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?

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SBP AGE SMK QUET BP 1 0.7752 0.2473 0.7420] AGE 0.7752 SMK 0.2473 -0.1395 QUET 0.7420 0.8028 0.0714 10.1395 0.8028 10.0714 Regression of SBP on AGE and SMK PARAMETER ESTIMATES Squared Partial Squared Partial Parameter Standard Error t Value PrCor Type 1 Corr Type II Variable DF Estimate Intercept AGE SMK 48.04960 11.12956 4.32 0.0002 1.70916 0.20176 847 0.60094 0.7 1220 1 10.29439 276811 3.72 000090.32290.32291 Regression of SBP on AGE and QUET PARAMETER ESTIMATES Squared Partial Squared Partial Parameter Standard Variable Intercept AGE QUET DF Estimate Error t Value PrCorr Type ! Corm Type I 55.32344 12.53475 441 0.0001 04516 0.38606 271 0.0113 975073 5.40246 0.60094 1.80 0.0815 010099 0 20175 0.10099 Regression of SBP on AGE, SMK, and QUET PARAMETER ESTIMATES Squared Partial Squared Partial Parameter Standard DF Estimate Error t Value Pr> 10.76488 Corr Type Corr Typell Variable Intorcept AGE SMK QUET 45.10319 1.21271 9.94557 8.59245 4.19 0.0003 0.32382 3.75 0.0008 3.74 0.0008 1.91 0.0664 0.80094 0.32291 0.11527 0.33373 033367 011527 2.65606 4.49868