1 options ls=99 ps=256 nocenter nodate nonumber; 2 3 data surgical; Title1 'Surgical example from Chapter 8'; 4 input x1 x2 x3 x4 y; 5 * label x1='blood clotting score'; 6 * label x2='Prognostic data (inc age)'; 7 * label x3='enzyme function score'; 8 * label x4='liver function score'; 9 * label Y='Survival time'; 10 logy=log(y); 11 cards; NOTE: The data set WORK.SURGICAL has 54 observations and 6 variables. NOTE: DATA statement used: real time 0.05 seconds cpu time 0.05 seconds 66 ; 67 proc print data=surgical; title2 'Raw data listing'; run; NOTE: There were 54 observations read from the data set WORK.SURGICAL. NOTE: The PROCEDURE PRINT printed page 1. NOTE: PROCEDURE PRINT used: real time 0.03 seconds cpu time 0.03 seconds
Surgical example from Chapter 8 Raw data listing Obs x1 x2 x3 x4 y logy 1 6.7 62 81 2.59 200 5.29832 2 5.1 59 66 1.70 101 4.61512 3 7.4 57 83 2.16 204 5.31812 4 6.5 73 41 2.01 101 4.61512 5 7.8 65 115 4.30 509 6.23245 6 5.8 38 72 1.42 80 4.38203 7 5.7 46 63 1.91 80 4.38203 8 3.7 68 81 2.57 127 4.84419 9 6.0 67 93 2.50 202 5.30827 10 3.7 76 94 2.40 203 5.31321 11 6.3 84 83 4.13 329 5.79606 12 6.7 51 43 1.86 65 4.17439 13 5.8 96 114 3.95 830 6.72143 14 5.8 83 88 3.95 330 5.79909 15 7.7 62 67 3.40 168 5.12396 16 7.4 74 68 2.40 217 5.37990 17 6.0 85 28 2.98 87 4.46591 18 3.7 51 41 1.55 34 3.52636 19 7.3 68 74 3.56 215 5.37064 20 5.6 57 87 3.02 172 5.14749 21 5.2 52 76 2.85 109 4.69135 22 3.4 83 53 1.12 136 4.91265 23 6.7 26 68 2.10 70 4.24850 24 5.8 67 86 3.40 220 5.39363 25 6.3 59 100 2.95 276 5.62040 26 5.8 61 73 3.50 144 4.96981 27 5.2 52 86 2.45 181 5.19850 28 11.2 76 90 5.59 574 6.35263 29 5.2 54 56 2.71 72 4.27667 30 5.8 76 59 2.58 178 5.18178 31 3.2 64 65 0.74 71 4.26268 32 8.7 45 23 2.52 58 4.06044 33 5.0 59 73 3.50 116 4.75359 34 5.8 72 93 3.30 295 5.68698 35 5.4 58 70 2.64 115 4.74493 36 5.3 51 99 2.60 184 5.21494 37 2.6 74 86 2.05 118 4.77068 38 4.3 8 119 2.85 120 4.78749 39 4.8 61 76 2.45 151 5.01728 40 5.4 52 88 1.81 148 4.99721 41 5.2 49 72 1.84 95 4.55388 42 3.6 28 99 1.30 75 4.31749 43 8.8 86 88 6.40 483 6.18002 44 6.5 56 77 2.85 153 5.03044 45 3.4 77 93 1.48 191 5.25227 46 6.5 40 84 3.00 123 4.81218 47 4.5 73 106 3.05 311 5.73979 48 4.8 86 101 4.10 398 5.98645 49 5.1 67 77 2.86 158 5.06260 50 3.9 82 103 4.55 310 5.73657 51 6.6 77 46 1.95 124 4.82028 52 6.4 85 40 1.21 125 4.82831 53 6.4 59 85 2.33 198 5.28827 54 8.8 78 72 3.20 313 5.74620 69 options ls=99 ps=56; title2 'Scatter plots'; 70 proc plot data=surgical; plot y*x1 y*x2 y*x3 y*x4; run; NOTE: There were 54 observations read from the data set WORK.SURGICAL. NOTE: The PROCEDURE PLOT printed pages 2-5. NOTE: PROCEDURE PLOT used: real time 0.01 seconds cpu time 0.01 seconds 71 proc plot data=surgical; plot logy*x1 logy*x2 logy*x3 logy*x4; run; 72 options ls=99 ps=256; NOTE: There were 54 observations read from the data set WORK.SURGICAL. NOTE: The PROCEDURE PLOT printed pages 6-9. NOTE: PROCEDURE PLOT used: real time 0.01 seconds cpu time 0.01 seconds Surgical example from Chapter 8 Scatter plots Plot of y*x1. Legend: A = 1 obs, B = 2 obs, etc. y | | 900 + | | | A 800 + | | | 700 + | | | 600 + | A | | 500 + A | A | | 400 + A | | | A A A 300 + A A A | A | | A AA 200 + A A A A A A | AA A A A | A A A A A | A A A A A A AB 100 + AB A | A A A AA A B | A | A 0 + | --+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+-- 2 3 4 5 6 7 8 9 10 11 12 x1 Plot of y*x2. Legend: A = 1 obs, B = 2 obs, etc. y | | 900 + | | | A 800 + | | | 700 + | | | 600 + | A | | 500 + A | A | | 400 + A | | | A AA 300 + AA A | A | | AA A 200 + A A A A AA | AA A A A | A A B A | A A AA A A A A A 100 + A A A A | A A A A A A A A | A | A 0 + | --+---------+---------+---------+---------+---------+---------+---------+---------+---------+-- 8 18 28 38 48 58 68 78 88 98 x2 Surgical example from Chapter 8 Scatter plots Plot of y*x3. Legend: A = 1 obs, B = 2 obs, etc. y | | 900 + | | | A 800 + | | | 700 + | | | 600 + | A | | 500 + A | A | | 400 + A | | | A A A 300 + A A A | A | | A A A 200 + AA A BA | A A B A | A AB A | A A A A A A A A A 100 + A A A A | A A A A A A A A | A | A 0 + | ---+--------------+--------------+--------------+--------------+--------------+-- 20 40 60 80 100 120 x3 Plot of y*x4. Legend: A = 1 obs, B = 2 obs, etc. y | | 900 + | | | A 800 + | | | 700 + | | | 600 + | A | | 500 + A | A | | 400 + A | | | A A A 300 + A A A | A | | A A A 200 + A A AA AA | A B A A | A A B A | AA A A AA A A A 100 + A A A A | A AA AA A A A | A | A 0 + | --+------------+------------+------------+------------+------------+------------+------------+- 0 1 2 3 4 5 6 7 x4 Surgical example from Chapter 8 Scatter plots Plot of logy*x1. Legend: A = 1 obs, B = 2 obs, etc. logy | 7.0 + | | | A | | 6.5 + | | A | A | A | 6.0 + A | | A A | A A A | A | A 5.5 + | A A | A A A AA | A A A | A A A | A A 5.0 + A A A A | A | A AB | A A A A | A | AA A 4.5 + A | AA | A | A A A | A | A 4.0 + | | | | | 3.5 + A --+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+- 2 3 4 5 6 7 8 9 10 11 12 x1 Plot of logy*x2. Legend: A = 1 obs, B = 2 obs, etc. logy | 7.0 + | | | A | | 6.5 + | | A | A | A | 6.0 + A | | AA | A A A | A | A 5.5 + | A A | A A AA A | A A A | A A A | A A 5.0 + A A B | A | A A A A | A AA A | A | A A A 4.5 + A | A A | A | A A A | A | A 4.0 + | | | | | 3.5 + A --+---------+---------+---------+---------+---------+---------+---------+---------+---------+- 8 18 28 38 48 58 68 78 88 98 x2 Surgical example from Chapter 8 Scatter plots Plot of logy*x3. Legend: A = 1 obs, B = 2 obs, etc. logy | 7.0 + | | | A | | 6.5 + | | A | A | A | 6.0 + A | | A A | A A A | A | A 5.5 + | A A | A AA AA | A A A | A B | A A 5.0 + A AA A | A | A A A A | A A A A | A | A A A 4.5 + A | A A | A | A A A | A | A 4.0 + | | | | | 3.5 + A ---+--------------+--------------+--------------+--------------+--------------+-- 20 40 60 80 100 120 x3 Plot of logy*x4. Legend: A = 1 obs, B = 2 obs, etc. logy | 7.0 + | | | A | | 6.5 + | | A | A | A | 6.0 + A | | A A | A A A | A | A 5.5 + | A A | A A AA A | A A A | A A A | A A 5.0 + A A A A | A | A A A A | A A A A | A | A A A 4.5 + A | A A | A | A A A | A | A 4.0 + | | | | | 3.5 + A -+------------+------------+------------+------------+------------+------------+------------+- 0 1 2 3 4 5 6 7 x4
