R Markdown
set.seed(123)
n <- 200
u <- runif(n)
x1 <- round(60*(-(log(1-u)/12)))
x1
## [1] 2 8 3 11 14 0 4 11 4 3 16 3 6 4 1 12 1 0 2 15 11 6 5 26 5
## [26] 6 4 5 2 1 16 12 6 8 0 3 7 1 2 1 1 3 3 2 1 1 1 3 2 10
## [51] 0 3 8 1 4 1 1 7 11 2 5 0 2 2 8 3 8 8 8 3 7 5 6 0 3
## [76] 1 2 5 2 1 1 6 3 8 1 3 21 11 11 1 1 5 2 5 2 1 8 0 3 4
## [101] 5 2 3 15 3 11 12 5 3 1 14 2 0 15 6 1 4 15 4 3 5 2 2 1 2
## [126] 21 1 0 1 6 5 11 6 7 4 5 9 8 20 3 2 3 0 1 9 1 1 0 1 7
## [151] 9 3 2 1 1 2 4 1 3 1 3 2 5 2 2 4 7 1 3 2 5 1 10 7 6
## [176] 5 2 4 10 4 9 2 6 2 5 3 2 4 12 12 2 2 21 5 14 3 3 5 1 4
set.seed(1234)
x2 <- round(runif(n))
x2
## [1] 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0
## [38] 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1
## [75] 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1
## [112] 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1
## [149] 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 1
## [186] 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1
set.seed(123)
x3 <- round(runif(n))
x3
## [1] 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1
## [38] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0
## [75] 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1
## [112] 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0
## [149] 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1
## [186] 0 0 1 1 1 0 0 1 1 1 0 0 1 0 1
set.seed(222)
x4 <- round(rnorm(n,3,0.5),2)
x4
## [1] 3.74 3.00 3.69 2.81 3.09 2.88 2.39 3.78 3.21 2.40 3.53 2.35 2.65 3.30 2.90
## [16] 2.41 2.00 3.00 3.26 2.63 3.36 3.36 2.67 3.75 2.28 1.92 3.20 2.80 2.85 3.67
## [31] 2.59 3.34 2.89 2.94 2.90 3.20 3.33 3.05 2.91 3.47 3.10 3.25 2.72 3.56 4.10
## [46] 3.16 2.53 3.41 2.81 3.17 3.30 3.26 2.52 2.39 2.90 3.53 3.19 3.62 3.16 2.48
## [61] 2.43 3.62 3.39 3.37 3.03 3.42 3.10 3.73 2.77 1.61 3.03 2.97 2.41 1.74 3.41
## [76] 3.13 2.97 3.34 3.01 3.27 3.34 2.40 2.38 3.11 2.27 2.94 3.27 3.36 2.21 3.55
## [91] 2.83 3.31 3.25 3.84 3.19 3.12 3.21 2.41 2.68 3.03 2.89 3.17 3.27 3.13 3.19
## [106] 2.79 3.40 2.82 4.68 2.82 2.96 2.68 2.52 2.50 2.86 3.21 2.45 2.69 3.17 2.77
## [121] 4.37 3.01 3.16 2.97 2.64 2.83 3.12 3.30 2.81 2.81 1.86 2.94 3.31 3.04 3.29
## [136] 3.06 2.52 2.05 2.26 3.28 3.68 3.39 3.19 3.47 3.19 3.83 3.83 3.41 2.11 3.33
## [151] 2.58 2.75 2.05 3.70 3.21 2.84 1.90 3.14 3.29 3.15 3.44 2.81 3.27 2.70 3.46
## [166] 4.47 2.41 2.44 2.64 2.92 3.47 2.40 2.33 3.12 2.57 2.88 2.75 2.78 3.05 2.55
## [181] 3.25 3.51 3.58 2.33 3.57 3.40 3.27 2.95 3.30 2.14 2.17 2.94 3.50 3.43 3.52
## [196] 2.95 3.05 2.47 2.57 2.47
set.seed(222)
x44 <- round(rnorm(n,2.7,0.5),2)
x44
