library(lmtest)
## Warning: package 'lmtest' was built under R version 4.6.1
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(MASS)
## Warning: package 'MASS' was built under R version 4.6.1
library(car)
## Loading required package: carData
library(pastecs)
## Warning: package 'pastecs' was built under R version 4.6.1
library(pracma)
## Warning: package 'pracma' was built under R version 4.6.1
##
## Attaching package: 'pracma'
## The following object is masked from 'package:car':
##
## logit
library(Matrix)
## Warning: package 'Matrix' was built under R version 4.6.1
##
## Attaching package: 'Matrix'
## The following objects are masked from 'package:pracma':
##
## expm, lu, tril, triu
data=read.table(file.choose(),header=TRUE)
data
## X1 X2 X3 X4 X5 X6 Y
## 1 12.10 34.05 8.50 2.22 64.81 40.2 73.84
## 2 12.45 44.19 10.13 2.20 68.65 32.9 76.87
## 3 13.39 38.66 8.99 1.68 69.07 29.7 77.19
## 4 14.38 26.30 10.04 2.16 69.18 23.6 69.08
## 5 17.86 23.36 10.27 1.46 68.34 33.4 78.27
## 6 13.38 10.06 10.87 1.38 70.14 30.1 84.72
## 7 18.78 31.46 9.29 0.70 67.29 29.5 76.69
## 8 16.64 37.08 9.37 0.56 69.15 25.2 77.12
## 9 17.92 17.76 9.91 1.68 65.61 30.7 77.54
## 10 19.15 40.31 9.02 1.74 67.78 34.1 46.10
## 11 12.12 27.66 9.67 0.46 71.66 32.9 80.83
## 12 15.43 24.17 9.20 1.70 65.48 27.9 78.05
## 13 18.82 20.48 8.39 6.33 65.92 15.4 77.06
## 14 12.42 26.92 8.98 4.54 67.55 34.0 79.69
## 15 17.25 24.00 9.14 2.19 69.60 31.6 76.60
## 16 12.51 14.56 9.58 1.27 70.04 35.9 81.16
## 17 18.31 61.03 10.30 1.15 69.64 32.2 46.98
## 18 18.40 32.95 9.85 0.46 70.60 29.4 78.95
## 19 7.04 0.11 12.74 0.01 72.02 21.7 87.96
## 20 14.59 3.95 10.94 0.20 70.98 25.6 73.80
## 21 10.73 1.81 11.31 0.08 72.06 20.7 83.03
## 22 10.53 6.24 11.27 0.17 69.78 25.6 78.05
## 23 16.41 55.11 8.78 1.40 64.41 29.6 41.12
## 24 11.50 35.19 8.96 1.42 67.90 23.8 73.81
## 25 8.54 51.69 10.19 2.22 69.57 27.4 78.14
## 26 7.01 55.31 9.57 3.22 65.56 15.6 77.29
## 27 15.10 64.15 7.06 0.87 70.34 20.3 72.41
## 28 9.23 26.92 8.97 1.85 69.64 16.9 79.92
## 29 7.98 41.28 10.28 1.51 72.28 24.7 82.28
## 30 3.44 14.42 10.41 0.51 72.31 33.8 86.20
## 31 7.87 41.91 9.78 1.78 72.20 17.7 82.42
## 32 8.21 24.26 9.18 1.82 69.09 11.0 76.65
## 33 7.99 41.36 9.69 1.39 70.77 20.2 76.96
## 34 7.47 36.67 10.08 2.02 70.11 32.6 82.50
## 35 8.04 25.69 10.50 2.06 71.24 28.0 84.33
## 36 8.86 55.14 9.37 3.08 63.47 20.7 70.54
## 37 16.39 63.23 6.99 1.20 69.58 31.8 65.87
## 38 7.54 56.82 9.90 3.57 66.89 28.9 75.32
## 39 8.69 49.20 9.93 3.18 70.27 18.4 81.16
## 40 11.66 47.18 9.20 2.85 72.24 22.4 80.35
## 41 7.44 33.30 9.14 1.51 69.59 14.4 85.35
## 42 11.38 35.54 9.13 0.72 67.88 17.7 78.37
## 43 8.79 42.52 9.74 3.26 67.82 21.8 75.14
## 44 7.89 39.91 9.86 2.67 67.71 17.7 76.75
## 45 8.06 24.70 9.32 2.79 69.54 16.0 57.85
## 46 9.08 37.52 9.28 2.18 70.25 9.6 80.30
## 47 21.79 46.34 7.01 1.41 70.24 20.3 73.17
## 48 22.81 85.31 7.19 0.69 69.96 28.9 65.35
## 49 8.00 2.92 11.59 0.02 73.93 5.8 90.25
## 50 7.24 8.31 11.56 0.04 74.75 7.7 89.82
## 51 11.42 4.27 10.45 0.01 70.18 10.6 81.03
## 52 12.21 1.10 10.13 0.07 64.28 5.7 74.59
## 53 4.79 5.42 11.07 0.05 73.13 19.4 88.22
## 54 9.49 28.45 10.88 0.04 71.63 10.4 77.31
## 55 6.85 37.86 11.11 0.14 70.20 26.1 71.32
## 56 14.78 20.47 8.52 0.25 72.09 18.9 66.12
## 57 7.34 15.76 9.13 2.78 71.52 27.0 86.71
## 58 7.13 32.61 8.57 3.29 69.56 25.4 82.56
## 59 5.88 27.30 9.23 3.62 67.02 28.5 82.05
## 60 4.16 15.74 9.56 1.37 70.84 18.5 89.40
## 61 6.34 23.54 8.86 0.92 69.70 19.4 85.08
## 62 6.60 20.57 9.63 1.95 73.23 20.1 86.92
## 63 6.80 33.84 8.37 3.12 70.30 28.6 82.59
## 64 6.80 33.26 8.37 2.69 68.29 29.4 82.09
## 65 13.72 72.89 7.85 8.11 65.10 33.7 53.86
## 66 5.56 26.93 9.23 2.33 72.24 17.7 84.98
## 67 6.45 26.75 9.36 6.80 68.71 14.7 85.60
## 68 6.92 34.36 9.69 2.10 68.53 29.7 80.91
## 69 4.17 4.19 11.60 0.10 74.16 24.2 89.63
## 70 3.05 2.11 11.27 0.05 74.39 16.3 92.90
## 71 2.27 6.49 10.45 0.44 70.69 19.5 83.45
## 72 5.24 12.33 12.23 0.05 73.23 15.8 87.05
## 73 4.11 2.64 11.77 0.02 75.13 20.1 92.86
## 74 5.44 3.37 11.25 0.09 74.43 19.8 89.33
## 75 4.20 14.32 10.93 0.07 70.95 17.7 84.08
## 76 7.04 24.67 9.44 4.21 71.42 7.6 59.69
## 77 6.06 16.34 8.61 5.19 70.69 12.7 60.71
## 78 6.31 36.88 9.51 4.00 71.79 17.9 65.75
## 79 5.64 73.12 7.77 5.86 68.62 18.8 69.30
## 80 8.15 13.63 9.07 7.97 72.00 10.1 71.59
## 81 9.72 15.70 9.26 4.42 70.84 15.9 58.88
## 82 7.07 37.28 8.89 3.59 70.99 16.6 68.67
## 83 5.23 9.90 10.01 4.77 71.64 10.4 77.06
## 84 8.07 28.94 9.01 4.29 69.13 23.0 73.80
## 85 22.98 89.58 8.47 5.21 68.41 19.6 71.15
## 86 3.16 7.83 11.82 0.08 73.02 8.7 92.20
## 87 3.21 13.10 10.35 1.18 71.67 14.9 76.30
## 88 7.54 32.30 8.25 3.39 70.55 8.7 83.76
## 89 8.90 50.04 8.61 3.48 71.75 14.9 75.01
## 90 8.54 49.63 8.20 4.47 69.70 4.8 65.64
## 91 9.45 28.95 8.42 4.41 71.22 10.1 74.13
## 92 4.43 29.18 9.09 3.41 71.84 12.0 68.51
## 93 9.79 53.10 8.59 4.23 68.67 14.1 69.60
## 94 10.85 49.09 8.15 4.79 66.98 23.7 69.99
## 95 5.29 26.74 8.53 2.66 68.43 13.7 73.39
## 96 6.46 28.31 8.40 5.11 70.49 22.7 71.36
## 