Stepwise Regression on Cancer Remission Data 1 Obs remiss cell smear infil li blast temp 1 1 0.80 0.83 0.66 1.9 1.100 0.996 2 1 0.90 0.36 0.32 1.4 0.740 0.992 3 0 0.80 0.88 0.70 0.8 0.176 0.982 4 0 1.00 0.87 0.87 0.7 1.053 0.986 5 1 0.90 0.75 0.68 1.3 0.519 0.980 6 0 1.00 0.65 0.65 0.6 0.519 0.982 7 1 0.95 0.97 0.92 1.0 1.230 0.992 8 0 0.95 0.87 0.83 1.9 1.354 1.020 9 0 1.00 0.45 0.45 0.8 0.322 0.999 10 0 0.95 0.36 0.34 0.5 0.000 1.038 11 0 0.85 0.39 0.33 0.7 0.279 0.988 12 0 0.70 0.76 0.53 1.2 0.146 0.982 13 0 0.80 0.46 0.37 0.4 0.380 1.006 14 0 0.20 0.39 0.08 0.8 0.114 0.990 15 0 1.00 0.90 0.90 1.1 1.037 0.990 16 1 1.00 0.84 0.84 1.9 2.064 1.020 17 0 0.65 0.42 0.27 0.5 0.114 1.014 18 0 1.00 0.75 0.75 1.0 1.322 1.004 19 0 0.50 0.44 0.22 0.6 0.114 0.990 20 1 1.00 0.63 0.63 1.1 1.072 0.986 21 0 1.00 0.33 0.33 0.4 0.176 1.010 22 0 0.90 0.93 0.84 0.6 1.591 1.020 23 1 1.00 0.58 0.58 1.0 0.531 1.002 24 0 0.95 0.32 0.30 1.6 0.886 0.988 25 1 1.00 0.60 0.60 1.7 0.964 0.990 26 1 1.00 0.69 0.69 0.9 0.398 0.986 27 0 1.00 0.73 0.73 0.7 0.398 0.986 Stepwise Regression on Cancer Remission Data 2 The LOGISTIC Procedure Model Information Data Set WORK.REMISSION Response Variable remiss Complete Remission Number of Response Levels 2 Model binary logit Optimization Technique Fisher's scoring Number of Observations Read 27 Number of Observations Used 27 Response Profile Ordered Total Value remiss Frequency 1 1 9 2 0 18 Probability modeled is remiss=1. Stepwise Selection Procedure Step 0. Intercept entered: Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. -2 Log L = 34.372 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -0.6931 0.4082 2.8827 0.0895 Stepwise Regression on Cancer Remission Data 3 The LOGISTIC Procedure Residual Chi-Square Test Chi-Square DF Pr > ChiSq 9.4609 6 0.1493 Analysis of Effects Eligible for Entry Score Effect DF Chi-Square Pr > ChiSq cell 1 1.8893 0.1693 smear 1 1.0745 0.2999 infil 1 1.8817 0.1701 li 1 7.9311 0.0049 blast 1 3.5258 0.0604 temp 1 0.6591 0.4169 Step 1. Effect li entered: Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 36.372 30.073 SC 37.668 32.665 -2 Log L 34.372 26.073 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 8.2988 1 0.0040 Score 7.9311 1 0.0049 Wald 5.9594 1 0.0146 Stepwise Regression on Cancer Remission Data 4 The LOGISTIC Procedure Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -3.7771 1.3786 7.5064 0.0061 li 1 2.8973 1.1868 5.9594 0.0146 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits li 18.124 1.770 185.563 Association of Predicted Probabilities and Observed Responses Percent Concordant 84.0 Somers' D 0.710 Percent Discordant 13.0 Gamma 0.732 Percent Tied 3.1 Tau-a 0.328 Pairs 162 c 0.855 Residual Chi-Square Test Chi-Square DF Pr > ChiSq 3.1174 5 0.6819 Analysis of Effects Eligible for Removal Wald Effect DF Chi-Square Pr > ChiSq li 1 5.9594 0.0146 NOTE: No effects for the model in Step 1 are removed. Analysis of Effects Eligible for Entry Score Effect DF Chi-Square Pr > ChiSq cell 1 1.1183 0.2903 smear 1 0.1369 0.7114 Stepwise Regression on Cancer Remission Data 5 The LOGISTIC Procedure Analysis of Effects Eligible for Entry Score Effect DF Chi-Square Pr > ChiSq infil 1 0.5715 0.4497 blast 1 0.0932 0.7601 temp 1 1.2591 0.2618 Step 2. Effect temp entered: Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 36.372 30.648 SC 37.668 34.535 -2 Log L 34.372 24.648 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 9.7239 