## [1] 3.44 2.70 3.39 2.51 2.79 2.58 2.09 3.48 2.91 2.10 3.23 2.05 2.35 3.00 2.60
## [16] 2.11 1.70 2.70 2.96 2.33 3.06 3.06 2.37 3.45 1.98 1.62 2.90 2.50 2.55 3.37
## [31] 2.29 3.04 2.59 2.64 2.60 2.90 3.03 2.75 2.61 3.17 2.80 2.95 2.42 3.26 3.80
## [46] 2.86 2.23 3.11 2.51 2.87 3.00 2.96 2.22 2.09 2.60 3.23 2.89 3.32 2.86 2.18
## [61] 2.13 3.32 3.09 3.07 2.73 3.12 2.80 3.43 2.47 1.31 2.73 2.67 2.11 1.44 3.11
## [76] 2.83 2.67 3.04 2.71 2.97 3.04 2.10 2.08 2.81 1.97 2.64 2.97 3.06 1.91 3.25
## [91] 2.53 3.01 2.95 3.54 2.89 2.82 2.91 2.11 2.38 2.73 2.59 2.87 2.97 2.83 2.89
## [106] 2.49 3.10 2.52 4.38 2.52 2.66 2.38 2.22 2.20 2.56 2.91 2.15 2.39 2.87 2.47
## [121] 4.07 2.71 2.86 2.67 2.34 2.53 2.82 3.00 2.51 2.51 1.56 2.64 3.01 2.74 2.99
## [136] 2.76 2.22 1.75 1.96 2.98 3.38 3.09 2.89 3.17 2.89 3.53 3.53 3.11 1.81 3.03
## [151] 2.28 2.45 1.75 3.40 2.91 2.54 1.60 2.84 2.99 2.85 3.14 2.51 2.97 2.40 3.16
## [166] 4.17 2.11 2.14 2.34 2.62 3.17 2.10 2.03 2.82 2.27 2.58 2.45 2.48 2.75 2.25
## [181] 2.95 3.21 3.28 2.03 3.27 3.10 2.97 2.65 3.00 1.84 1.87 2.64 3.20 3.13 3.22
## [196] 2.65 2.75 2.17 2.27 2.17
summary(x44)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.310 2.380 2.745 2.703 3.010 4.380
b0 <- -9
b1 <- 1.5
b2 <- 1
b3 <- 1.7
b4 <- 1.2
set.seed(1)
datapendukung <- b0+(b1*x1)+(b2*x2)+(b3*x3)+(b4*x4)
datapendukung
## [1] -1.512 9.300 0.928 13.572 18.408 -4.544 1.568 13.736 3.552 -0.620
## [11] 21.936 -0.680 4.880 3.660 -4.020 14.592 -5.100 -5.400 -2.088 18.356
## [21] 13.232 5.732 3.404 36.200 2.936 5.004 3.540 4.560 -1.580 -3.096
## [31] 19.808 14.708 5.168 9.228 -5.520 0.340 7.196 -3.840 -1.508 -2.336
## [41] -2.780 0.400 -1.236 -0.728 -2.580 -2.708 -3.464 -0.408 -2.628 12.504
## [51] -5.040 -0.588 8.724 -3.632 2.180 -2.264 -3.672 8.544 12.992 -2.024
## [61] 4.116 -4.656 -1.932 -1.956 8.336 0.604 8.420 10.176 8.024 -1.568
## [71] 6.836 4.764 4.592 -5.912 -0.408 -2.744 -2.436 4.208 -2.388 -2.576
## [81] -2.492 4.580 -1.644 9.432 -4.776 0.028 28.124 13.232 11.852 -2.240
## [91] -4.104 5.172 -2.100 4.808 -2.172 -2.756 8.552 -6.108 -1.284 3.336
## [101] 3.668 -1.196 -0.576 18.956 -0.672 12.548 14.780 3.584 1.116 -4.116
## [111] 18.252 -2.784 -4.976 18.200 5.132 -2.648 2.640 18.428 2.504 -0.176
## [121] 6.444 -1.388 -1.208 -2.936 -2.832 27.596 -3.756 -4.040 -4.128 5.072
## [131] 3.432 13.728 5.672 6.848 3.648 3.872 10.224 8.160 26.412 0.436
## [141] -0.584 0.568 -5.172 -3.336 10.028 -1.904 -1.904 -3.908 -3.968 8.196
## [151] 9.296 -1.200 -3.540 -2.060 -3.648 -1.592 1.980 -2.732 -0.552 -2.720
## [161] 1.328 -1.628 4.124 -2.760 -1.848 5.064 6.092 -4.572 -0.332 -2.496
## [171] 5.364 -3.620 11.496 6.944 4.784 4.656 -2.700 3.036 11.360 1.760
## [181] 10.100 -1.788 6.996 -3.204 5.484 -0.420 -1.076 3.240 14.660 14.268
## [191] -2.396 -1.472 28.400 5.316 18.924 0.040 0.160 4.164 -3.416 2.664
p <- exp(datapendukung)/(1+exp(datapendukung))