97 8.24 9.34 11.34 0.04 73.29 13.5 85.88
## 98 3.00 8.00 10.04 0.32 72.86 4.1 87.06
## 99 11.46 27.60 9.40 1.75 68.85 15.7 73.01
## 100 13.15 31.03 7.51 6.17 69.31 32.5 79.54
## 101 10.93 30.27 8.12 2.57 69.72 25.9 75.62
## 102 15.00 40.77 8.73 1.94 66.87 7.8 75.19
## 103 14.13 39.52 7.85 3.73 68.95 21.9 77.66
## 104 14.90 28.89 8.14 6.17 69.51 16.5 79.48
## 105 9.58 55.26 7.60 5.17 69.76 20.4 79.17
## 106 9.99 37.40 8.40 1.46 69.78 9.3 85.17
## 107 10.36 49.77 8.40 2.53 67.88 23.0 75.37
## 108 13.28 28.50 8.35 1.34 66.33 22.9 77.55
## 109 11.80 71.69 7.83 2.38 65.73 32.6 67.42
## 110 10.91 31.52 7.53 1.98 68.96 15.4 78.79
## 111 18.26 44.73 7.70 6.83 66.37 33.1 59.58
## 112 10.22 2.15 11.09 0.04 71.99 18.9 83.62
## 113 8.88 41.12 9.68 0.87 67.70 23.3 57.79
## 114 12.65 33.15 9.51 0.26 70.25 17.5 66.10
## 115 11.23 40.09 10.31 0.24 71.27 15.4 68.11
## 116 17.51 59.02 9.53 1.05 68.40 24.0 74.91
## 117 14.79 55.84 9.31 1.16 69.22 28.6 73.11
## 118 11.29 43.03 8.22 3.15 68.77 21.6 72.62
## 119 17.83 46.75 8.25 3.87 67.27 14.3 74.75
## 120 18.00 57.84 8.20 2.06 68.35 26.0 71.61
## 121 10.76 36.02 8.87 4.18 67.30 27.1 76.57
## 122 11.15 44.85 8.49 3.00 63.93 15.7 77.06
## 123 14.12 55.68 8.41 0.95 68.46 22.1 72.43
## 124 9.40 60.54 7.57 1.55 68.52 23.2 62.14
## 125 14.71 12.26 11.90 0.05 70.74 6.7 78.72
## 126 12.79 20.90 8.07 0.92 69.97 10.3 84.46
## 127 10.65 31.53 8.00 1.41 70.29 16.7 84.93
## 128 17.17 60.90 8.55 1.23 69.83 23.5 76.82
## 129 11.17 52.76 8.57 1.90 68.13 24.6 76.18
## 130 8.04 22.06 7.89 2.34 70.42 9.8 88.78
## 131 10.52 53.84 7.35 2.13 69.23 17.1 76.40
## 132 13.80 30.49 8.34 2.07 71.25 14.2 85.22
## 133 11.02 44.87 7.83 2.51 69.91 22.7 79.61
## 134 12.89 43.85 8.21 0.94 69.74 10.0 80.85
## 135 9.14 11.49 8.56 0.37 71.05 15.8 87.35
## 136 6.73 22.71 7.20 3.02 68.75 5.0 88.18
## 137 7.25 55.59 8.05 1.35 70.42 10.5 83.74
## 138 13.49 59.30 8.75 4.24 64.29 16.1 75.77
## 139 7.77 8.71 10.94 0.03 71.91 13.4 84.64
## 140 7.28 9.50 10.80 0.04 72.12 7.1 85.78
## 141 4.32 11.86 8.79 1.69 71.60 23.2 74.35
## 142 6.46 8.85 9.16 2.66 71.54 20.8 62.34
## 143 3.11 23.99 7.49 5.04 68.98 20.7 84.87
## 144 5.29 14.30 7.48 2.89 72.11 18.2 60.38
## 145 2.71 20.73 7.87 3.40 70.43 20.6 60.25
## 146 6.73 14.77 9.09 3.85 72.59 17.3 62.02
## 147 4.27 7.03 10.39 0.07 73.96 20.7 87.27
## 148 5.90 20.42 9.82 1.26 71.09 21.6 60.42
## 149 5.95 12.19 9.20 0.84 72.01 17.9 62.68
## 150 5.25 8.26 9.28 2.67 66.22 16.1 60.51
## 151 11.26 23.63 7.92 3.31 63.50 20.5 53.02
## 152 6.95 45.37 8.25 1.16 68.10 15.2 55.34
## 153 5.02 2.72 11.12 0.20 73.94 16.1 88.83
## 154 7.95 12.38 10.90 0.10 72.85 15.2 83.22
## 155 13.13 1.54 9.01 0.05 69.61 18.6 58.05
## 156 4.68 2.40 11.33 0.00 74.81 19.1 91.63
## 157 6.78 0.86 10.65 0.02 73.59 19.8 87.42
## 158 4.09 2.09 10.94 0.01 74.16 17.1 91.35
## 159 3.10 13.99 11.63 0.01 74.78 16.6 90.52
## 160 4.20 8.10 11.77 0.01 75.12 16.8 91.81
## 161 7.27 31.89 8.67 0.29 71.92 27.6 70.01
## 162 7.01 44.67 7.62 0.87 71.83 27.0 78.59
## 163 10.22 32.56 7.13 0.84 70.79 11.4 80.60
## 164 6.40 22.97 9.28 0.31 74.27 29.2 80.63
## 165 9.77 46.60 8.04 0.63 72.07 24.1 78.99
## 166 10.28 35.61 8.24 0.98 70.19 20.7 78.47
## 167 7.42 21.45 8.32 0.64 72.57 25.4 83.20
## 168 12.12 29.18 7.94 0.39 74.29 23.4 81.43
## 169 11.20 15.84 7.97 0.18 72.76 22.9 82.77
## 170 11.21 26.26 7.74 0.43 71.05 24.1 82.58
## 171 9.36 17.60 8.89 0.61 73.19 14.4 86.88
## 172 12.13 6.41 7.09 0.57 72.46 18.4 86.52
## 173 9.52 27.91 7.67 0.65 73.24 18.7 85.65
## 174 8.46 29.17 8.04 0.30 71.74 24.0 80.19
## 175 7.87 11.45 8.13 0.27 72.90 17.1 89.04
## 176 4.93 6.36 9.79 0.13 74.30 23.2 87.48
## 177 10.52 24.46 8.16 0.48 73.10 25.1 75.79
## 178 8.98 22.31 8.16 0.98 72.17 23.9 83.86
## 179 6.67 9.88 10.36 0.02 74.45 18.2 85.53
## 180 7.50 12.32 10.26 0.02 73.11 26.9 80.90
## 181 3.96 4.68 10.91 0.01 75.04 16.3 91.55
## 182 9.16 3.34 10.35 0.01 73.08 19.9 83.78
## 183 4.10 7.14 11.69 0.02 75.79 10.3 93.90
## 184 2.38 19.52 11.42 0.03 75.23 14.3 89.81
## 185 4.66 6.98 11.12 0.01 74.80 24.5 88.68
## 186 11.53 16.47 9.64 0.06 72.92 27.1 74.37
## 187 6.14 9.82 8.77 0.12 71.80 23.6 78.92
## 188 10.99 27.64 7.46 0.54 74.25 18.5 84.69
## 189 12.53 30.51 8.04 0.22 73.98 20.9 80.74
## 190 14.99 28.37 7.65 0.30 73.37 26.0 78.47
## 191 14.90 23.50 7.15 0.51 74.47 19.9 79.40
## 192 16.34 33.23 7.74 0.33 73.83 21.9 81.21
## 193 11.33 23.10 8.34 0.49 75.21 20.6 86.22
## 194 15.58 20.14 7.07 0.59 72.17 29.2 77.87
## 195 10.96 26.04 7.80 0.48 74.20 25.8 80.20
## 196 9.81 19.18 7.98 0.37 76.23 21.5 87.70
## 197 12.28 28.11 9.08 0.17 77.07 24.5 85.64
## 198 7.58 17.61 9.91 0.12 77.86 24.3 90.93
## 199 10.94 21.08 7.66 0.72 76.56 19.5 88.91
## 200 9.79 12.04 9.05 0.32 77.72 22.2 89.67
## 201 12.87 8.69 7.83 0.29 75.97 18.4 89.37
## 202 11.72 9.41 7.35 0.53 75.04 20.2 87.29
## 203 11.49 8.14 7.36 0.84 74.71 21.2 88.53
## 204 14.17 7.08 7.86 0.51 74.77 19.5 86.85
## 205 9.31 9.89 7.96 0.38 76.39 18.5 90.88
## 206 7.24 16.34 9.32 0.13 76.86 15.7 88.81
## 207 6.61 23.56 8.39 0.36 76.04 18.9 87.00
