Refer to the Financial Analysts Journal (July/August 2008) comparison of earnings forecasts of buy-side and sell-side analysts, Exercise 12.90. Recall that the professors used regression to model the relative optimism (y) of the analysts' 3-month horizon forecasts as a function of x1 = {1 if the analyst worked for a buy-side firm, 0 if the analyst worked for a sell-side firm} and x2 = number of days between forecast and fiscal year-end (i.e., forecast horizon). Consider the complete second-order model

a. What null hypothesis would you test to determine whether the quadratic terms in the model are statistically useful for predicting relative optimism (y)?
b. Give the complete and reduced models for conducting the test, part a.
c. What null hypothesis would you test to determine whether the interaction terms in the model are statistically useful for predicting relative optimism (y)?
d. Give the complete and reduced models for conducting the test, part c.
e. What null hypothesis would you test to determine whether the dummy variable terms in the model are statistically useful for predicting relative optimism (y)?
f. Give the complete and reduced models for conducting the test, part e.

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E(y) = Bo + Bix1 + Bx2 + Bx1x2 + B4(x2)2 + Bsx1(x2)2