Inputting the Supervisor Performance data, p. 54.
data p054; input Y X1 X2 X3 X4 X5 X6 ; cards; 43 51 30 39 61 92 45 63 64 51 54 63 73 47 71 70 68 69 76 86 48 61 63 45 47 54 84 35 81 78 56 66 71 83 47 43 55 49 44 54 49 34 58 67 42 56 66 68 35 71 75 50 55 70 66 41 72 82 72 67 71 83 31 67 61 45 47 62 80 41 64 53 53 58 58 67 34 67 60 47 39 59 74 41 69 62 57 42 55 63 25 68 83 83 45 59 77 35 77 77 54 72 79 77 46 81 90 50 72 60 54 36 74 85 64 69 79 79 63 65 60 65 75 55 80 60 65 70 46 57 75 85 46 50 58 68 54 64 78 52 50 40 33 34 43 64 33 64 61 52 62 66 80 41 53 66 52 50 63 80 37 40 37 42 58 50 57 49 63 54 42 48 66 75 33 66 77 66 63 88 76 72 78 75 58 74 80 78 49 48 57 44 45 51 83 38 85 85 71 71 77 74 55 82 82 39 59 64 78 39 ; run;
Table 11.1, p. 294. The values in the eigenvalue column are the eigenvalues on the bottom of p. 295.
proc princomp data = p054; var x1-x6; run;
The PRINCOMP Procedure
Observations 30
Variables 6
Simple Statistics
X1 X2 X3 X4 X5 X6
Mean 66.60000000 53.13333333 56.36666667 64.63333333 74.76666667 42.93333333
StD 13.31475717 12.23542999 11.73701288 10.39722554 9.89490755 10.28870601
Correlation Matrix
X1 X2 X3 X4 X5 X6
X1 1.0000 0.5583 0.5967 0.6692 0.1877 0.2246
X2 0.5583 1.0000 0.4933 0.4455 0.1472 0.3433
X3 0.5967 0.4933 1.0000 0.6403 0.1160 0.5316
X4 0.6692 0.4455 0.6403 1.0000 0.3769 0.5742
X5 0.1877 0.1472 0.1160 0.3769 1.0000 0.2833
X6 0.2246 0.3433 0.5316 0.5742 0.2833 1.0000
Eigenvalues of the Correlation Matrix
Eigenvalue Difference Proportion Cumulative
1 3.16922321 2.16287646 0.5282 0.5282
2 1.00634675 0.24343802 0.1677 0.6959
3 0.76290873 0.21039227 0.1272 0.8231
4 0.55251646 0.23526997 0.0921 0.9152
5 0.31724648 0.12548811 0.0529 0.9680
6 0.19175838 0.0320 1.0000
Eigenvectors
Prin1 Prin2 Prin3 Prin4 Prin5 Prin6
X1 0.439375 -.312642 0.445167 -.316019 -.191521 0.611949
X2 0.394711 -.308751 0.217414 0.814847 -.037686 -.190294
X3 0.461401 -.217087 -.271981 -.224796 0.775648 -.117671
X4 0.492658 0.115532 0.005605 -.365108 -.460364 -.631404
X5 0.224813 0.802247 0.457246 0.099947 0.288875 0.057847
X6 0.380801 0.320706 -.686643 0.205742 -.254728 0.416465
The values in the VIF column in the output are the VIF’s in middle of p. 295.
proc reg data = p054; model y = x1-x6/vif ; run; quit;
The REG Procedure Model: MODEL1 Dependent Variable: YAnalysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 6 3147.96634 524.66106 10.50 <.0001 Error 23 1149.00032 49.95654 Corrected Total 29 4296.96667
Root MSE 7.06799 R-Square 0.7326 Dependent Mean 64.63333 Adj R-Sq 0.6628 Coeff Var 10.93552 Parameter Estimates
Parameter Standard Variance Variable DF Estimate Error t Value Pr > |t| Inflation Intercept 1 10.78708 11.58926 0.93 0.3616 0 X1 1 0.61319 0.16098 3.81 0.0009 2.66706 X2 1 -0.07305 0.13572 -0.54 0.5956 1.60089 X3 1 0.32033 0.16852 1.90 0.0699 2.27104 X4 1 0.08173 0.22148 0.37 0.7155 3.07823 X5 1 0.03838 0.14700 0.26 0.7963 1.22811 X6 1 -0.21706 0.17821 -1.22 0.2356 1.95159
Table 11.2, p. 296.