## 208 12.01 4.64 8.47 0.38 75.60 9.5 90.47
## 209 7.17 21.70 8.46 0.38 75.95 18.8 85.57
## 210 9.26 12.34 7.87 0.43 75.77 25.1 78.91
## 211 9.39 19.24 7.96 0.35 74.58 22.4 84.83
## 212 8.92 20.88 7.38 0.46 74.85 24.7 84.77
## 213 9.67 26.99 7.70 0.41 73.87 28.6 80.65
## 214 15.03 21.40 6.84 0.40 73.85 15.3 81.81
## 215 7.30 18.31 7.55 0.27 72.00 21.5 83.71
## 216 15.78 25.43 6.68 0.43 69.96 21.6 78.79
## 217 6.11 6.68 11.08 0.01 77.22 15.4 91.41
## 218 8.44 10.65 10.91 0.01 77.63 16.0 87.67
## 219 4.66 10.74 11.30 0.03 77.93 16.9 91.35
## 220 4.23 4.00 10.57 0.03 77.90 15.7 92.74
## 221 6.81 21.88 9.53 0.03 74.60 28.2 78.27
## 222 7.68 1.64 9.90 0.02 74.77 22.3 85.73
## 223 15.64 18.44 9.17 0.33 75.29 21.2 85.73
## 224 11.96 18.86 9.97 0.15 73.94 20.5 82.92
## 225 15.60 41.29 7.32 0.78 74.24 22.2 82.97
## 226 7.52 17.85 11.10 0.07 75.08 12.4 84.91
## 227 6.49 26.33 12.14 0.01 74.91 16.8 84.21
## 228 13.65 28.82 7.95 1.04 72.86 20.9 82.94
## 229 9.53 17.71 7.63 0.49 73.55 16.1 88.74
## 230 10.63 36.23 7.80 0.68 74.64 15.8 83.17
## 231 6.53 25.05 8.72 0.29 74.91 21.5 87.35
## 232 8.69 18.29 7.95 0.71 74.34 20.3 86.43
## 233 10.72 31.55 8.37 0.46 73.27 16.8 81.19
## 234 9.45 28.02 7.97 0.53 73.26 19.5 81.09
## 235 8.93 33.64 7.36 0.62 70.96 29.9 79.58
## 236 9.51 32.29 6.66 0.58 70.03 29.7 78.97
## 237 7.34 17.57 7.82 0.92 71.38 21.9 85.77
## 238 13.34 35.14 6.40 0.69 67.60 17.0 78.44
## 239 11.90 36.32 6.90 0.79 69.94 4.1 80.22
## 240 17.19 34.59 6.49 0.71 68.12 35.4 74.22
## 241 9.24 20.80 7.56 0.42 70.81 27.9 80.31
## 242 5.00 12.26 10.82 0.09 74.69 8.4 84.49
## 243 9.80 11.52 9.09 0.30 73.25 16.2 87.32
## 244 9.15 16.41 8.65 0.29 73.22 18.0 86.43
## 245 10.89 26.30 8.27 0.52 72.28 17.1 84.88
## 246 11.04 20.54 7.81 0.65 72.28 16.5 86.22
## 247 9.80 17.53 8.48 0.38 73.29 19.2 87.98
## 248 14.40 11.10 7.81 0.56 73.20 14.0 87.53
## 249 12.18 10.93 7.44 0.67 72.57 14.1 87.63
## 250 14.91 7.08 7.46 0.79 72.36 17.8 85.85
## 251 12.42 4.97 8.29 0.40 73.22 9.4 90.30
## 252 10.96 0.79 10.20 0.27 73.30 15.4 90.90
## 253 19.35 34.55 6.04 0.49 70.79 10.2 76.02
## 254 21.76 11.31 5.46 0.55 68.64 14.1 78.97
## 255 13.85 10.80 7.28 0.32 68.31 25.1 79.08
## 256 18.70 21.19 5.70 0.66 72.47 16.7 79.77
## 257 7.15 40.23 10.77 0.02 74.67 18.6 76.67
## 258 7.30 27.37 10.87 0.03 74.66 17.7 80.80
## 259 4.26 11.17 11.19 0.02 74.13 17.3 88.76
## 260 6.48 8.81 9.60 0.05 70.99 31.8 78.62
## 261 6.60 8.66 9.73 0.04 72.31 11.7 84.16
## 262 5.77 9.94 11.32 0.01 74.10 11.0 89.30
## 263 4.74 1.25 11.53 0.02 73.44 12.8 92.29
## 264 4.65 0.00 10.71 0.02 74.75 1.6 93.06
## 265 3.31 20.60 10.05 0.19 73.29 23.1 81.31
## 266 9.27 53.73 7.26 1.14 65.58 28.6 75.63
## 267 8.68 58.52 6.95 1.01 68.13 35.5 72.76
## 268 6.93 13.62 9.16 0.11 70.65 26.4 77.60
## 269 4.85 27.36 8.14 0.50 65.60 23.9 81.39
## 270 5.89 7.38 10.76 0.02 72.24 17.6 85.92
## 271 3.98 11.17 10.32 0.08 67.39 22.0 80.12
## 272 6.20 25.44 8.72 0.10 68.98 22.3 71.95
## 273 2.57 20.29 11.44 0.02 73.11 9.2 88.67
## 274 4.96 18.29 8.40 0.77 73.20 8.7 87.64
## 275 4.70 15.09 9.00 0.35 74.48 6.3 92.51
## 276 2.30 7.11 10.88 0.09 75.88 4.9 92.90
## 277 4.47 5.08 9.66 0.13 74.52 6.3 92.77
## 278 5.61 13.91 8.09 0.21 72.28 4.9 87.47
## 279 5.28 37.96 7.67 0.34 71.33 10.2 77.19
## 280 6.56 24.50 6.22 0.60 71.25 6.4 83.97
## 281 5.85 16.00 7.35 0.55 72.70 6.2 83.26
## 282 2.68 0.49 11.37 0.01 75.69 10.8 96.37
## 283 13.67 28.81 7.24 0.52 68.08 19.9 75.74
## 284 12.93 22.48 6.97 0.37 67.12 17.6 79.50
## 285 15.63 35.08 7.59 0.35 66.95 27.6 73.32
## 286 13.91 7.04 8.83 2.41 68.54 25.7 85.82
## 287 12.62 37.61 9.07 1.26 67.76 12.4 81.24
## 288 14.39 25.58 8.83 1.41 67.27 36.7 78.26
## 289 12.95 9.76 8.88 1.83 69.20 10.5 86.47
## 290 25.80 37.84 6.36 0.87 68.17 33.5 68.39
## 291 8.62 6.16 9.45 0.01 72.55 25.6 80.15
## 292 8.67 16.57 10.82 0.19 71.19 31.8 75.53
## 293 21.78 35.11 7.85 3.69 65.64 38.4 70.45
## 294 25.18 32.28 7.49 2.37 66.89 50.1 67.02
## 295 21.85 24.02 8.48 1.63 67.61 42.7 73.61
## 296 14.30 36.62 7.65 0.96 65.63 48.1 71.21
## 297 19.97 55.04 8.26 1.87 62.35 39.3 63.81
## 298 11.77 27.31 7.91 1.05 65.96 37.2 68.61
## 299 12.56 20.42 7.32 0.90 68.30 33.3 77.22
## 300 22.86 21.14 8.51 1.11 66.12 27.5 72.93
## 301 12.06 24.86 9.01 1.45 68.71 21.3 82.72
## 302 19.69 17.70 7.83 0.59 67.63 36.8 75.69
## 303 28.08 43.49 8.11 4.48 65.82 26.3 70.98
## 304 27.17 26.10 7.33 0.89 67.57 42.5 71.31
## 305 24.78 37.63 7.68 1.47 67.87 35.1 70.11
## 306 27.05 26.04 8.03 1.62 65.60 39.8 71.27
## 307 16.82 32.38 8.20 1.91 68.00 36.2 78.00
## 308 12.33 43.78 8.29 1.56 67.91 24.9 75.20
## 309 31.78 57.42 7.40 2.89 68.87 39.5 65.96
## 310 27.48 63.65 6.95 1.14 68.99 44.3 62.53
## 311 25.06 48.86 8.22 1.22 68.49 43.7 66.92
## 312 28.37 53.35 7.47 0.92 61.06 36.9 56.66
## 313 14.42 43.40 7.42 0.90 65.67 47.7 71.78
## 314 8.61 21.61 11.36 0.04 70.52 29.9 75.94
## 315 7.08 92.51 6.71 3.67 69.76 30.8 70.83
## 316 5.21 81.54 7.70 2.55 71.74 27.2 73.85
## 317 4.79 43.57 7.70 9.04 71.77 22.1 78.51
## 318 9.25 45.82 8.05 12.71 71.45 0.0 