Refer to the following ANOVA tables and to SAS output given here (from data in Problem 8 of Chapter 8) to answer the following questions dealing with factors related to soil erosion.
a. Using the accompanying SAS output, compute rYX2|X1 and rYX3|X1.
b. Based on your results in part (a), which variable (if any) should next be entered into a regression model that already contains X1?
c. Test H0: pYX2|X1 = 0 using the t test described in Problem 2.
d. Determine the squared multiple partial correlation r2Y(X2,X3)|X1, and test H0: pY(X2,X3)|X1 = 0.
ANOVA Table

Regression of Y on X1 and X2

Regression of Y on X1 and X3

Regression of Y on X1, X2, and X3

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Source d.f. Source d.f '趁 661 .7279 5.8228 6.9406 16.0942 640.4249 32.7819 7.2844 16.0942 Xi Residual 7 Residual 7 ANALYSIS OF VARIANCE Sum of DF Squares Mean Square F Value Pr> F Source Model Error Corrected Total 2 673.20680 336 60340 115.18 <0001 2 92233 8 23.37865 10 696,58545 Root MSE Dependent Mean Coeff Var 1.70948 40.23636 4.24860 PARAMETER ESTIMATES R-Square 0.9664 Adj R-Sq 0.9580 Squarec Partial Corr Type Squared Partial Parameter Standard Variable DF Estimate Intercept X1 X2 Error t Vaiue P Corn Type I 8.08481 20.06315 .40 06975 1 68 25068 49.84521 1.37 02081 3.35 00131 0 18988 058372 0.91938 1 2.29387 0.68488 0.56372 ANALYSIS OF VARIANCE Sum of DFI Squares Mean Square F Valus Pr>F Sourca Model Error Carrected Total 2 670.13094 335 06547 101.33 000 8 26.45452 3.30681 10 G00 58545 Root MSE Dependent Mean Coeff Var 1.81846 40.23536 51946 R-Squero 0.9620 0.9525 Adj R-Sq PARAMETER ESTIMATES Squared Partial Squaied Partial Parameter Error Value Pr Cem Type Cor Type l VariableDF Estinsate intercept X1 XJ 2670451 16.62113 1.61 0.168 5.53 0.0006 139 92595 13.3213 3.00 00171 1 157 26713 28.44374 .91933 79259 ANALYSIS OF VARIANCE Sum of DFI Squares Mean Source Model Error Corrected Tatal F Value Pr>F 3 60 49122 226 83041 7 16.09423 10 696.58545 98.66 0001 2.29918 Root MSE Dependent Mean Coeff Var 1.51630 40.23636 376849 630 R-Square Adj R-5q 0.9769 0.9670 PARAMETER ESTIMATES Squared Partial Squared Partial Parameter Standard Variable DF Estimate t Value Pr>Corr Type Corr Type lB Error 0.10 0 9204 77.32578 44,50547 1.740.1259 212 0014 1.87932 18.13420 Intercept x1 x2 x3 0.30131 0.39163 1.78 0.1183 0.31158 0.31158 0.91938 1.55910 0.73447 1 23.9037813.42936 0.58372