The probability (p-value) for entering was set at .99 so that all the variables will be entered into the model. The reason is that we are mainly interested in the order in which they entered the model.proc reg data = p054; model y = x1-x6/ selection = forward slentry = 0.99; run; quit;The REG Procedure Model: MODEL1 Dependent Variable: YForward Selection: Step 1 Variable X1 Entered: R-Square = 0.6813 and C(p) = 1.4115 Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 1 2927.58425 2927.58425 59.86 <.0001 Error 28 1369.38241 48.90651 Corrected Total 29 4296.96667 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 14.37632 6.61999 230.64710 4.72 0.0385 X1 0.75461 0.09753 2927.58425 59.86 <.0001
Bounds on condition number: 1, 1 ————————————————————————————————
Forward Selection: Step 2
Variable X3 Entered: R-Square = 0.7080 and C(p) = 1.1148 Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 2 3042.31770 1521.15885 32.74 <.0001 Error 27 1254.64897 46.46848 Corrected Total 29 4296.96667 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 9.87088 7.06122 90.80512 1.95 0.1735 X1 0.64352 0.11848 1370.90744 29.50 <.0001 X3 0.21119 0.13440 114.73344 2.47 0.1278 Bounds on condition number: 1.553, 6.2121 ————————————————————————————————
Forward Selection: Step 3
Variable X6 Entered: R-Square = 0.7256 and C(p) = 1.6027 Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 3 3117.85753 1039.28584 22.92 <.0001 Error 26 1179.10914 45.35035 Corrected Total 29 4296.96667
Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 13.57774 7.54390 146.90747 3.24 0.0835 X1 0.62273 0.11815 1259.90769 27.78 <.0001 X3 0.31239 0.15420 186.12267 4.10 0.0532 X6 -0.18695 0.14485 75.53983 1.67 0.2082
Bounds on condition number: 2.0946, 15.292 ————————————————————————————————
Forward Selection: Step 4
Variable X2 Entered: R-Square = 0.7293 and C(p) = 3.2805 Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 4 3133.95504 783.48876 16.84 <.0001 Error 25 1163.01163 46.52047 Corrected Total 29 4296.96667
Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 14.30347 7.73957 158.88895 3.42 0.0765 X1 0.65338 0.13051 1165.93982 25.06 <.0001 X2 -0.07682 0.13059 16.09751 0.35 0.5616 X3 0.32395 0.15741 197.03481 4.24 0.0502 X6 -0.17151 0.14904 61.60475 1.32 0.2607
Bounds on condition number: 2.1278, 28.27 ————————————————————————————————
Forward Selection: Step 5
Variable X4 Entered: R-Square = 0.7318 and C(p) = 5.0682 < Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 3144.56048 628.91210 13.10 <.0001 Error 24 1152.40619 48.01692 Corrected Total 29 4296.96667 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 12.79791 8.49061 109.09234 2.27 0.1448 X1 0.61315 0.15783 724.70295 15.09 0.0007 X2 -0.07224 0.13303 14.15892 0.29 0.5921 X3 0.31172 0.16202 177.73703 3.70 0.0663 X4 0.09795 0.20842 10.60544 0.22 0.6426 X6 -0.21111 0.17328 71.26802 1.48 0.2350 Bounds on condition number: 2.8361, 56.035 ------------------------------------------------------------------------------------------------ Forward Selection: Step 6 Variable X5 Entered: R-Square = 0.7326 and C(p) = 7.0000 Forward Selection: Step 6 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 6 3147.96634 524.66106 10.50 <.0001 Error 23 1149.00032 49.95654 Corrected Total 29 4296.96667 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 10.78708 11.58926 43.28014 0.87 0.3616 X1 0.61319 0.16098 724.80036 14.51 0.0009 X2 -0.07305 0.13572 14.47161 0.29 0.5956 X3 0.32033 0.16852 180.50479 3.61 0.0699 X4 0.08173 0.22148 6.80328 0.14 0.7155 X5 0.03838 0.14700 3.40586 0.07 0.7963 X6 -0.21706 0.17821 74.11004 1.48 0.2356 Bounds on condition number: 3.0782, 76.782 ------------------------------------------------------------------------------------------------ All variables have been entered into the model. Summary of Forward Selection Variable Number Partial Model Step Entered Vars In R-Square R-Square C(p) F Value Pr > F 1 X1 1 0.6813 0.6813 1.4115 59.86 <.0001 2 X3 2 0.0267 0.7080 1.1148 2.47 0.1278 3 X6 3 0.0176 0.7256 1.6027 1.67 0.2082 4 X2 4 0.0037 0.7293 3.2805 0.35 0.5616 5 X4 5 0.0025 0.7318 5.0682 0.22 0.6426 6 X5 6 0.0008 0.7326 7.0000 0.07 0.7963
The equation on the bottom of p. 296.