74 proc transreg data=surgical; title2 'Box-Cox transformation'; 75 MODEL BOXCOX(Y) = identity(X1 X2 X3 X4); run; NOTE: Algorithm converged. NOTE: There were 54 observations read from the data set WORK.SURGICAL. NOTE: The PROCEDURE TRANSREG printed pages 10-11. NOTE: PROCEDURE TRANSREG used: real time 0.04 seconds cpu time 0.04 seconds Surgical example from Chapter 8 Box-Cox transformation The TRANSREG Procedure Transformation Information for BoxCox(y) Lambda R-Square Log Like -3.00 0.28 -353.091 -2.75 0.32 -335.979 -2.50 0.36 -319.102 -2.25 0.41 -302.473 -2.00 0.48 -286.098 -1.75 0.55 -269.960 -1.50 0.62 -254.005 -1.25 0.70 -238.105 -1.00 0.78 -222.020 -0.75 0.86 -205.344 -0.50 0.91 -187.536 -0.25 0.95 -168.735 0.00 + 0.97 -154.624 < 0.25 0.97 -160.106 0.50 0.94 -180.331 0.75 0.90 -201.921 1.00 0.84 -222.037 1.25 0.77 -240.961 1.50 0.69 -259.200 1.75 0.62 -277.117 2.00 0.55 -294.936 2.25 0.49 -312.792 2.50 0.44 -330.763 2.75 0.39 -348.891 3.00 0.35 -367.194 < - Best Lambda * - Confidence Interval + - Convenient Lambda Surgical example from Chapter 8 Box-Cox transformation The TRANSREG Procedure TRANSREG Univariate Algorithm Iteration History for BoxCox(y) Iteration Average Maximum Criterion Number Change Change R-Square Change Note ------------------------------------------------------------------------- 1 0.00000 0.00000 0.97236 Converged Algorithm converged.
77 proc corr data=surgical; title2 'Simple correlations'; 78 var x1 x2 x3 x4; with y logy; run; NOTE: The PROCEDURE CORR printed page 12. NOTE: PROCEDURE CORR used: real time 0.02 seconds cpu time 0.02 seconds Surgical example from Chapter 8 Simple correlations The CORR Procedure 2 With Variables: y logy 4 Variables: x1 x2 x3 x4 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum y 54 197.16667 145.29940 10647 34.00000 830.00000 logy 54 5.07983 0.63041 274.31096 3.52636 6.72143 x1 54 5.78333 1.60303 312.30000 2.60000 11.20000 x2 54 63.24074 16.90253 3415 8.00000 96.00000 x3 54 77.11111 21.25378 4164 23.00000 119.00000 x4 54 2.74426 1.07036 148.19000 0.74000 6.40000 Pearson Correlation Coefficients, N = 54 Prob > |r| under H0: Rho=0 x1 x2 x3 x4 y 0.37252 0.55398 0.58024 0.72233 0.0055 <.0001 <.0001 <.0001 logy 0.34643 0.59290 0.66509 0.72620 0.0103 <.0001 <.0001 <.0001 80 proc reg data=surgical lineprinter; title2 'Full model'; 81 model logy = x1 x2 x3 x4; run; NOTE: 54 observations read. NOTE: 54 observations used in computations. 82 options ls=99 ps=56; plot residual.*predicted.; run; 83 options ls=99 ps=256; 84 NOTE: The PROCEDURE REG printed pages 13-14. NOTE: PROCEDURE REG used: real time 0.06 seconds cpu time 0.06 seconds Surgical example from Chapter 8 Full model The REG Procedure Model: MODEL1 Dependent Variable: logy Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 20.48086 5.12022 430.98 <.0001 Error 49 0.58214 0.01188 Corrected Total 53 21.06300 Root MSE 0.10900 R-Square 0.9724 Dependent Mean 5.07983 Adj R-Sq 0.9701 Coeff Var 2.14568 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 1.12536 0.11568 9.73 <.0001 x1 1 0.15779 0.01253 12.60 <.0001 x2 1 0.02131 0.00101 21.19 <.0001 x3 1 0.02182 0.00091252 23.91 <.0001 x4 1 0.00442 0.02236 0.20 0.8442 ------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+------ RESIDUAL | | | | 0.4 + + | | | | | | | 1 | 0.3 + + | | | 1 | | | | 1 | 0.2 + 1 + | | | 1 | | 1 | R | | e 0.1 + 1 + s | | i | 1 11 | d | 1 1 1 1 | u | 1 1 1 1 1 2 1 | a 0.0 + 1 1 111 1 1 1 + l | 1 1 1 1 1 2 | | 1 1 1 1 1 1 | | 1 | | 1 1 | -0.1 + 1 + | 1 | | 1 1 | | 1 | | 1 | -0.2 + + | 1 | | 1 | | | | | -0.3 + + | | ------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+------ 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 Predicted Value of logy PRED