77.17
## 319 8.18 38.35 7.89 12.07 72.41 24.8 76.17
## 320 8.16 41.91 8.16 22.35 72.88 16.7 74.43
## 321 6.28 40.03 8.15 4.09 74.20 32.7 81.24
## 322 9.97 54.82 7.60 7.32 73.77 31.0 76.96
## 323 5.90 67.93 7.18 7.16 72.74 12.2 73.84
## 324 11.12 46.91 7.63 10.67 73.32 35.3 59.56
## 325 9.13 60.21 6.58 7.70 69.22 22.9 76.53
## 326 4.23 85.45 7.50 5.49 71.26 25.4 68.90
## 327 4.45 57.92 10.34 0.03 73.87 16.7 72.55
## 328 4.70 47.34 8.50 0.30 72.81 20.1 68.27
## 329 4.18 13.52 8.94 8.01 71.28 17.9 62.27
## 330 5.69 26.11 7.92 8.45 70.39 35.5 73.03
## 331 5.21 36.50 8.50 11.12 69.23 16.2 82.66
## 332 4.72 34.12 9.40 6.39 67.75 23.9 67.09
## 333 5.35 19.30 8.95 9.96 71.68 15.3 81.65
## 334 4.99 34.52 9.25 21.48 66.43 34.0 77.99
## 335 7.12 30.94 7.78 18.29 69.63 25.8 65.03
## 336 3.96 23.05 8.51 8.22 72.03 29.1 61.78
## 337 3.12 24.79 8.63 12.59 69.84 13.2 59.34
## 338 5.47 43.53 9.48 10.31 70.96 12.9 56.38
## 339 4.58 44.92 8.58 14.03 68.60 24.0 81.88
## 340 6.44 49.56 8.38 23.69 69.94 21.0 51.29
## 341 6.63 33.78 9.96 4.63 68.91 21.7 81.16
## 342 3.44 8.72 11.69 1.13 73.70 28.0 80.69
## 343 3.73 28.97 8.09 2.79 70.11 41.7 80.59
## 344 4.32 22.59 7.66 8.06 69.77 20.1 75.34
## 345 2.44 28.92 8.18 2.01 68.01 30.1 81.54
## 346 4.60 35.70 7.90 2.63 66.80 15.9 82.85
## 347 3.19 24.05 8.13 2.40 71.16 14.4 88.58
## 348 4.01 30.53 8.19 1.31 66.90 25.4 83.19
## 349 5.84 40.01 8.46 1.25 66.86 13.0 81.30
## 350 6.25 27.66 8.06 0.95 64.97 36.0 81.20
## 351 5.77 20.34 9.21 3.12 71.28 18.1 85.94
## 352 4.12 11.33 8.53 2.95 70.94 25.1 83.15
## 353 5.22 12.79 8.36 2.35 68.40 33.4 82.70
## 354 4.63 0.01 10.05 0.02 71.89 26.5 85.62
## 355 3.92 13.93 11.05 0.18 72.62 12.4 86.34
## 356 9.11 16.49 9.35 7.27 72.99 22.4 80.04
## 357 7.61 2.51 9.15 10.69 72.75 17.6 87.17
## 358 5.54 6.56 9.54 14.55 72.41 23.0 81.91
## 359 9.72 21.44 8.90 10.26 73.19 22.0 60.87
## 360 9.06 12.47 9.40 13.67 73.57 29.0 61.64
## 361 6.97 4.31 8.65 3.81 71.83 24.6 88.11
## 362 11.38 12.76 9.10 47.25 72.46 0.0 56.53
## 363 2.31 2.06 10.67 0.13 74.89 21.6 91.23
## 364 4.81 0.89 11.41 0.16 74.68 24.4 89.68
## 365 4.11 0.01 11.12 0.13 74.67 27.4 88.89
## 366 8.99 18.80 9.06 13.78 72.78 22.6 76.61
## 367 6.54 27.49 9.22 42.89 71.51 20.5 74.67
## 368 5.53 30.10 8.53 13.26 71.42 15.8 78.80
## 369 4.62 16.79 8.66 10.43 71.53 15.1 61.25
## 370 6.10 3.61 10.57 0.17 74.08 14.8 87.53
## 371 7.37 28.53 8.81 3.02 70.07 24.8 84.02
## 372 6.87 20.89 10.61 0.71 71.82 23.1 79.61
## 373 11.01 27.43 9.23 0.65 70.78 19.0 60.47
## 374 8.46 29.79 10.01 1.41 70.91 19.3 79.36
## 375 8.89 21.34 9.76 2.02 70.71 26.4 72.82
## 376 6.65 10.85 10.49 0.78 71.99 10.9 78.79
## 377 11.84 13.73 9.18 1.40 70.86 15.0 75.82
## 378 7.90 26.84 8.92 2.91 68.33 27.8 80.12
## 379 8.76 49.95 9.68 0.44 71.59 24.9 53.11
## 380 5.80 23.25 8.61 1.14 68.51 28.4 75.22
## 381 12.04 27.48 8.65 3.16 64.95 33.0 71.81
## 382 5.79 2.91 11.25 0.03 72.50 21.8 87.56
## 383 6.56 4.42 10.11 0.29 71.68 19.5 82.00
## 384 5.60 19.78 11.24 0.19 72.84 10.5 83.92
## 385 5.03 17.60 10.08 0.11 71.34 20.5 80.21
## 386 6.94 30.04 8.83 3.99 71.02 29.1 85.14
## 387 15.16 15.74 9.53 5.38 71.33 26.5 84.60
## 388 16.25 39.70 8.20 4.74 67.86 34.1 73.97
## 389 12.85 31.23 8.87 2.60 66.78 29.0 79.39
## 390 13.36 17.55 9.58 4.27 69.73 30.0 79.97
## 391 12.31 14.99 8.86 2.97 69.37 26.0 81.44
## 392 12.90 14.24 8.79 2.79 66.87 27.7 66.50
## 393 14.91 30.86 8.34 3.29 64.62 28.5 78.91
## 394 16.74 13.32 8.93 4.41 66.41 21.3 73.78
## 395 12.83 43.58 9.39 4.20 70.35 26.4 80.06
## 396 14.15 25.14 8.61 0.96 66.08 25.6 51.91
## 397 12.85 26.66 8.88 8.65 69.97 24.7 81.21
## 398 6.56 13.53 11.43 0.10 71.45 22.1 82.43
## 399 12.27 14.34 8.62 0.77 69.04 31.3 72.03
## 400 7.22 22.48 8.38 0.51 68.84 33.7 83.73
## 401 9.18 12.43 7.53 0.28 71.11 15.8 86.59
## 402 13.06 11.07 7.75 0.39 66.99 36.3 81.67
## 403 8.29 10.38 8.00 0.27 67.90 35.4 84.63
## 404 7.42 20.29 8.84 0.74 70.89 21.1 87.53
## 405 8.55 22.62 8.19 0.48 67.92 33.5 82.31
## 406 10.53 22.10 7.85 1.26 67.85 26.0 85.66
## 407 9.65 21.50 8.15 0.74 69.45 34.7 83.73
## 408 13.40 24.18 8.87 0.40 67.36 30.0 81.00
## 409 8.46 19.02 8.91 0.99 69.55 22.1 86.67
## 410 7.48 22.95 8.58 0.86 70.50 24.0 87.90
## 411 6.73 20.04 7.98 1.47 68.10 27.4 86.65
## 412 5.14 24.51 8.43 0.99 70.74 26.4 87.92
## 413 8.90 22.62 8.82 0.91 70.49 17.6 86.94
## 414 12.69 26.74 8.96 1.23 71.34 34.9 80.31
## 415 12.71 34.16 9.19 1.23 71.00 32.1 82.23
## 416 12.48 48.81 8.63 1.49 73.99 36.9 76.88
## 417 12.66 20.67 8.52 4.12 69.36 15.5 85.66
## 418 6.93 20.83 8.83 3.09 71.19 26.0 87.73
## 419 12.12 40.06 9.03 0.84 73.83 28.7 80.25
## 420 5.07 2.39 11.33 0.01 72.60 25.6 87.95
## 421 5.34 6.50 10.82 0.07 71.78 26.7 82.76
## 422 7.69 3.66 11.29 0.14 71.39 25.5 83.05
## 423 11.80 17.27 9.82 1.94 71.42 23.8 83.69
## 424 13.02 17.39 9.64 2.07 70.44 27.8 85.89
## 425 14.07 27.59 8.24 0.83 70.56 29.2 71.93
## 426 13.77 17.89 8.81 1.64 68.56 37.2 72.59
## 427 11.26 10.60 8.71 3.16 71.02 33.6 84.41
## 428 10.73 5.66 8.39 3.27 69.34 30.4 85.33
## 429 14.81 30.22 8.62 