2 0.0077 Score 8.3648 2 0.0153 Wald 5.9052 2 0.0522 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 47.8448 46.4381 1.0615 0.3029 li 1 3.3017 1.3593 5.9002 0.0151 temp 1 -52.4214 47.4897 1.2185 0.2697 Stepwise Regression on Cancer Remission Data 6 The LOGISTIC Procedure Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits li 27.158 1.892 389.856 temp <0.001 <0.001 >999.999 Association of Predicted Probabilities and Observed Responses Percent Concordant 87.0 Somers' D 0.747 Percent Discordant 12.3 Gamma 0.752 Percent Tied 0.6 Tau-a 0.345 Pairs 162 c 0.873 Residual Chi-Square Test Chi-Square DF Pr > ChiSq 2.1429 4 0.7095 Analysis of Effects Eligible for Removal Wald Effect DF Chi-Square Pr > ChiSq li 1 5.9002 0.0151 temp 1 1.2185 0.2697 NOTE: No effects for the model in Step 2 are removed. Analysis of Effects Eligible for Entry Score Effect DF Chi-Square Pr > ChiSq cell 1 1.4700 0.2254 smear 1 0.1730 0.6775 infil 1 0.8274 0.3630 blast 1 1.1013 0.2940 Step 3. Effect cell entered: Stepwise Regression on Cancer Remission Data 7 The LOGISTIC Procedure Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 36.372 29.953 SC 37.668 35.137 -2 Log L 34.372 21.953 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 12.4184 3 0.0061 Score 9.2502 3 0.0261 Wald 4.8281 3 0.1848 Analysis of Maximum Likelihood Estimates Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 67.6339 56.8875 1.4135 0.2345 cell 1 9.6521 7.7511 1.5507 0.2130 li 1 3.8671 1.7783 4.7290 0.0297 temp 1 -82.0737 61.7124 1.7687 0.1835 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits cell >999.999 0.004 >999.999 li 47.804 1.465 >999.999 temp <0.001 <0.001 >999.999 Stepwise Regression on Cancer Remission Data 8 The LOGISTIC Procedure Association of Predicted Probabilities and Observed Responses Percent Concordant 88.9 Somers' D 0.778 Percent Discordant 11.1 Gamma 0.778 Percent Tied 0.0 Tau-a 0.359 Pairs 162 c 0.889 Residual Chi-Square Test Chi-Square DF Pr > ChiSq 0.1831 3 0.9803 Analysis of Effects Eligible for Removal Wald Effect DF Chi-Square Pr > ChiSq cell 1 1.5507 0.2130 li 1 4.7290 0.0297 temp 1 1.7687 0.1835 NOTE: No effects for the model in Step 3 are removed. Analysis of Effects Eligible for Entry Score Effect DF Chi-Square Pr > ChiSq smear 1 0.0956 0.7572 infil 1 0.0844 0.7714 blast 1 0.0208 0.8852 NOTE: No (additional) effects met the 0.3 significance level for entry into the model. Stepwise Regression on Cancer Remission Data 9 The LOGISTIC Procedure Summary of Stepwise Selection Effect Number Score Wald Step Entered Removed DF In Chi-Square Chi-Square 1 li 1 1 7.9311 2 temp 1 2 1.2591 3 cell 1 3 1.4700 Summary of Stepwise Selection Step Pr > ChiSq 1 0.0049 2 0.2618 3 0.2254 Partition for the Hosmer and Lemeshow Test remiss = 1 remiss = 0 Group Total Observed Expected Observed Expected 1 3 0 0.00 3 3.00 2 3 0 0.01 3 2.99 3 3 0 0.19 3 2.81 4 3 0 0.56 3 2.44 5 4 1 1.09 3 2.91 6 3 2 1.35 1 1.65 7 3 2 1.84 1 1.16 8 3 3 2.15 0 0.85 9 2 1 1.80 1 0.20 Hosmer and Lemeshow Goodness-of-Fit Test Chi-Square DF Pr > ChiSq 6.2983 7 0.5054 Stepwise Regression on Cancer Remission Data 10 Parameter Estimates and Covariance Matrix Obs _LINK_ _TYPE_ _STATUS_ _NAME_ Intercept cell 1 LOGIT PARMS 0 Converged remiss 67.63 9.652 2 LOGIT COV 0 Converged Intercept 3236.19 157.097 3 LOGIT COV 0 Converged cell 157.10 60.079 4 LOGIT COV 0 Converged smear . . 5 LOGIT COV 0 Converged infil . . 6 LOGIT COV 0 Converged li 64.57 6.945 7 LOGIT COV 0 Converged blast . . 