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Apply Bartlett's test to the data of Table 11.1 and verify that the hypothesis that population variances of employee compensation are the same in each employment size of the establishment cannot be rejected at the 5 percent level of significance.

Note: fi, the df for each sample variance, is 9, since ni for each sample (i.e., employment class) is 10.

11.14. Consider the following regression-through-the origin model:

You are told that u1 ~ N(0, o2) and u2 ~ N(0, 2o2) and that they are statistically independent. If X\ = +1 and X2 = -1, obtain the weighted least-squares (WLS) estimate of / and its variance. If in this situation you had assumed incorrectly that the two error variances are the same (say, equal to o2), what would be the OLS estimator of /? And its variance? Compare these estimates with the estimates obtained by the method of WLS? What general conclusion do you draw?1'

11.15. Table 11.7 gives data on 81 cars about MPG (average miles per gallons), HP (engine horsepower), VOL (cubic feet of cab space), SP (top speed, miles per hour), and WT (vehicle weight in 100 lb).

See "Properties of Sufficiency and Statistical Tests," Proceedings of the Royal Society of London A, vol. 160, 1937, p. 268.

^Adapted from F. A. F. Seber, Linear Regression Analysis, John Wiley & Sons, New York, 1977, p. 64.

CHAPTER ELEVEN: HETEROSCEDASTICITY 433

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