0.50 70.72 31.9 62.54
## 430 13.57 9.23 9.22 2.58 70.47 31.8 70.26
## 431 13.48 12.53 9.54 4.72 69.68 24.7 79.71
## 432 14.06 11.93 8.94 2.36 71.02 33.9 81.40
## 433 14.04 19.30 8.83 4.62 73.01 31.3 85.54
## 434 15.90 21.11 9.33 1.80 68.52 31.3 54.01
## 435 14.03 34.15 8.58 1.15 70.46 24.4 79.06
## 436 15.43 10.97 6.88 1.07 67.90 36.8 67.07
## 437 14.76 48.86 7.89 0.56 67.86 37.1 70.01
## 438 4.59 3.79 12.08 0.08 74.07 25.7 89.67
## 439 7.53 5.69 11.10 0.24 71.51 29.7 80.49
## 440 17.48 16.35 8.63 1.06 68.09 34.7 79.50
## 441 18.38 16.23 8.21 1.97 69.92 16.0 81.91
## 442 15.51 11.21 8.91 1.84 69.24 27.1 80.32
## 443 17.64 3.40 8.28 4.97 64.95 18.4 81.71
## 444 17.03 13.44 7.85 2.24 66.67 30.5 78.88
## 445 5.64 3.53 10.58 0.04 73.25 23.6 86.50
## 446 4.79 17.14 8.51 4.10 67.33 27.9 57.34
## 447 7.57 24.96 8.31 2.25 68.66 32.8 81.47
## 448 14.31 70.51 8.58 2.49 71.45 37.6 73.19
## 449 16.08 30.23 8.01 0.90 63.20 28.1 75.87
## 450 14.54 9.18 9.66 0.77 62.56 30.5 65.80
## 451 7.32 20.96 7.88 2.99 69.37 27.9 78.29
## 452 17.84 22.59 10.13 4.12 67.04 29.4 71.92
## 453 21.79 32.96 9.74 1.27 65.78 34.0 49.43
## 454 24.47 24.47 10.35 4.93 63.99 25.1 49.94
## 455 16.53 28.66 9.34 4.57 67.03 20.3 80.21
## 456 21.08 39.59 8.88 4.38 60.46 27.5 70.57
## 457 22.39 45.87 9.78 4.36 62.61 31.4 61.29
## 458 24.21 30.55 9.43 11.36 63.57 40.6 43.15
## 459 28.78 39.73 9.31 5.56 63.39 29.9 65.95
## 460 15.28 36.60 8.92 4.08 66.96 35.5 53.32
## 461 5.25 13.20 12.05 0.09 71.37 20.7 84.56
## 462 20.68 12.48 10.70 0.35 66.65 32.0 59.11
## 463 8.74 42.60 8.65 3.39 66.91 26.1 53.07
## 464 11.44 35.58 9.48 3.12 65.06 29.5 52.96
## 465 4.62 27.66 8.87 2.80 70.11 24.3 62.34
## 466 5.68 38.45 8.41 4.27 66.50 30.4 52.69
## 467 8.17 47.20 9.34 4.27 63.94 18.8 51.76
## 468 12.47 36.14 8.88 8.88 69.90 19.0 79.63
## 469 5.38 33.98 7.91 4.00 68.10 11.7 60.71
## 470 7.31 45.09 8.62 5.23 62.79 30.6 48.28
## 471 3.39 6.54 11.74 0.12 71.70 21.1 88.24
## 472 6.35 37.75 10.17 1.44 70.10 21.3 64.68
## 473 10.01 23.56 10.06 32.29 67.60 23.8 84.07
## 474 34.71 77.16 6.19 3.68 60.50 33.2 30.40
## 475 11.45 38.66 9.99 13.14 67.78 26.9 66.89
## 476 23.35 21.23 10.45 10.20 68.73 22.2 66.97
## 477 25.89 27.44 9.16 3.34 69.63 39.9 46.80
## 478 23.53 39.30 10.17 1.82 68.74 33.7 49.23
## 479 35.60 88.21 4.51 29.20 65.90 0.0 24.19
## 480 35.39 99.01 3.97 7.96 67.22 0.0 22.27
## 481 13.55 20.61 9.96 9.57 72.83 24.7 83.64
## 482 13.21 40.22 10.03 37.92 67.07 26.5 63.07
## 483 15.68 75.39 8.41 18.50 67.24 34.4 54.21
## 484 29.79 79.27 3.52 39.40 64.99 0.0 25.07
## 485 36.08 66.40 4.13 45.09 66.42 0.0 25.62
## 486 31.57 97.09 2.38 10.42 66.33 0.0 22.83
## 487 29.16 59.99 8.86 35.11 66.92 26.2 47.38
## 488 19.80 39.30 9.16 35.64 60.97 31.4 43.19
## 489 25.72 81.80 6.96 45.27 65.90 28.6 35.44
## 490 24.36 83.74 6.30 40.28 59.19 0.0 45.99
## 491 36.99 63.52 9.27 1.64 66.66 37.7 32.69
## 492 29.63 98.98 8.59 86.82 58.54 40.0 23.09
## 493 35.42 99.00 5.00 32.55 64.14 33.0 21.51
## 494 30.97 50.98 6.78 17.30 65.95 0.0 37.80
## 495 36.94 99.62 4.28 8.67 66.51 39.5 21.33
## 496 37.09 98.15 4.64 26.28 55.72 0.0 17.10
## 497 36.44 21.79 1.43 53.48 66.40 0.0 30.12
## 498 29.20 66.66 4.30 12.95 66.39 0.0 31.37
## 499 40.01 92.00 1.28 60.62 66.12 0.0 14.14
## 500 38.66 92.00 2.23 20.93 65.93 50.2 21.35
## 501 10.50 9.55 11.68 0.35 71.07 21.3 78.35
## 502 26.88 52.18 9.07 6.37 66.89 27.3 50.88
## 503 18.73 43.21 9.64 2.07 69.55 0.0 71.81
## 504 21.38 50.37 10.78 10.15 69.02 30.5 48.20
## 505 18.11 79.81 8.23 10.30 67.01 31.3 40.39
## 506 16.76 49.35 8.55 9.53 65.41 30.9 54.42
## 507 28.24 42.97 9.90 24.62 61.76 19.6 43.12
## 508 28.90 72.04 8.44 10.80 60.86 19.7 36.76
## 509 14.57 43.79 9.86 24.48 65.62 25.7 48.19
## 510 31.23 47.00 8.33 56.66 61.14 31.8 45.92
## 511 30.28 61.00 9.97 15.17 65.82 0.0 41.27
## 512 27.80 18.33 8.48 5.89 68.09 20.4 74.91
## 513 32.29 58.55 6.35 20.75 67.71 34.7 35.53
## 514 14.41 5.16 11.63 0.17 71.92 31.0 76.32
summary(data)
## X1 X2 X3 X4
## Min. : 2.270 Min. : 0.00 Min. : 1.280 Min. : 0.000
## 1st Qu.: 6.570 1st Qu.:13.65 1st Qu.: 7.985 1st Qu.: 0.370
## Median : 9.615 Median :25.00 Median : 8.800 Median : 1.260
## Mean :11.500 Mean :28.69 Mean : 8.851 Mean : 4.032
## 3rd Qu.:14.107 3rd Qu.:38.61 3rd Qu.: 9.775 3rd Qu.: 3.585
## Max. :40.010 Max. :99.62 Max. :12.740 Max. :86.820
## X5 X6 Y
## Min. :55.72 Min. : 0.00 Min. :14.14
## 1st Qu.:68.03 1st Qu.:16.62 1st Qu.:71.28
## Median :70.45 Median :22.20 Median :79.03
## Mean :70.20 Mean :22.35 Mean :75.11
## 3rd Qu.:72.57 3rd Qu.:28.60 3rd Qu.:84.64
## Max. :77.93 Max. :50.20 Max. :96.37
stat.desc(data)
