Using the ANOVA table given in Problem 8 of Chapter 9, which deals with the regression relationship of 12th-grade mean verbal SAT scores (Y) to per pupil expenditures (X1), percentage of teachers with advanced degrees (X2), and pupil-teacher ratio (X3), test the following null hypotheses:
a. H0: pYX3|X1 = 0
b. H0: PYX2|X1,X3 = 0
c. H0: pY(X2,X3)|X1= 0
d. Based on these results, and assuming that X1 is an important predictor of Y, what additional variables would you include in your regression model?