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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: 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 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: Y
Forward 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: Y
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
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: Y
Backward 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: Y
C(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: Y
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
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 RSquare 2 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 '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 noint; run; quit;
The REG Procedure
Model: MODEL1
Dependent Variable: zH
NOTE: No intercept in model. R-Square is redefined
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 11.69500 3.89833 127.82 <.0001
Error 10 0.30500 0.03050
Uncorrected Total 13 12.00000
Root MSE 0.17464 R-Square 0.9746
Dependent Mean -1.708E-17 Adj R-Sq 0.9670
Coeff Var -1.02247E18
Parameter Estimates
Parameter Standard Variance
Variable DF Estimate Error t Value Pr > |t| Inflation
zG 1 0.23541 0.32763 0.72 0.4889 42.23355
zM 1 -0.40468 0.08585 -4.71 0.0008 2.89965
zW 1 -1.02455 0.35851 -2.86 0.0170 50.56904
Table 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 .
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