85 proc reg data=surgical; title2 'Cp selection criteria'; 86 model logy = x1 x2 x3 x4 / selection=cp; run; NOTE: 54 observations read. NOTE: 54 observations used in computations. NOTE: The PROCEDURE REG printed page 15. NOTE: PROCEDURE REG used: real time 0.05 seconds cpu time 0.05 seconds Surgical example from Chapter 8 Cp selection criteria The REG Procedure Model: MODEL1 Dependent Variable: logy C(p) Selection Method Number in Model C(p) R-Square Variables in Model 3 3.0390 0.9723 x1 x2 x3 4 5.0000 0.9724 x1 x2 x3 x4 3 161.6520 0.8829 x2 x3 x4 2 283.6276 0.8129 x2 x3 3 451.8957 0.7192 x1 x3 x4 2 507.8069 0.6865 x3 x4 2 573.2766 0.6496 x2 x4 3 574.5468 0.6500 x1 x2 x4 2 580.0075 0.6458 x1 x3 1 787.9471 0.5274 x4 2 789.1422 0.5278 x1 x4 1 938.6707 0.4424 x3 2 948.2417 0.4381 x1 x2 1 1099.691 0.3515 x2 1 1510.148 0.1200 x1
87 proc reg data=surgical; title2 'RSquare selection criteria'; 88 model logy = x1 x2 x3 x4 / selection = RSquare; run; NOTE: 54 observations read. NOTE: 54 observations used in computations. NOTE: The PROCEDURE REG printed page 16. NOTE: PROCEDURE REG used: real time 0.05 seconds cpu time 0.05 seconds R-Square Selection Method Number in Model R-Square Variables in Model 1 0.5274 x4 1 0.4424 x3 1 0.3515 x2 1 0.1200 x1 ------------------------------------------- 2 0.8129 x2 x3 2 0.6865 x3 x4 2 0.6496 x2 x4 2 0.6458 x1 x3 2 0.5278 x1 x4 2 0.4381 x1 x2 ------------------------------------------- 3 0.9723 x1 x2 x3 3 0.8829 x2 x3 x4 3 0.7192 x1 x3 x4 3 0.6500 x1 x2 x4 ------------------------------------------- 4 0.9724 x1 x2 x3 x4
89 proc reg data=surgical; title2 'Adjusted RSquare selection criteria'; 90 model logy = x1 x2 x3 x4 / selection = AdjRSq; run; NOTE: 54 observations read. NOTE: 54 observations used in computations. 91 NOTE: The PROCEDURE REG printed page 17. NOTE: PROCEDURE REG used: real time 0.05 seconds cpu time 0.05 seconds Surgical example from Chapter 8 Adjusted RSquare selection criteria The REG Procedure Model: MODEL1 Dependent Variable: logy Adjusted R-Square Selection Method Number in Adjusted Model R-Square R-Square Variables in Model 3 0.9707 0.9723 x1 x2 x3 4 0.9701 0.9724 x1 x2 x3 x4 3 0.8758 0.8829 x2 x3 x4 2 0.8056 0.8129 x2 x3 3 0.7023 0.7192 x1 x3 x4 2 0.6742 0.6865 x3 x4 2 0.6358 0.6496 x2 x4 2 0.6319 0.6458 x1 x3 3 0.6290 0.6500 x1 x2 x4 1 0.5183 0.5274 x4 2 0.5093 0.5278 x1 x4 1 0.4316 0.4424 x3 2 0.4160 0.4381 x1 x2 1 0.3391 0.3515 x2 1 0.1031 0.1200 x1 92 proc rsquare data=surgical; title2 'various selection criteria'; 93 model logy = x1 x2 x3 x4 / cp sse mse adjrsq; run; NOTE: 54 observations read. NOTE: 54 observations used in computations. NOTE: PROCEDURE RSQUARE used: real time 0.03 seconds cpu time 0.03 seconds NOTE: The PROCEDURE RSQUARE printed page 18. Surgical example from Chapter 8 various selection criteria The RSQUARE Procedure Model: MODEL1 Dependent Variable: logy R-Square Selection Method Number in Adjusted Model R-Square R-Square