Page 743 -

742 Chapter 17 The Theory of Linear Regression with One Regressor

MyEconLab Can Help You Get a Better Grade

MyEconLab If your exam were tomorrow, would you be ready? For each chapter,

MyEconLab Practice Tests and Study Plan help you prepare for your exams.
You can also find similar Exercises and Review the Concepts Questions now in MyEconLab.
To see how it works, turn to the MyEconLab spread on pages 2 and 3 of this book and then go to
www.myeconlab.com.
For additional Empirical Exercises and Data Sets, log on to the Companion Website at
www.pearsonglobaleditions.com/Stock_Watson.

Review the Concepts

17.1 Suppose that Assumption #4 in Key Concept 17.1 is true, but you
construct a 95% confidence interval for b1 using the heteroskedastic-
robust standard error in a large sample. Would this confidence interval
be valid asymptotically in the sense that it contained the true value of
b1 in 95% of all repeated samples for large n? Suppose instead that
Assumption #4 in Key Concept 17.1 is false, but you construct a 95%
confidence interval for b1 using the homoskedasticity-only standard
error formula in a large sample. Would this confidence interval be
valid asymptotically?

17.2 Suppose that An is a sequence of random variables that converges in
probability to 3. Suppose that Bn is a sequence of random variables that
converges in distribution to a standard normal. What is the asymptotic dis-
tribution of AnBn? Use this asymptotic distribution to compute an approxi-
mate value of Pr(AnBn < 2).

17.3 Suppose that Y and X are related by the regression Y = 1.0 + 2.0X + u.
A researcher has observations on Y and X, where 0 … X … 20, where

the conditional variance is var(ui 0 Xi = x) = 1 for 0 … x … 10 and
var(ui 0 Xi = x) = 16 for 10 6 x … 20. Draw a hypothetical scatterplot

of the observations (Xi, Yi), i = 1, c, n. Does WLS put more weight on
observations with x … 10 or x 7 10? Why?

17.4 Instead of using WLS, the researcher in the previous problem decides to
compute the OLS estimator using only the observations for which x … 10,
then using only the observations for which x 7 10, and then using the
average the two OLS of estimators. Is this estimator more efficient than
WLS?