proc reg data = p054; model y = x1 x3 x6; run; quit;The REG Procedure Model: MODEL1 Dependent Variable: YAnalysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 3 3117.85753 1039.28584 22.92 <.0001 Error 26 1179.10914 45.35035 Corrected Total 29 4296.96667
Root MSE 6.73427 R-Square 0.7256 Dependent Mean 64.63333 Adj R-Sq 0.6939 Coeff Var 10.41919 Parameter Estimates
Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 13.57774 7.54390 1.80 0.0835 X1 1 0.62273 0.11815 5.27 <.0001 X3 1 0.31239 0.15420 2.03 0.0532 X6 1 -0.18695 0.14485 -1.29 0.2082
Table 11.3, p. 297.
proc reg data = p054; model y = x1-x6/ selection = backward slstay = 0.01; run; quit;The REG Procedure Model: MODEL1 Dependent Variable: YBackward Elimination: Step 0 All Variables Entered: R-Square = 0.7326 and C(p) = 7.0000 Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 6 3147.96634 524.66106 10.50 <.0001 Error 23 1149.00032 49.95654 Corrected Total 29 4296.96667 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 10.78708 11.58926 43.28014 0.87 0.3616 X1 0.61319 0.16098 724.80036 14.51 0.0009 X2 -0.07305 0.13572 14.47161 0.29 0.5956 X3 0.32033 0.16852 180.50479 3.61 0.0699 X4 0.08173 0.22148 6.80328 0.14 0.7155 X5 0.03838 0.14700 3.40586 0.07 0.7963 X6 -0.21706 0.17821 74.11004 1.48 0.2356
Bounds on condition number: 3.0782, 76.782 ————————————————————————————————
Backward Elimination: Step 1
Variable X5 Removed: R-Square = 0.7318 and C(p) = 5.0682 Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 5 3144.56048 628.91210 13.10 <.0001 Error 24 1152.40619 48.01692 Corrected Total 29 4296.96667
Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 12.79791 8.49061 109.09234 2.27 0.1448 X1 0.61315 0.15783 724.70295 15.09 0.0007 X2 -0.07224 0.13303 14.15892 0.29 0.5921 X3 0.31172 0.16202 177.73703 3.70 0.0663 X4 0.09795 0.20842 10.60544 0.22 0.6426 X6 -0.21111 0.17328 71.26802 1.48 0.2350
Bounds on condition number: 2.8361, 56.035 ————————————————————————————————
Backward Elimination: Step 2
Variable X4 Removed: R-Square = 0.7293 and C(p) = 3.2805 Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 4 3133.95504 783.48876 16.84 <.0001 Error 25 1163.01163 46.52047 Corrected Total 29 4296.96667 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 14.30347 7.73957 158.88895 3.42 0.0765 X1 0.65338 0.13051 1165.93982 25.06 <.0001 X2 -0.07682 0.13059 16.09751 0.35 0.5616 X3 0.32395 0.15741 197.03481 4.24 0.0502 X6 -0.17151 0.14904 61.60475 1.32 0.2607
Bounds on condition number: 2.1278, 28.27 ————————————————————————————————
Backward Elimination: Step 3
Variable X2 Removed: R-Square = 0.7256 and C(p) = 1.6027
Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 3 3117.85753 1039.28584 22.92 <.0001 Error 26 1179.10914 45.35035 Corrected Total 29 4296.96667 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 13.57774 7.54390 146.90747 3.24 0.0835 X1 0.62273 0.11815 1259.90769 27.78 <.0001 X3 0.31239 0.15420 186.12267 4.10 0.0532 X6 -0.18695 0.14485 75.53983 1.67 0.2082
Bounds on condition number: 2.0946, 15.292 ————————————————————————————————
Backward Elimination: Step 4
Variable X6 Removed: R-Square = 0.7080 and C(p) = 1.1148 Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 2 3042.31770 1521.15885 32.74 <.0001 Error 27 1254.64897 46.46848 Corrected Total 29 4296.96667 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 9.87088 7.06122 90.80512 1.95 0.1735 X1 0.64352 0.11848 1370.90744 29.50 <.0001 X3 0.21119 0.13440 114.73344 2.47 0.1278
Bounds on condition number: 1.553, 6.2121 ————————————————————————————————
Backward Elimination: Step 5 Variable X3 Removed: R-Square = 0.6813 and C(p) = 1.4115 Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 1 2927.58425 2927.58425 59.86 <.0001 Error 28 1369.38241 48.90651 Corrected Total 29 4296.96667 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 14.37632 6.61999 230.64710 4.72 0.0385 X1 0.75461 0.09753 2927.58425 59.86 <.0001
Bounds on condition number: 1, 1 ———————————————————————————————— All variables left in the model are significant at the 0.0100 level. Summary of Backward Elimination
Variable Number Partial Model Step Removed Vars In R-Square R-Square C(p) F Value Pr > F 1 X5 5 0.0008 0.7318 5.0682 0.07 0.7963 2 X4 4 0.0025 0.7293 3.2805 0.22 0.6426 3 X2 3 0.0037 0.7256 1.6027 0.35 0.5616 4 X6 2 0.0176 0.7080 1.1148 1.67 0.2082 5 X3 1 0.0267 0.6813 1.4115 2.47 0.1278
In order to get all the information in Table 11.2 and 11.3 from the SAS output remember that the t-value is the square-root of the F-value for that variable and that the RMS is the square-root of the Mean Square Error.
proc reg data = p054 ; model y = x1-x6/ selection = cp; run; quit;The REG Procedure Model: MODEL1 Dependent Variable: YC(p) Selection Method
Number in Model C(p) R-Square Variables in Model
2 1.1148 0.7080 X1 X3 1 1.4115 0.6813 X1 3 1.6027 0.7256 X1 X3 X6 3 2.5136 0.7150 X1 X2 X3 3 3.0910 0.7083 X1 X3 X4 3 3.1148 0.7080 X1 X3 X5 2 3.1892 0.6839 X1 X4 2 3.2610 0.6831 X1 X2 4 3.2805 0.7293 X1 X2 X3 X6 2 3.3284 0.6823 X1 X6 4 3.3516 0.7285 X1 X3 X4 X6 2 3.4113 0.6813 X1 X5 4 3.4590 0.7273 X1 X3 X5 X6 4 4.4948 0.7152 X1 X2 X3 X4 4 4.5114 0.7150 X1 X2 X3 X5 3 4.7049 0.6895 X1 X4 X6 3 4.9904 0.6862 X1 X2 X4 5 5.0682 0.7318 X1 X2 X3 X4 X6 4 5.0862 0.7083 X1 X3 X4 X5 5 5.1362 0.7310 X1 X2 X3 X5 X6 3 5.1643 0.6842 X1 X4 X5 3 5.2246 0.6835 X1 X2 X6 3 5.2598 0.6831 X1 X2 X5 5 5.2897 0.7292 X1 X3 X4 X5 X6 3 5.3204 0.6824 X1 