C(p) MSE SSE Variables in Model 1 0.5274 0.5183 787.9471 0.19144 9.95512 x4 1 0.4424 0.4316 938.6707 0.22588 11.74577 x3 1 0.3515 0.3391 1099.691 0.26267 13.65876 x2 1 0.1200 0.1031 1510.148 0.35644 18.53513 x1 ------------------------------------------------------------------------------------------------- 2 0.8129 0.8056 283.6276 0.07725 3.93986 x2 x3 2 0.6865 0.6742 507.8069 0.12947 6.60319 x3 x4 2 0.6496 0.6358 573.2766 0.14473 7.38099 x2 x4 2 0.6458 0.6319 580.0075 0.14629 7.46096 x1 x3 2 0.5278 0.5093 789.1422 0.19501 9.94556 x1 x4 2 0.4381 0.4160 948.2417 0.23207 11.83572 x1 x2 ------------------------------------------------------------------------------------------------- 3 0.9723 0.9707 3.0390 0.01165 0.58260 x1 x2 x3 3 0.8829 0.8758 161.6520 0.04934 2.46698 x2 x3 x4 3 0.7192 0.7023 451.8957 0.11830 5.91518 x1 x3 x4 3 0.6500 0.6290 574.5468 0.14745 7.37232 x1 x2 x4 ------------------------------------------------------------------------------------------------- 4 0.9724 0.9701 5.0000 0.01188 0.58214 x1 x2 x3 x4
95 proc reg data=surgical; title2 'Backward stepwise regression'; 96 model logy = x1 x2 x3 x4 / selection=backward cp sse mse adjrsq; run; NOTE: 54 observations read. NOTE: 54 observations used in computations. NOTE: The PROCEDURE REG printed page 19. NOTE: PROCEDURE REG used: real time 0.06 seconds cpu time 0.06 seconds Surgical example from Chapter 8 Backward stepwise regression The REG Procedure Model: MODEL1 Dependent Variable: logy Backward Elimination: Step 0 All Variables Entered: R-Square = 0.9724 and C(p) = 5.0000 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 20.48086 5.12022 430.98 <.0001 Error 49 0.58214 0.01188 Corrected Total 53 21.06300 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 1.12536 0.11568 1.12432 94.64 <.0001 x1 0.15779 0.01253 1.88484 158.65 <.0001 x2 0.02131 0.00101 5.33305 448.90 <.0001 x3 0.02182 0.00091252 6.79019 571.55 <.0001 x4 0.00442 0.02236 0.00046344 0.04 0.8442 Bounds on condition number: 2.5553, 29.286 --------------------------------------------------------------------------------------- Backward Elimination: Step 1 Variable x4 Removed: R-Square = 0.9723 and C(p) = 3.0390 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 20.48040 6.82680 585.89 <.0001 Error 50 0.58260 0.01165 Corrected Total 53 21.06300 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 1.11358 0.09817 1.49935 128.68 <.0001 x1 0.15940 0.00939 3.35726 288.13 <.0001 x2 0.02140 0.00088086 6.87836 590.31 <.0001 x3 0.02193 0.00070561 11.25312 965.76 <.0001 Bounds on condition number: 1.0308, 9.1864 --------------------------------------------------------------------------------------- All variables left in the model are significant at the 0.1000 level. Summary of Backward Elimination Variable Number Partial Model Step Removed Vars In R-Square R-Square C(p) F Value Pr > F 1 x4 3 0.0000 0.9723 3.0390 0.04 0.8442 98 proc reg data=surgical; title2 'Stepwise regression'; 99 model logy = x1 x2 x3 x4 / selection=stepwise; run; NOTE: 54 observations read. NOTE: 54 observations used in computations. Surgical example from Chapter 8 Stepwise regression The REG Procedure Model: MODEL1 Dependent Variable: logy Stepwise Selection: Step 1 