p
## [1] 0.180642582 0.999908584 0.716669353 0.999998724 0.999999990 0.010518973
## [7] 0.827498306 0.999998917 0.972131661 0.349781451 1.000000000 0.336261303
## [13] 0.992460265 0.974913038 0.017636340 0.999999540 0.006059801 0.004496273
## [19] 0.110268640 0.999999989 0.999998208 0.996769878 0.967829312 1.000000000
## [25] 0.949597623 0.993333689 0.971804712 0.989646262 0.170795482 0.043272553
## [31] 0.999999998 0.999999590 0.994336311 0.999901760 0.003989865 0.584190523
## [37] 0.999250983 0.021041347 0.181235382 0.088185019 0.058414556 0.598687660
## [43] 0.225133011 0.325633767 0.070436731 0.062502942 0.030354081 0.399391780
## [49] 0.067357984 0.999996288 0.006432108 0.357093879 0.999837391 0.025780958
## [55] 0.898439072 0.094148676 0.024795137 0.999805328 0.999997722 0.116706015
## [61] 0.983952112 0.009414921 0.126529376 0.123900592 0.999760328 0.646570909
## [67] 0.999779634 0.999961928 0.999672600 0.172501694 0.998926761 0.991540754
## [73] 0.989969066 0.002699461 0.399391780 0.060426403 0.080468389 0.985341963
## [79] 0.084092345 0.070699083 0.076420916 0.989849199 0.161921517 0.999919888
## [85] 0.008359185 0.506999543 1.000000000 0.999998208 0.999992876 0.096215542
## [91] 0.016238476 0.994358793 0.109096821 0.991901942 0.102293229 0.059748686
## [97] 0.999806879 0.002220057 0.216870104 0.965643384 0.975107957 0.232187558
## [103] 0.359853512 0.999999994 0.338049152 0.999996448 0.999999619 0.972985620
## [109] 0.753246004 0.016047888 0.999999988 0.058194935 0.006854308 0.999999988
## [115] 0.994129922 0.066112385 0.933391964 0.999999990 0.924421760 0.456113228
## [121] 0.998412490 0.199727237 0.230055119 0.050402377 0.055619253 1.000000000
## [127] 0.022843058 0.017293157 0.015859500 0.993769198 0.968689784 0.999998909
## [133] 0.996570823 0.998939549 0.974617868 0.979607804 0.999963712 0.999714219
## [139] 1.000000000 0.607305499 0.358012714 0.638301558 0.005641207 0.034356616
## [145] 0.999955856 0.129656423 0.129656423 0.019685329 0.018560221 0.999724322
## [151] 0.999908218 0.231475217 0.028195288 0.113045830 0.025382132 0.169102697
## [157] 0.878681162 0.061111309 0.365400518 0.061803466 0.790509619 0.164104525
## [163] 0.984077947 0.059524366 0.136107891 0.993719466 0.997744217 0.010231499
## [169] 0.417754072 0.076139071 0.995339680 0.026084075 0.999989829 0.999036525
## [175] 0.991706869 0.990585079 0.062973356 0.954174244 0.999988348 0.853209660
## [181] 0.999958922 0.143318104 0.999085301 0.039015473 0.995864488 0.396516750
## [187] 0.254263726 0.962312109 0.999999570 0.999999364 0.083478225 0.186638814
## [193] 1.000000000 0.995111649 0.999999994 0.509998667 0.539914885 0.984692703
## [199] 0.031799150 0.934868648
set.seed(2)