X5 X6 5 6.4835 0.7154 X1 X2 X3 X4 X5 4 6.6260 0.6904 X1 X2 X4 X6 4 6.6924 0.6897 X1 X4 X5 X6 4 6.9672 0.6865 X1 X2 X4 X5 6 7.0000 0.7326 X1 X2 X3 X4 X5 X6 4 7.2175 0.6836 X1 X2 X5 X6 5 8.6132 0.6906 X1 X2 X4 X5 X6 3 16.5020 0.5524 X3 X4 X6 4 17.5748 0.5632 X2 X3 X4 X6 4 18.4232 0.5533 X3 X4 X5 X6 5 19.5086 0.5639 X2 X3 X4 X5 X6 2 23.2501 0.4507 X3 X4 3 24.5582 0.4587 X2 X3 X4 3 24.6196 0.4580 X2 X3 X6 2 24.8228 0.4324 X3 X6 3 25.0216 0.4533 X3 X5 X6 4 25.1081 0.4756 X2 X3 X5 X6 3 25.2305 0.4509 X3 X4 X5 3 25.9098 0.4430 X2 X4 X6 4 26.5310 0.4590 X2 X3 X4 X5 1 26.5568 0.3890 X3 2 26.9622 0.4075 X2 X3 2 27.7253 0.3986 X4 X6 4 27.7426 0.4449 X2 X4 X5 X6 2 27.9400 0.3961 X3 X5 3 28.5300 0.4125 X2 X3 X5 2 29.1996 0.3815 X2 X4 3 29.4961 0.4013 X4 X5 X6 1 30.0585 0.3483 X4 3 30.8168 0.3860 X2 X4 X5 2 31.6221 0.3533 X4 X5 1 44.3960 0.1816 X2 2 45.6241 0.1905 X2 X5 2 46.3885 0.1817 X2 X6 3 47.6052 0.1908 X2 X5 X6 1 57.9091 0.0245 X5 1 57.9453 0.0241 X6 2 58.7617 0.0378 X5 X6
Table 11.5, p. 297 (except for the Cp values).
proc reg data = p054 outest = temp; model y = x1; model y = x1 x4; model y = x1 x4 x6; model y = x1 x3 x4 x5; model y = x1-x5; model y = x1-x6; run; quit;The REG Procedure Model: MODEL1 Dependent Variable: YAnalysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 1 2927.58425 2927.58425 59.86 <.0001 Error 28 1369.38241 48.90651 Corrected Total 29 4296.96667
Root MSE 6.99332 R-Square 0.6813 Dependent Mean 64.63333 Adj R-Sq 0.6699 Coeff Var 10.81999 Parameter Estimates
Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 14.37632 6.61999 2.17 0.0385 X1 1 0.75461 0.09753 7.74 <.0001
The REG Procedure Model: MODEL2 Dependent Variable: Y
Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 2 2938.68666 1469.34333 29.21 <.0001 Error 27 1358.28001 50.30667 Corrected Total 29 4296.96667
Root MSE 7.09272 R-Square 0.6839 Dependent Mean 64.63333 Adj R-Sq 0.6605 Coeff Var 10.97378
Parameter Estimates
Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 11.98732 8.42257 1.42 0.1661 X1 1 0.71276 0.13312 5.35 <.0001 X4 1 0.08009 0.17047 0.47 0.6423
The REG Procedure Model: MODEL3 Dependent Variable: Y
Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F
Model 3 2962.88197 987.62732 19.25 <.0001 Error 26 1334.08469 51.31095 Corrected Total 29 4296.96667
Root MSE 7.16317 R-Square 0.6895 Dependent Mean 64.63333 Adj R-Sq 0.6537 Coeff Var 11.08277
Parameter Estimates
Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 12.96654 8.62492 1.50 0.1448 X1 1 0.68765 0.13933 4.94 <.0001 X4 1 0.16545 0.21236 0.78 0.4429 X6 1 -0.11237 0.16365 -0.69 0.4984
The REG Procedure Model: MODEL4 Dependent Variable: Y
Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 4 3043.74506 760.93626 15.18 <.0001 Error 25 1253.22161 50.12886 Corrected Total 29 4296.96667
Root MSE 7.08017 R-Square 0.7083 Dependent Mean 64.63333 Adj R-Sq 0.6617 Coeff Var 10.95437
Parameter Estimates
Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 9.98146 11.53149 0.87 0.3949 X1 1 0.65392 0.13920 4.70 <.0001 X3 1 0.22235 0.15451 1.44 0.1625 X4 1 -0.03383 0.20061 -0.17 0.8675 X5 1 0.01009 0.14587 0.07 0.9454
The REG Procedure Model: MODEL5 Dependent Variable: Y
Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 5 3073.85630 614.77126 12.06 <.0001 Error 24 1223.11037 50.96293 Corrected Total 29 4296.96667
Root MSE 7.13883 R-Square 0.7154 Dependent Mean 64.63333 Adj R-Sq 0.6561 Coeff Var 11.04513
Parameter Estimates
Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 11.01113 11.70394 0.94 0.3562 X1 1 0.69205 0.14886 4.65 0.0001 X2 1 -0.10356 0.13473 -0.77 0.4496 X3 1 0.24906 0.15962 1.56 0.1318 X4 1 -0.03346 0.20228 -0.17 0.8700 X5 1 0.01549 0.14725 0.11 0.9171
The REG Procedure Model: MODEL6 Dependent Variable: Y
Analysis of Variance
Sum of Mean Source DF Squares Square F Value Pr > F Model 6 3147.96634 524.66106 10.50 <.0001 Error 23 1149.00032 49.95654 Corrected Total 29 4296.96667
Root MSE 7.06799 R-Square 0.7326 Dependent Mean 64.63333 Adj R-Sq 0.6628 Coeff Var 10.93552
Parameter Estimates
Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 10.78708 11.58926 0.93 0.3616 X1 1 0.61319 0.16098 3.81 0.0009 X2 1 -0.07305 0.13572 -0.54 0.5956 X3 1 0.32033 0.16852 1.90 0.0699 X4 1 0.08173 0.22148 0.37 0.7155 X5 1 0.03838 0.14700 0.26 0.7963 X6 1 -0.21706 0.17821 -1.22 0.2356
The Cp and R-square values in table 11.5, p. 297.
ods listing close; proc reg data = p054; model y = x1-x6/ selection = cp; ods output SubsetSelSummary=temp; run; quit; ods listing; proc print data = temp; where varsinmodel = 'X1' or varsinmodel = 'X1 X4' OR varsinmodel = 'X1 X4 X6' OR varsinmodel = 'X1 X2 X3 X4 X5' OR varsinmodel = 'X1 X2 X3 X4 X5 X6'; var varsinmodel Cp rsquare ; run;Obs VarsInModel Cp RSquare2 X1 1.4115 0.6813 7 X1 X4 3.1892 0.6839 16 X1 X4 X6 4.7049 0.6895 26 X1 X2 X3 X4 X5 6.4835 0.7154 30 X1 X2 X3 X4 X5 X6 7.0000 0.7326
Fig. 11.1, p. 298.
symbol1 v=dot c=blue h = .8; proc reg data = p054 outest = temp covout; model y = x1-x6/ selection= rsquare cp noprint; run; quit; data templess (keep = _P_ _CP_ ); set temp; if _CP_ < 10; run; goptions reset = all; filename outfile 'https://stats.idre.ucla.edu/wp-content/uploads/2016/02/chpsasch11_1.gif'; goptions gsfname=outfile dev=gif373; axis1 order=(1 to 7 by 1) offset=(3, 5); symbol1 v=star c=blue h = .8; proc gplot data = templess; plot _CP_*_p_ / haxis = axis1; run; quit;
Inputting the Homicide data, table 11.6-11.8, p. 300-301.
