| Coefficients of Bias-Reduced Logistic Regression | ||||
| Variable | Parameter | S.E. | t-stat | 2-sided p-value |
| (Intercept) | -3.33650625869123 | 0.518219260258353 | -6.43840650968443 | 1.51899159916979e-09 |
| Treatment | 1.10880042014505 | 0.603526773244514 | 1.83720171051273 | 0.0681459356313998 |
| Useful | 1.42229015658365 | 0.601528247955397 | 2.36446112284507 | 0.0193282098592307 |
| Summary of Bias-Reduced Logistic Regression | |
| Deviance | 75.3746680766465 |
| Penalized deviance | 70.9417562385813 |
| Residual Degrees of Freedom | 151 |
| ROC Area | 0.699530516431925 |
| Hosmer–Lemeshow test | |
| Chi-square | NA |
| Degrees of Freedom | NA |
| P(>Chi) | NA |
| Fit of Logistic Regression | |||
| Index | Actual | Fitted | Error |
| 1 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 2 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 3 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 4 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 5 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 6 | 0 | 0.128507935494802 | -0.128507935494802 |
| 7 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 8 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 9 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 10 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 11 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 12 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 13 | 0 | 0.128507935494802 | -0.128507935494802 |
| 14 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 15 | 0 | 0.128507935494802 | -0.128507935494802 |
| 16 | 0 | 0.30886824546662 | -0.30886824546662 |
| 17 | 1 | 0.30886824546662 | 0.69113175453338 |
| 18 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 19 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 20 | 1 | 0.30886824546662 | 0.69113175453338 |
| 21 | 0 | 0.128507935494802 | -0.128507935494802 |
| 22 | 0 | 0.128507935494802 | -0.128507935494802 |
| 23 | 0 | 0.128507935494802 | -0.128507935494802 |
| 24 | 0 | 0.128507935494802 | -0.128507935494802 |
| 25 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 26 | 0 | 0.128507935494802 | -0.128507935494802 |
| 27 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 28 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 29 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 30 | 0 | 0.128507935494802 | -0.128507935494802 |
| 31 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 32 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 33 | 0 | 0.128507935494802 | -0.128507935494802 |
| 34 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 35 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 36 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 37 | 0 | 0.30886824546662 | -0.30886824546662 |
| 38 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 39 | 0 | 0.128507935494802 | -0.128507935494802 |
| 40 | 0 | 0.30886824546662 | -0.30886824546662 |
| 41 | 1 | 0.128507935494802 | 0.871492064505198 |
| 42 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 43 | 0 | 0.128507935494802 | -0.128507935494802 |
| 44 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 45 | 0 | 0.128507935494802 | -0.128507935494802 |
| 46 | 0 | 0.128507935494802 | -0.128507935494802 |
| 47 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 48 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 49 | 0 | 0.128507935494802 | -0.128507935494802 |
| 50 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 51 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 52 | 1 | 0.30886824546662 | 0.69113175453338 |
| 53 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 54 | 1 | 0.0343398239573444 | 0.965660176042656 |
| 55 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 56 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 57 | 0 | 0.128507935494802 | -0.128507935494802 |
| 58 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 59 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 60 | 1 | 0.30886824546662 | 0.69113175453338 |
| 61 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 62 | 0 | 0.128507935494802 | -0.128507935494802 |
| 63 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 64 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 65 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 66 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 67 | 1 | 0.30886824546662 | 0.69113175453338 |
| 68 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 69 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 70 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 71 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 72 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 73 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 74 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 75 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 76 | 0 | 0.30886824546662 | -0.30886824546662 |
| 77 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 78 | 0 | 0.128507935494802 | -0.128507935494802 |
| 79 | 1 | 0.0972899387499355 | 0.902710061250064 |
| 80 | 0 | 0.30886824546662 | -0.30886824546662 |
| 81 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 82 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 83 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 84 | 1 | 0.0343398239573444 | 0.965660176042656 |
| 85 | 0 | 0.128507935494802 | -0.128507935494802 |
| 86 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 87 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 88 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 89 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 90 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 91 | 0 | 0.128507935494802 | -0.128507935494802 |
| 92 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 93 | 0 | 0.128507935494802 | -0.128507935494802 |