Variable x4 Entered: R-Square = 0.5274 and C(p) = 787.9471 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 11.10788 11.10788 58.02 <.0001 Error 52 9.95512 0.19144 Corrected Total 53 21.06300 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 3.90609 0.16520 107.03572 559.10 <.0001 x4 0.42771 0.05615 11.10788 58.02 <.0001 Bounds on condition number: 1, 1 --------------------------------------------------------------------------------------- Stepwise Selection: Step 2 Variable x3 Entered: R-Square = 0.6865 and C(p) = 507.8069 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 14.45981 7.22991 55.84 <.0001 Error 51 6.60319 0.12947 Corrected Total 53 21.06300 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 3.19784 0.19450 34.99819 270.31 <.0001 x3 0.01301 0.00256 3.35193 25.89 <.0001 x4 0.32010 0.05079 5.14258 39.72 <.0001 Bounds on condition number: 1.2098, 4.8392 --------------------------------------------------------------------------------------- Stepwise Selection: Step 3 Variable x2 Entered: R-Square = 0.8829 and C(p) = 161.6520 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 18.59602 6.19867 125.63 <.0001 Error 50 2.46698 0.04934 Corrected Total 53 21.06300 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 2.16970 0.16440 8.59420 174.18 <.0001 x2 0.01819 0.00199 4.13621 83.83 <.0001 x3 0.01612 0.00161 4.91401 99.60 <.0001 x4 0.18846 0.03449 1.47288 29.85 <.0001 Bounds on condition number: 1.4642, 11.822 --------------------------------------------------------------------------------------- Stepwise Selection: Step 4 Variable x1 Entered: R-Square = 0.9724 and C(p) = 5.0000 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 20.48086 5.12022 430.98 <.0001 Error 49 0.58214 0.01188 Corrected Total 53 21.06300 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 1.12536 0.11568 1.12432 94.64 <.0001 x1 0.15779 0.01253 1.88484 158.65 <.0001 x2 0.02131 0.00101 5.33305 448.90 <.0001 x3 0.02182 0.00091252 6.79019 571.55 <.0001 x4 0.00442 0.02236 0.00046344 0.04 0.8442 Bounds on condition number: 2.5553, 29.286 --------------------------------------------------------------------------------------- Stepwise Selection: Step 5 Variable x4 Removed: R-Square = 0.9723 and C(p) = 3.0390 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 20.48040 6.82680 585.89 <.0001 Error 50 0.58260 0.01165 Corrected Total 53 21.06300 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 1.11358 0.09817 1.49935 128.68 <.0001 x1 0.15940 0.00939 3.35726 288.13 <.0001 x2 0.02140 0.00088086 6.87836 590.31 <.0001 x3 0.02193 0.00070561 11.25312 965.76 <.0001 Bounds on condition number: 1.0308, 9.1864 --------------------------------------------------------------------------------------- All variables left in the model are significant at the 0.1500 level. No other variable met the 0.1500 significance level for entry into the model. Summary of Stepwise Selection Variable Variable Number Partial Model Step Entered Removed Vars In R-Square R-Square C(p) F Value Pr > F 1 x4 1 0.5274 0.5274 787.947 58.02 <.0001 2 x3 2 0.1591 0.6865 507.807 25.89 <.0001 3 x2 3 0.1964 0.8829 161.652 83.83 <.0001 4 x1 4 0.0895 0.9724 5.0000 158.65 <.0001 5 x4 3 0.0000 0.9723 3.0390 0.04 0.8442