## X1 X2 X3 X4 X5
## nbr.val 514.0000000 5.140000e+02 5.140000e+02 514.0000000 5.140000e+02
## nbr.null 0.0000000 1.000000e+00 0.000000e+00 1.0000000 0.000000e+00
## nbr.na 0.0000000 0.000000e+00 0.000000e+00 0.0000000 0.000000e+00
## min 2.2700000 0.000000e+00 1.280000e+00 0.0000000 5.572000e+01
## max 40.0100000 9.962000e+01 1.274000e+01 86.8200000 7.793000e+01
## range 37.7400000 9.962000e+01 1.146000e+01 86.8200000 2.221000e+01
## sum 5910.9500000 1.474862e+04 4.549390e+03 2072.5100000 3.608291e+04
## median 9.6150000 2.500500e+01 8.800000e+00 1.2600000 7.045000e+01
## mean 11.4999027 2.869381e+01 8.850953e+00 4.0321206 7.020021e+01
## SE.mean 0.3155689 8.844743e-01 6.816275e-02 0.3855870 1.493169e-01
## CI.mean.0.95 0.6199663 1.737637e+00 1.339125e-01 0.7575239 2.933478e-01
## var 51.1860318 4.020996e+02 2.388127e+00 76.4201684 1.145990e+01
## std.dev 7.1544414 2.005242e+01 1.545357e+00 8.7418630 3.385248e+00
## coef.var 0.6221306 6.988412e-01 1.745977e-01 2.1680559 4.822276e-02
## X6 Y
## nbr.val 5.140000e+02 5.140000e+02
## nbr.null 1.500000e+01 0.000000e+00
## nbr.na 0.000000e+00 0.000000e+00
## min 0.000000e+00 1.414000e+01
## max 5.020000e+01 9.637000e+01
## range 5.020000e+01 8.223000e+01
## sum 1.148700e+04 3.860677e+04
## median 2.220000e+01 7.902500e+01
## mean 2.234825e+01 7.511045e+01
## SE.mean 4.045886e-01 6.364823e-01
## CI.mean.0.95 7.948544e-01 1.250432e+00
## var 8.413767e+01 2.082264e+02
## std.dev 9.172659e+00 1.443005e+01
## coef.var 4.104419e-01 1.921178e-01
model=(lm(formula=Y~X1+X2+X3+X4+X5+X6,data=data))
model
##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5 + X6, data = data)
##
## Coefficients:
## (Intercept) X1 X2 X3 X4 X5
## 26.47106 -0.61512 -0.21398 -0.21664 -0.42017 0.92267
## X6
## 0.03101
summary(model)
##
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X4 + X5 + X6, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.041 -3.610 2.047 5.431 21.434
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 26.47106 11.16110 2.372 0.0181 *
## X1 -0.61512 0.07038 -8.740 < 2e-16 ***
## X2 -0.21398 0.02453 -8.721 < 2e-16 ***
## X3 -0.21664 0.29665 -0.730 0.4656
## X4 -0.42017 0.04933 -8.518 < 2e-16 ***
## X5 0.92267 0.14182 6.506 1.85e-10 ***
## X6 0.03101 0.04248 0.730 0.4657
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.209 on 507 degrees of freedom
## Multiple R-squared: 0.6801, Adjusted R-squared: 0.6763
## F-statistic: 179.7 on 6 and 507 DF, p-value: < 2.2e-16
vif(model)
## X1 X2 X3 X4 X5 X6
## 1.930060 1.842417 1.599757 1.415399 1.754443 1.155668
plot(data$X1,data$Y,main="Y dan
X1"
, xlab="X1"
, ylab="Y"
,col="black")
abline(lm(data$Y~data$X1), col="darkred", lwd=3)
plot(data$X2,data$Y,main="Y dan
X2"
, xlab="X2"
, ylab="Y"
,col="black")
abline(lm(data$Y~data$X2), col="darkred", lwd=3)
plot(data$X3,data$Y,main="Y dan
3"
, xlab="X3"
, ylab="Y"
,col="black")
abline(lm(data$Y~data$X3), col="darkred", lwd=3)
plot(data$X4,data$Y,main="Y dan
X4"
, xlab="X4"
, ylab="Y"
,col="black")
abline(lm(data$Y~data$X4), col="darkred", lwd=3)
plot(data$X5,data$Y,main="Y dan
X5"
, xlab="X5"
, ylab="Y"
,col="black")
abline(lm(data$Y~data$X5), col="darkred", lwd=3)
plot(data$X6,data$Y,main="Y dan
X6"
, xlab="X6"
, ylab="Y"
,col="black")
abline(lm(data$Y~data$X6), col="darkred", lwd=3)
# ============================================================
# BAGIAN 2: PEMILIHAN 1 TITIK KNOT (GCV)
# ============================================================
GCV1 = function(data, para = 0, nk = 50)
{
library(Matrix)
library(pracma)
data = as.matrix(data)
N = nrow(data)
M = ncol(data)
m = M - para - 1 # jumlah variabel prediktor
dataA = as.matrix(data[, (para + 2):M])
y = data[, 1]
X = data[, 2:M, drop = FALSE]
# kandidat knot: nk titik per variabel, buang titik min & max
knot1 = matrix(ncol = m, nrow = nk)
for (i in 1:m)
knot1[, i] = seq(min(dataA[, i]), max(dataA[, i]), length.out = nk)
knot1 = knot1[2:(nk - 1), , drop = FALSE]
colnames(knot1) = paste0("knot_x", 1:m)
nk1 = nrow(knot1)
aa = rep(1, N)
GCV = rep(NA, nk1)
MSE = rep(NA, nk1)
Rsq = rep(NA, nk1)
I_N = diag(N)
for (i in 1:nk1)
{
data1 = matrix(0, N, m)
for (j in 1:m) data1[, j] = pmax(dataA[, j] - knot1[i, j], 0)
mx = cbind(aa, X, data1)
C = pinv(t(mx) %*% mx)
B = C %*% (t(mx) %*% y)
yhat = mx %*% B
SSE = sum((y - yhat)^2)
SSR = sum((yhat - mean(y))^2)
MSE[i] = SSE / N
Rsq[i] = SSR / (SSR + SSE) * 100
A = mx %*% C %*% t(mx)
A2 = (sum(diag(I_N - A)) / N)^2
GCV[i] = MSE[i] / A2
}
knotke = 1:nk1
dataAll = cbind(GCV = GCV, Rsq = Rsq, knot_ke = knotke, knot1)
write.csv(dataAll, file = "D:/DOKUMEN KULIAH/REGRESI NONPAR- SEM 5/TUGAS PERTEMUAN 6/Data knot 1.csv")
# urutkan berdasarkan GCV
dataG = dataAll[order(GCV), -2] # kolom: GCV, knot_ke, knot_x1..x4
cat("==============================================", "\n")
cat("HASIL GCV terkecil dengan 1 knot", "\n")
cat("==============================================", "\n")
print(dataG[1, ])
cat("\nNilai GCV 10 terkecil pertama", "\n")
print(dataG[1:10, ])
# ---- estimasi parameter di knot OPTIMAL ----
best = which.min(GCV)
knotopt = knot1[best, ]
datagcv1 = matrix(0, N, m)
for (j in 1:m) datagcv1[, j] = pmax(dataA[, j] - knotopt[j], 0)
mxgcv = cbind(aa, X, datagcv1)
Bopt = pinv(t(mxgcv) %*% mxgcv) %*% t(mxgcv) %*% y
rownames(Bopt) = c("b0",
paste0("b", 1:m, "_x", 1:m),
paste0("b", (m + 1):(2 * m), "_(x", 1:m, "-k", 1:m, ")+
"))
cat("\nKnot optimal ke-", best, " GCV =", min(GCV), "\n")
print(knotopt)
cat("\n==============================================", "\n")