y <- rbinom(n,1,p)
y
## [1] 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1
## [38] 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0
## [75] 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1
## [112] 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0
## [149] 0 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1
## [186] 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1
datagab <- data.frame(y,x1,x2,x3,x4)
datagab
## y x1 x2 x3 x4
## 1 0 2 0 0 3.74
## 2 1 8 1 1 3.00
## 3 1 3 1 0 3.69
## 4 1 11 1 1 2.81
## 5 1 14 1 1 3.09
## 6 0 0 1 0 2.88
## 7 1 4 0 1 2.39
## 8 1 11 0 1 3.78
## 9 1 4 1 1 3.21
## 10 0 3 1 0 2.40
## 11 1 16 1 1 3.53
## 12 0 3 1 0 2.35
## 13 1 6 0 1 2.65
## 14 1 4 1 1 3.30
## 15 0 1 0 0 2.90
## 16 1 12 1 1 2.41
## 17 0 1 0 0 2.00
## 18 0 0 0 0 3.00
## 19 0 2 0 0 3.26
## 20 1 15 0 1 2.63
## 21 1 11 0 1 3.36
## 22 1 6 0 1 3.36
## 23 1 5 0 1 2.67
## 24 1 26 0 1 3.75
## 25 1 5 0 1 2.28
## 26 1 6 1 1 1.92
## 27 1 4 1 1 3.20
## 28 1 5 1 1 2.80
## 29 1 2 1 0 2.85
## 30 0 1 0 0 3.67
## 31 1 16 0 1 2.59
## 32 1 12 0 1 3.34
## 33 1 6 0 1 2.89
## 34 1 8 1 1 2.94
## 35 0 0 0 0 2.90
## 36 0 3 1 0 3.20
## 37 1 7 0 1 3.33
## 38 0 1 0 0 3.05
## 39 0 2 1 0 2.91
## 40 0 1 1 0 3.47
## 41 1 1 1 0 3.10
## 42 1 3 1 0 3.25
## 43 0 3 0 0 2.72
## 44 0 2 1 0 3.56
## 45 1 1 0 0 4.10
## 46 0 1 1 0 3.16
## 47 1 1 1 0 2.53
## 48 0 3 0 0 3.41
## 49 0 2 0 0 2.81
## 50 1 10 1 1 3.17
## 51 0 0 0 0 3.30
## 52 0 3 0 0 3.26
## 53 1 8 1 1 2.52
## 54 0 1 1 0 2.39
## 55 1 4 0 1 2.90
## 56 0 1 1 0 3.53
## 57 0 1 0 0 3.19
## 58 1 7 1 1 3.62
## 59 1 11 0 1 3.16
## 60 0 2 1 0 2.48
## 61 1 5 1 1 2.43
## 62 0 0 0 0 3.62
## 63 0 2 0 0 3.39
## 64 0 2 0 0 3.37
## 65 1 8 0 1 3.03
## 66 1 3 1 0 3.42
## 67 1 8 0 1 3.10
## 68 1 8 1 1 3.73
## 69 1 8 0 1 2.77
## 70 0 3 1 0 1.61
## 71 1 7 0 1 3.03
## 72 1 5 1 1 2.97
## 73 1 6 0 1 2.41
## 74 0 0 1 0 1.74
## 75 0 3 0 0 3.41
## 76 0 1 1 0 3.13
## 77 0 2 0 0 2.97
## 78 1 5 0 1 3.34
## 79 0 2 0 0 3.01
## 80 0 1 1 0 3.27
## 81 0 1 1 0 3.34
## 82 1 6 0 1 2.40
## 83 0 3 0 0 2.38
## 84 1 8 1 1 3.11
## 85 0 1 0 0 2.27
## 86 0 3 1 0 2.94
## 87 1 21 0 1 3.27
## 88 1 11 0 1 3.36
## 89 1 11 0 1 2.21
## 90 0 1 1 0 3.55
## 91 0 1 0 0 2.83
## 92 1 5 1 1 3.31
## 93 0 2 0 0 3.25
## 94 1 5 0 1 3.84
## 95 0 2 0 0 3.19
## 96 0 1 1 0 3.12
## 97 1 8 0 1 3.21
## 98 0 0 0 0 2.41
## 99 0 3 0 0 2.68
## 100 1 4 1 1 3.03
## 101 1 5 0 1 2.89
## 102 0 2 1 0 3.17
## 103 1 3 0 0 