8 LOGIT COV 0 Converged temp -3483.23 -223.669 Obs smear infil li blast temp _LNLIKE_ 1 . . 3.8671 . -82.07 -10.9767 2 . . 64.5726 . -3483.23 -10.9767 3 . . 6.9454 . -223.67 -10.9767 4 . . . . . -10.9767 5 . . . . . -10.9767 6 . . 3.1623 . -75.35 -10.9767 7 . . . . . -10.9767 8 . . -75.3513 . 3808.42 -10.9767 Stepwise Regression on Cancer Remission Data 11 Predicted Probabilities and 95% Confidence Limits Obs remiss cell smear infil li blast temp _FROM_ _INTO_ IP_1 1 1 0.80 0.83 0.66 1.9 1.100 0.996 1 1 0.72265 2 1 0.90 0.36 0.32 1.4 0.740 0.992 1 1 0.57874 3 0 0.80 0.88 0.70 0.8 0.176 0.982 0 0 0.10460 4 0 1.00 0.87 0.87 0.7 1.053 0.986 0 0 0.28258 5 1 0.90 0.75 0.68 1.3 0.519 0.980 1 1 0.71418 6 0 1.00 0.65 0.65 0.6 0.519 0.982 0 0 0.27089 7 1 0.95 0.97 0.92 1.0 1.230 0.992 1 0 0.32156 8 0 0.95 0.87 0.83 1.9 1.354 1.020 0 1 0.60723 9 0 1.00 0.45 0.45 0.8 0.322 0.999 0 0 0.16632 10 0 0.95 0.36 0.34 0.5 0.000 1.038 0 0 0.00157 11 0 0.85 0.39 0.33 0.7 0.279 0.988 0 0 0.07285 12 0 0.70 0.76 0.53 1.2 0.146 0.982 0 0 0.17286 13 0 0.80 0.46 0.37 0.4 0.380 1.006 0 0 0.00346 14 0 0.20 0.39 0.08 0.8 0.114 0.990 0 0 0.00018 15 0 1.00 0.90 0.90 1.1 1.037 0.990 0 1 0.57122 16 1 1.00 0.84 0.84 1.9 2.064 1.020 1 1 0.71470 17 0 0.65 0.42 0.27 0.5 0.114 1.014 0 0 0.00062 18 0 1.00 0.75 0.75 1.0 1.322 1.004 0 0 0.22289 19 0 0.50 0.44 0.22 0.6 0.114 0.990 0 0 0.00154 20 1 1.00 0.63 0.63 1.1 1.072 0.986 1 1 0.64911 21 0 1.00 0.33 0.33 0.4 0.176 1.010 0 0 0.01693 22 0 0.90 0.93 0.84 0.6 1.591 1.020 0 0 0.00622 23 1 1.00 0.58 0.58 1.0 0.531 1.002 1 0 0.25261 Obs IP_0 XP_1 XP_0 _LEVEL_ phat lcl ucl 1 0.27735 0.56127 0.43873 1 0.72265 0.16892 0.97093 2 0.42126 0.52539 0.47461 1 0.57874 0.26788 0.83762 3 0.89540 0.12940 0.87060 1 0.10460 0.00781 0.63419 4 0.71742 0.32741 0.67259 1 0.28258 0.07498 0.65683 5 0.28582 0.63099 0.36901 1 0.71418 0.25218 0.94876 6 0.72911 0.32731 0.67269 1 0.27089 0.05852 0.68951 7 0.67844 0.27077 0.72923 1 0.32156 0.13255 0.59516 8 0.39277 0.90094 0.09906 1 0.60723 0.10572 0.95287 9 0.83368 0.19136 0.80864 1 0.16632 0.03018 0.56123 10 0.99843 0.00160 0.99840 1 0.00157 0.00000 0.68962 11 0.92715 0.08277 0.91723 1 0.07285 0.00614 0.49982 12 0.82714 0.36162 0.63838 1 0.17286 0.00637 0.87206 13 0.99654 0.00356 0.99644 1 0.00346 0.00001 0.46530 14 0.99982 0.00019 0.99981 1 0.00018 0.00000 0.96482 15 0.42878 0.64646 0.35354 1 0.57122 0.25303 0.83973 16 0.28530 0.52787 0.47213 1 0.71470 0.15362 0.97189 17 0.99938 0.00063 0.99937 1 0.00062 0.00000 0.62665 18 0.77711 0.26388 0.73612 1 0.22289 0.04483 0.63670 19 0.99846 0.00158 0.99842 1 0.00154 0.00000 0.79644 20 0.35089 0.57947 0.42053 1 0.64911 0.26305 0.90555 21 0.98307 0.01830 0.98170 1 0.01693 0.00029 0.50475 22 0.99378 0.00652 0.99348 1 0.00622 0.00003 0.56062 23 0.74739 0.15577 0.84423 1 0.25261 0.06137 0.63597 Stepwise Regression on Cancer Remission Data 12 Predicted Probabilities and 95% Confidence Limits Obs remiss cell smear infil li blast temp _FROM_ _INTO_ IP_1 24 0 0.95 0.32 0.30 1.6 0.886 0.988 0 1 0.87011 25 1 1.00 0.60 0.60 1.7 0.964 0.990 1 1 0.93132 26 1 1.00 0.69 0.69 0.9 0.398 0.986 1 0 0.46051 27 0 1.00 0.73 0.73 0.7 0.398 0.986 0 0 0.28258 Obs IP_0 XP_1 XP_0 _LEVEL_ phat lcl ucl 24 0.12989 0.96363 0.03637 1 0.87011 0.40910 0.98481 25 0.06868 0.91983 0.08017 1 0.93132 0.44114 0.99573 26 0.53949 0.37688 0.62312 1 0.46051 0.16612 0.78529 27 0.71742 0.32741 0.67259 1 0.28258 0.07498 0.65683