data p301; input Year FTP UNEMP M LIC GR CLEAR W NMAN G HE WE H ; cards; 1961 260.35 11.0 455.5 178.15 215.98 93.4 558724 538.1 133.9 2.98 117.18 8.60 1962 269.80 7.0 480.2 156.41 180.48 88.5 538584 547.6 137.6 3.09 134.02 8.90 1963 272.04 5.2 506.1 198.02 209.57 94.4 519171 562.8 143.6 3.23 141.68 8.52 1964 272.96 4.3 535.8 222.10 231.67 92.0 500457 591.0 150.3 3.33 147.98 8.89 1965 272.51 3.5 576.0 301.92 297.65 91.0 482418 626.1 164.3 3.46 159.85 13.07 1966 261.34 3.2 601.7 391.22 367.62 87.4 465029 659.8 179.5 3.60 157.19 14.57 1967 268.89 4.1 577.3 665.56 616.54 88.3 448267 686.2 187.5 3.73 155.29 21.36 1968 295.99 3.9 596.9 1131.21 1029.75 86.1 432109 699.6 195.4 2.91 131.75 28.03 1969 319.87 3.6 613.5 837.80 786.23 79.0 416533 729.9 210.3 4.25 178.74 31.49 1970 341.43 7.1 569.3 794.90 713.77 73.9 401518 757.8 223.8 4.47 178.30 37.39 1971 356.59 8.4 548.8 817.74 750.43 63.4 398046 755.3 227.7 5.04 209.54 46.26 1972 376.69 7.7 563.4 583.17 1027.38 62.5 373095 787.0 230.9 5.47 240.05 47.24 1973 390.19 6.3 609.3 709.59 666.50 58.9 359647 819.8 230.2 5.76 258.05 52.33 ; run;Creating the standardized variables (11.8), p.300.
proc sql; create table p301 as select *, (H - mean(H))/std(H) as zH, (G - mean(G))/std(G) as zG, (M - mean(M))/std(M) as zM, (W - mean(W))/std(W) as zW from p301; quit;Table 11.9, p. 301.
proc reg data = p301; model zH = zG zM zW/vif; run; quit;The REG Procedure Model: MODEL1 Dependent Variable: zH Number of Observations Read 13 Number of Observations Used 13 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 11.69500 3.89833 115.03 <.0001 Error 9 0.30500 0.03389 Corrected Total 12 12.00000 Root MSE 0.18409 R-Square 0.9746 Dependent Mean 1.02482E-16 Adj R-Sq 0.9661 Coeff Var 1.796292E17 Parameter Estimates Parameter Standard Variance Variable DF Estimate Error t Value Pr > |t| Inflation Intercept 1 7.78776E-17 0.05106 0.00 1.0000 0 zG 1 0.23541 0.34535 0.68 0.5126 42.23355 zM 1 -0.40468 0.09049 -4.47 0.0016 2.89965 zW 1 -1.02455 0.37790 -2.71 0.0240 50.56904Table 11.10, p. 302. The coefficients are in the rows where _type_ = PARMS (parameters) and the t-values are in the rows where _type_ = T.
proc reg data = p301 outest = temp tableout noprint; model zH = zG /adjrsq; model zH = zM /adjrsq; model zH = zW/adjrsq; model zH = zG zM/adjrsq ; model zH = zG zW/adjrsq; model zH = zM zW /adjrsq; model zH = zG zM zW /adjrsq; run; quit; proc print data = temp; where _type_='PARMS' or _type_ = 'T'; var _type_ zG zM zW _adjrsq_ ; run;Obs _TYPE_ zG zM zW _ADJRSQ_1 PARMS 0.9581 . . 0.91040 3 T 11.0875 . . . 7 PARMS . 0.54642 . 0.23481 9 T . 2.16389 . . 13 PARMS . . -0.9469 0.88727 15 T . . -9.7696 . 19 PARMS 1.1491 -0.26919 . 0.94459 21 T 11.9125 -2.79057 . . 25 PARMS 0.8682 . -0.0912 0.90173 27 T 1.6182 . -0.1700 . 31 PARMS . -0.42995 -1.2759 0.96793 33 T . -5.35378 -15.8879 . 37 PARMS 0.2354 -0.40468 -1.0246 0.96611 39 T 0.6817 -4.47205 -2.7112 .