3.27
## 104 1 15 0 1 3.13
## 105 0 3 0 0 3.19
## 106 1 11 0 1 2.79
## 107 1 12 0 1 3.40
## 108 1 5 0 1 2.82
## 109 1 3 0 0 4.68
## 110 0 1 0 0 2.82
## 111 1 14 1 1 2.96
## 112 0 2 0 0 2.68
## 113 0 0 1 0 2.52
## 114 1 15 0 1 2.50
## 115 1 6 0 1 2.86
## 116 0 1 1 0 3.21
## 117 1 4 1 1 2.45
## 118 1 15 0 1 2.69
## 119 0 4 0 1 3.17
## 120 1 3 1 0 2.77
## 121 1 5 1 1 4.37
## 122 0 2 1 0 3.01
## 123 1 2 1 0 3.16
## 124 0 1 1 0 2.97
## 125 0 2 0 0 2.64
## 126 1 21 0 1 2.83
## 127 0 1 0 0 3.12
## 128 0 0 1 0 3.30
## 129 0 1 0 0 2.81
## 130 1 6 0 1 2.81
## 131 1 5 1 1 1.86
## 132 1 11 1 1 2.94
## 133 1 6 0 1 3.31
## 134 1 7 0 1 3.04
## 135 1 4 1 1 3.29
## 136 1 5 0 1 3.06
## 137 1 9 1 1 2.52
## 138 1 8 1 1 2.05
## 139 1 20 1 1 2.26
## 140 1 3 1 0 3.28
## 141 0 2 1 0 3.68
## 142 1 3 1 0 3.39
## 143 0 0 0 0 3.19
## 144 0 1 0 0 3.47
## 145 1 9 0 1 3.19
## 146 0 1 1 0 3.83
## 147 0 1 1 0 3.83
## 148 0 0 1 0 3.41
## 149 0 1 1 0 2.11
## 150 1 7 1 1 3.33
## 151 1 9 0 1 2.58
## 152 0 3 0 0 2.75
## 153 0 2 0 0 2.05
## 154 0 1 1 0 3.70
## 155 0 1 0 0 3.21
## 156 0 2 1 0 2.84
## 157 1 4 1 1 1.90
## 158 0 1 1 0 3.14
## 159 0 3 0 0 3.29
## 160 0 1 1 0 3.15
## 161 0 3 0 1 3.44
## 162 1 2 1 0 2.81
## 163 1 5 0 1 3.27
## 164 0 2 0 0 2.70
## 165 0 2 0 0 3.46
## 166 1 4 1 1 4.47
## 167 1 7 0 1 2.41
## 168 0 1 0 0 2.44
## 169 0 3 1 0 2.64
## 170 0 2 0 0 2.92
## 171 1 5 1 1 3.47
## 172 0 1 1 0 2.40
## 173 1 10 1 1 2.33
## 174 1 7 0 1 3.12
## 175 1 6 0 1 2.57
## 176 1 5 1 1 2.88
## 177 0 2 0 0 2.75
## 178 1 4 1 1 2.78
## 179 1 10 0 1 3.05
## 180 1 4 0 1 2.55
## 181 1 9 0 1 3.25
## 182 0 2 0 0 3.51
## 183 1 6 1 1 3.58
## 184 0 2 0 0 2.33
## 185 1 5 1 1 3.57
## 186 1 3 0 0 3.40
## 187 0 2 1 0 3.27
## 188 1 4 1 1 2.95
## 189 1 12 0 1 3.30
## 190 1 12 1 1 2.14
## 191 0 2 1 0 2.17
## 192 0 2 1 0 2.94
## 193 1 21 0 1 3.50
## 194 1 5 1 1 3.43
## 195 1 14 1 1 3.52
## 196 1 3 1 0 2.95
## 197 1 3 1 0 3.05
## 198 1 5 1 1 2.47
## 199 0 1 1 0 2.57
## 200 1 4 1 1 2.47
modelreglog <- glm(y~x1+x2+x3+x4, family = binomial(link = "logit"), data=datagab)
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
summary(modelreglog)
##
## Call:
## glm(formula = y ~ x1 + x2 + x3 + x4, family = binomial(link = "logit"),
## data = datagab)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -11.4256 2.8300 -4.037 5.41e-05 ***
## x1 1.6919 0.4170 4.057 4.96e-05 ***
## x2 2.2123 0.7286 3.036 0.00239 **
## x3 1.6773 1.1458 1.464 0.14325
## x4 1.5597 0.6810 2.290 0.02201 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 274.372 on 199 degrees of freedom
## Residual deviance: 73.361 on 195 degrees of freedom
## AIC: 83.361
##
## Number of Fisher Scoring iterations: 8