cat("HASIL ESTIMASI PARAMETER TITIK KNOT KE 1 (OPTIMAL)", "\n")
cat("==============================================", "\n")
print(Bopt)
cat("\n")
invisible(list(knotgcv = knotopt, mingcv = min(GCV), B = Bopt, dataAll = dataAll))
}
hasil1 = GCV1(data)
## ==============================================
## HASIL GCV terkecil dengan 1 knot
## ==============================================
## GCV knot_ke knot_x1 knot_x2 knot_x3 knot_x4 knot_x5 knot_x6
## 20.206458 27.000000 54.892653 7.594694 47.839592 67.958163 27.661224 59.450408
##
## Nilai GCV 10 terkecil pertama
## GCV knot_ke knot_x1 knot_x2 knot_x3 knot_x4 knot_x5 knot_x6
## [1,] 20.20646 27 54.89265 7.594694 47.83959 67.95816 27.66122 59.45041
## [2,] 20.21553 28 56.92571 7.828571 49.61143 68.41143 28.68571 61.12857
## [3,] 20.25827 26 52.85959 7.360816 46.06776 67.50490 26.63673 57.77224
## [4,] 20.29451 25 50.82653 7.126939 44.29592 67.05163 25.61224 56.09408
## [5,] 20.33676 29 58.95878 8.062449 51.38327 68.86469 29.71020 62.80673
## [6,] 20.33968 24 48.79347 6.893061 42.52408 66.59837 24.58776 54.41592
## [7,] 20.43170 23 46.76041 6.659184 40.75224 66.14510 23.56327 52.73776
## [8,] 20.53707 30 60.99184 8.296327 53.15510 69.31796 30.73469 64.48490
## [9,] 20.70568 22 44.72735 6.425306 38.98041 65.69184 22.53878 51.05959
## [10,] 20.75155 31 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306
##
## Knot optimal ke- 27 GCV = 20.20646
## knot_x1 knot_x2 knot_x3 knot_x4 knot_x5 knot_x6
## 54.892653 7.594694 47.839592 67.958163 27.661224 59.450408
##
## ==============================================
## HASIL ESTIMASI PARAMETER TITIK KNOT KE 1 (OPTIMAL)
## ==============================================
## [,1]
## b0 97.52697136
## b1_x1 0.02229463
## b2_x2 -1.90990877
## b3_x3 -0.02161166
## b4_x4 -0.67330763
## b5_x5 0.04263029
## b6_x6 -0.44524953
## b7_(x1-k1)+\n -0.10100488
## b8_(x2-k2)+\n 1.28323925
## b9_(x3-k3)+\n -0.07209349
## b10_(x4-k4)+\n 0.36647397
## b11_(x5-k5)+\n 0.32940003
## b12_(x6-k6)+\n 0.39371960
# BAGIAN 3: UJI SIGNIFIKANSI UNTUK 1 KNOT (KNOT OPTIMAL)
library(pracma)
uji = function(alpha = 0.1, para = 0)
{
data = read.table("D:/DOKUMEN KULIAH/REGRESI NONPAR- SEM 5/dataset 2 regnon.txt",header = TRUE)
data = as.matrix(data)
# --- Baca file knot (nama baru) & ambil knot dengan GCV minimum ---
# File tersimpan di working directory R; cek dengan getwd()
knot_all = read.csv("D:/DOKUMEN KULIAH/REGRESI NONPAR- SEM 5/TUGAS PERTEMUAN 6/Data knot 1.csv", header = TRUE, row.names = 1)
best = which.min(knot_all$GCV)
# kolom 1 = GCV, 2 = Rsq, 3 = knot_ke, 4+ = titik knot
knot = as.matrix(knot_all[best, 4:ncol(knot_all)]) # 1 baris saja
cat("Knot optimal ke-", best, " GCV =", knot_all$GCV[best], "\n")
print(knot)
cat("\n")
y = data[, 1]
n = nrow(data)
m = para + 2
dataA = data[, m:(m + 5)]
satu = rep(1, n)
n1k = ncol(knot)
data.knot = matrix(0, n, n1k)
for (i in 1:n1k) data.knot[, i] = pmax(dataA[, i] - knot[1, i], 0)
# susunan: 1, x1, (x1-k1)+, x2, (x2-k2)+, x3, (x3-k3)+, x4, (x4-k4)+
mx = cbind(satu,
data[, 2], data.knot[, 1],
data[, 3], data.knot[, 2],
data[, 4], data.knot[, 3],
data[, 5], data.knot[, 4],
data[, 6], data.knot[, 5],
data[, 7], data.knot[, 6])
B = pinv(t(mx) %*% mx) %*% t(mx) %*% y
p = nrow(B) # jumlah parameter (9)
yhat = mx %*% B
ybar = mean(y)
res = y - yhat
SSE = sum(res^2)
SSR = sum((yhat - ybar)^2)
SST = sum((y - ybar)^2)
MSE = SSE / (n - p) # PERBAIKAN: dibagi derajat bebas galat
MSR = SSR / (p - 1)
Rsq = SSR / (SSR + SSE) * 100
# --- Uji simultan (F) ---
Fhit = MSR / MSE
pvalue = pf(Fhit, p - 1, n - p, lower.tail = FALSE)
cat('---------------------------------------', '\n')
cat('Kesimpulan hasil uji simultan', '\n')
cat('---------------------------------------', '\n')
if (pvalue <= alpha) {
cat('Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan', '
\n\n')
} else {
cat('Gagal Tolak Ho yakni semua variabel bebas tidak berpengaruh signifikan', '\n\n')
}
# --- Uji parsial (t) ---
SE = sqrt(diag(MSE * pinv(t(mx) %*% mx)))
thit = rep(NA, p)
pval = rep(NA, p)
cat('---------------------------------------------', '\n')
cat('Kesimpulan hasil uji parsial', '\n')
cat('---------------------------------------------', '\n')
for (i in 1:p)
{
thit[i] = B[i, 1] / SE[i]
pval[i] = 2 * pt(abs(thit[i]), n - p, lower.tail = FALSE)
if (pval[i] <= alpha)
cat('Parameter', i - 1, ': Tolak Ho, signifikan, pvalue =', pval[i], '\
n') else
cat('Parameter', i - 1, ': Gagal tolak Ho, tidak signifikan, pvalue =
', pval[i], '\n')
}
cat('=============================================', '\n')
cat('Estimasi parameter, t hitung, p-value', '\n')
cat('=============================================', '\n')
print(cbind(Beta = B[, 1], SE = SE, t_hitung = thit, p_value = pval))
cat('\nAnalysis of Variance', '\n')
cat('=============================================', '\n')
cat('Sumber df SS MS Fhit', '\n')
cat('Regresi ', p - 1, ' ', SSR, ' ', MSR, ' ', Fhit, '\n')
cat('Error ', n - p, ' ', SSE, ' ', MSE, '\n')
cat('Total ', n - 1, ' ', SST, '\n')