| 94 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 95 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 96 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 97 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 98 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 99 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 100 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 101 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 102 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 103 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 104 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 105 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 106 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 107 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 108 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 109 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 110 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 111 | 0 | 0.30886824546662 | -0.30886824546662 |
| 112 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 113 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 114 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 115 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 116 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 117 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 118 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 119 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 120 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 121 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 122 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 123 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 124 | 0 | 0.128507935494802 | -0.128507935494802 |
| 125 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 126 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 127 | 0 | 0.128507935494802 | -0.128507935494802 |
| 128 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 129 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 130 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 131 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 132 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 133 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 134 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 135 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 136 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 137 | 0 | 0.128507935494802 | -0.128507935494802 |
| 138 | 0 | 0.30886824546662 | -0.30886824546662 |
| 139 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 140 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 141 | 1 | 0.0343398239573444 | 0.965660176042656 |
| 142 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 143 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 144 | 0 | 0.128507935494802 | -0.128507935494802 |
| 145 | 0 | 0.128507935494802 | -0.128507935494802 |
| 146 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 147 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 148 | 0 | 0.0972899387499355 | -0.0972899387499355 |
| 149 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 150 | 0 | 0.128507935494802 | -0.128507935494802 |
| 151 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| 152 | 1 | 0.0343398239573444 | 0.965660176042656 |
| 153 | 1 | 0.128507935494802 | 0.871492064505198 |
| 154 | 0 | 0.0343398239573444 | -0.0343398239573444 |
| Type I & II errors for various threshold values | ||
| Threshold | Type I | Type II |
| 0.01 | 0 | 1 |
| 0.02 | 0 | 1 |
| 0.03 | 0 | 1 |
| 0.04 | 0.333333333333333 | 0.429577464788732 |
| 0.05 | 0.333333333333333 | 0.429577464788732 |
| 0.06 | 0.333333333333333 | 0.429577464788732 |
| 0.07 | 0.333333333333333 | 0.429577464788732 |
| 0.08 | 0.333333333333333 | 0.429577464788732 |
| 0.09 | 0.333333333333333 | 0.429577464788732 |
| 0.1 | 0.416666666666667 | 0.23943661971831 |
| 0.11 | 0.416666666666667 | 0.23943661971831 |
| 0.12 | 0.416666666666667 | 0.23943661971831 |
| 0.13 | 0.583333333333333 | 0.0492957746478873 |
| 0.14 | 0.583333333333333 | 0.0492957746478873 |
| 0.15 | 0.583333333333333 | 0.0492957746478873 |
| 0.16 | 0.583333333333333 | 0.0492957746478873 |
| 0.17 | 0.583333333333333 | 0.0492957746478873 |
| 0.18 | 0.583333333333333 | 0.0492957746478873 |
| 0.19 | 0.583333333333333 | 0.0492957746478873 |
| 0.2 | 0.583333333333333 | 0.0492957746478873 |
| 0.21 | 0.583333333333333 | 0.0492957746478873 |
| 0.22 | 0.583333333333333 | 0.0492957746478873 |
| 0.23 | 0.583333333333333 | 0.0492957746478873 |
| 0.24 | 0.583333333333333 | 0.0492957746478873 |
| 0.25 | 0.583333333333333 | 0.0492957746478873 |
| 0.26 | 0.583333333333333 | 0.0492957746478873 |
| 0.27 | 0.583333333333333 | 0.0492957746478873 |
| 0.28 | 0.583333333333333 | 0.0492957746478873 |
| 0.29 | 0.583333333333333 | 0.0492957746478873 |
| 0.3 | 0.583333333333333 | 0.0492957746478873 |
| 0.31 | 1 | 0 |
| 0.32 | 1 | 0 |
| 0.33 | 1 | 0 |
| 0.34 | 1 | 0 |
| 0.35 | 1 | 0 |
| 0.36 | 1 | 0 |
| 0.37 | 1 | 0 |
| 0.38 | 1 | 0 |
| 0.39 | 1 | 0 |
| 0.4 | 1 | 0 |
| 0.41 | 1 | 0 |
| 0.42 | 1 | 0 |
| 0.43 | 1 | 0 |
| 0.44 | 1 | 0 |
| 0.45 | 1 | 0 |
| 0.46 | 1 | 0 |
| 0.47 | 1 | 0 |
| 0.48 | 1 | 0 |
| 0.49 | 1 | 0 |
| 0.5 | 1 | 0 |
| 0.51 | 1 | 0 |
| 0.52 | 1 | 0 |
| 0.53 | 1 | 0 |
| 0.54 | 1 | 0 |
| 0.55 | 1 | 0 |
| 0.56 | 1 | 0 |
| 0.57 | 1 | 0 |
| 0.58 | 1 | 0 |
| 0.59 | 1 | 0 |
| 0.6 | 1 | 0 |
| 0.61 | 1 | 0 |
| 0.62 | 1 | 0 |
| 0.63 | 1 | 0 |
| 0.64 | 1 | 0 |
| 0.65 | 1 | 0 |
| 0.66 | 1 | 0 |
| 0.67 | 1 | 0 |
| 0.68 | 1 | 0 |
| 0.69 | 1 | 0 |
| 0.7 | 1 | 0 |
| 0.71 | 1 | 0 |
| 0.72 | 1 | 0 |
| 0.73 | 1 | 0 |
| 0.74 | 1 | 0 |
| 0.75 | 1 | 0 |
| 0.76 | 1 | 0 |
| 0.77 | 1 | 0 |
| 0.78 | 1 | 0 |
| 0.79 | 1 | 0 |
| 0.8 | 1 | 0 |
| 0.81 | 1 | 0 |
| 0.82 | 1 | 0 |
| 0.83 | 1 | 0 |
| 0.84 | 1 | 0 |
| 0.85 | 1 | 0 |
| 0.86 | 1 | 0 |
| 0.87 | 1 | 0 |
| 0.88 | 1 | 0 |
| 0.89 | 1 | 0 |
| 0.9 | 1 | 0 |
| 0.91 | 1 | 0 |
| 0.92 | 1 | 0 |
| 0.93 | 1 | 0 |
| 0.94 | 1 | 0 |
| 0.95 | 1 | 0 |
| 0.96 | 1 | 0 |
| 0.97 | 1 | 0 |
| 0.98 | 1 | 0 |
| 0.99 | 1 | 0 |
