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11.20.      Table 11.8 gives data on median salaries of full professors in statistics in research universities in the United States for the academic year 2000–2001.
a.   Plot median salaries against years in rank (as a measure of years of experience). For the plotting purposes, assume that the median salaries refer to the midpoint of years in rank. Thus, the salary
$74,050 in the range 4–5 refers to 4.5 years in the rank, and so on. For the last group, assume that the range is 33–35.
b.   Consider the following regression models:
Yi   = α1 + α2 Xi  + ui                                                                                 (1)
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|
Yi   = β1 + β2 Xi  + β3 X2 + νi                                                                       (2)
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where Y = median salary, X = year in rank (measured at midpoint of the range), and u and v are the error terms. Can you argue why model
(2) might be preferable to model (1)? From the data given, estimate both the models.
c.   If you observe heteroscedasticity in model (1) but not in model (2), what conclusion would you draw? Show the necessary computations.
d.    If heteroscedasticity is observed in model (2), how would you trans- form the data so that in the transformed model there is no het- eroscedasticity?
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