b. Explain how you could construct an unbiased estimate of b1 using the OLS estimator in (a). c. Suppose now that your friend tells you that the X
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