The correlation matrix obtained for the variables SBP (Y), AGE (X1), SMK (X2), and QUET (X3), using the data from Problem 2 in Chapter 5, is given by

a. Based on this matrix, which of the independent variables AGE, SMK, and QUET explains the largest proportion of the total variation in the dependent variable SBP?
b. Using the available computer outputs, determine the partial correlations rSBP, SMK|AGE and rSBP, QUET|AGE.
c. Test for the significance of rSBP, SMK|AGE using the ANOVA results given in Problem 1 of Chapter 8. Express the appropriate null hypothesis in terms of a population partial correlation coefficient.

d. Determine the second-order partial rSBP, QUET|AGE, SMK, and test for the significance of this partial correlation (again, using the computer output here and in Chapter 8, Problem 1).
e. Based on the results you obtained in parts (a) through (d), how would you rank the independent variables in terms of their importance in predicting Y? Which of these variables are relatively unimportant?
f. Compute the squared multiple partial correlation r2SBP(QUET, SMK)|AGE using the output here and in Problem 1 of Chapter 8. Test for the significance of this correlation. Does this test result alter your decision in part (e) about which variables to include in the regression model?