cat('=============================================', '\n')
cat('s =', sqrt(MSE), ' Rsq =', Rsq, '\n')
cat('pvalue(F) =', pvalue, '\n')
write.csv(res, file = 'output_uji_residual_knot1.csv')
write.csv(mx, file = 'output_uji_mx_knot1.csv')
write.csv(yhat, file = 'output_uji_yhat_knot1.csv')
}
uji(0.1, 0)
## Knot optimal ke- 27 GCV = 20.20646
## knot_x1 knot_x2 knot_x3 knot_x4 knot_x5 knot_x6
## 27 54.89265 7.594694 47.83959 67.95816 27.66122 59.45041
##
## ---------------------------------------
## Kesimpulan hasil uji simultan
## ---------------------------------------
## Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan
##
##
## ---------------------------------------------
## Kesimpulan hasil uji parsial
## ---------------------------------------------
## Parameter 0 : Tolak Ho, signifikan, pvalue = 5.544233e-15
## nParameter 1 : Gagal tolak Ho, tidak signifikan, pvalue =
## 0.203702
## Parameter 2 : Tolak Ho, signifikan, pvalue = 0.04712455
## nParameter 3 : Tolak Ho, signifikan, pvalue = 0.0001480848
## nParameter 4 : Tolak Ho, signifikan, pvalue = 0.0280246
## nParameter 5 : Gagal tolak Ho, tidak signifikan, pvalue =
## 0.5345728
## Parameter 6 : Gagal tolak Ho, tidak signifikan, pvalue =
## 0.5923175
## Parameter 7 : Tolak Ho, signifikan, pvalue = 0.0001629148
## nParameter 8 : Gagal tolak Ho, tidak signifikan, pvalue =
## 0.1088224
## Parameter 9 : Gagal tolak Ho, tidak signifikan, pvalue =
## 0.2101112
## Parameter 10 : Tolak Ho, signifikan, pvalue = 0.0001764547
## nParameter 11 : Tolak Ho, signifikan, pvalue = 9.664797e-12
## nParameter 12 : Tolak Ho, signifikan, pvalue = 4.797697e-07
## n=============================================
## Estimasi parameter, t hitung, p-value
## =============================================
## Beta SE t_hitung p_value
## [1,] 97.52697136 12.09657434 8.0623628 5.544233e-15
## [2,] 0.02229463 0.01751709 1.2727361 2.037020e-01
## [3,] -0.10100488 0.05075404 -1.9900855 4.712455e-02
## [4,] -1.90990877 0.49950395 -3.8236110 1.480848e-04
## [5,] 1.28323925 0.58240442 2.2033474 2.802460e-02
## [6,] -0.02161166 0.03477503 -0.6214705 5.345728e-01
## [7,] -0.07209349 0.13454678 -0.5358247 5.923175e-01
## [8,] -0.67330763 0.17721725 -3.7993346 1.629148e-04
## [9,] 0.36647397 0.22813775 1.6063714 1.088224e-01
## [10,] 0.04263029 0.03397190 1.2548694 2.101112e-01
## [11,] 0.32940003 0.08716761 3.7789271 1.764547e-04
## [12,] -0.44524953 0.06382772 -6.9758020 9.664797e-12
## [13,] 0.39371960 0.07718219 5.1011715 4.797697e-07
##
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 12 16391.04 1365.92 69.35223
## Error 501 9867.395 19.6954
## Total 513 26258.43
## =============================================
## s = 4.43795 Rsq = 62.422
## pvalue(F) = 2.776326e-98
r = read.csv("D:/DOKUMEN KULIAH/REGRESI NONPAR- SEM 5/TUGAS PERTEMUAN 6/Data knot 1.csv", row.names = 1)
k48 = as.numeric(r[48, 4:7]) # knot kandidat terakhir
X = as.matrix(data[, 2:5]); y = data[, 1]
mx = cbind(1, X, sapply(1:4, function(j) pmax(X[, j] - k48[j], 0)))
print(pinv(t(mx) %*% mx) %*% t(mx) %*% y)
## [,1]
## [1,] 71.1416626
## [2,] 0.0424699
## [3,] -1.1695095
## [4,] 0.1371678
## [5,] -0.7288531
## [6,] 7.0888210
## [7,] 14.0408843
## [8,] -8.3451583
## [9,] 9.8393253
library(pracma)
data = read.table("D:/DOKUMEN KULIAH/REGRESI NONPAR- SEM 5/dataset 2 regnon.txt",header = TRUE)
nrow(data)
## [1] 514
buat_mx = function(X, knot, urut = "gcv")
{
N = nrow(X); m = ncol(X); k = nrow(knot)
if (urut == "gcv") {
trunc = do.call(cbind, lapply(1:k, function(s)
sapply(1:m, function(j) pmax(X[, j] - knot[s, j], 0))))
mx = cbind(1, X, trunc)
nama = c("b0", paste0("x", 1:m),
unlist(lapply(1:k, function(s) paste0("(x", 1:m, "-k", s, ")+
"))))
} else {
kol = list(rep(1, N)); nama = "b0"
for (j in 1:m) {
kol[[length(kol) + 1]] = X[, j]
nama = c(nama, paste0("x", j))
for (s in 1:k) {
kol[[length(kol) + 1]] = pmax(X[, j] - knot[s, j], 0)
nama = c(nama, paste0("(x", j, "-k", s, ")+"))
}
}
mx = do.call(cbind, kol)
}
colnames(mx) = nama
mx
}
GCVk = function(data, k = 2, nk = 50)
{
data = as.matrix(data)
N = nrow(data)
y = data[, 1]
X = data[, 2:ncol(data), drop = FALSE]
m = ncol(X)
# grid kandidat knot per variabel (buang titik min & max)
grid = sapply(1:m, function(j) seq(min(X[, j]), max(X[, j]), length.out = nk))
grid = grid[2:(nk - 1), , drop = FALSE]
ng = nrow(grid)
komb = t(combn(ng, k)) # tiap baris = indeks kandidat (naik)
nkomb = nrow(komb)
cat("Jumlah kombinasi knot:", nkomb, "\n")
GCV = rep(NA, nkomb)
Rsq = rep(NA, nkomb)
knotmat = matrix(NA, nkomb, k * m)
nama.knot = as.vector(t(outer(1:k, 1:m, function(s, j) paste0("k", s, "_x",j))))
for (i in 1:nkomb)
{
knot = matrix(0, k, m)
for (s in 1:k) knot[s, ] = grid[komb[i, s], ]
knotmat[i, ] = as.vector(t(knot))
mx = buat_mx(X, knot, "gcv")
C = pinv(t(mx) %*% mx)
B = C %*% (t(mx) %*% y)
yhat = mx %*% B
SSE = sum((y - yhat)^2)
SSR = sum((yhat - mean(y))^2)
trA = sum((mx %*% C) * mx) # trace matriks hat
GCV[i] = (SSE / N) / (((N - trA) / N)^2)
Rsq[i] = SSR / (SSR + SSE) * 100
if (i %% 2000 == 0) cat(" selesai", i, "dari", nkomb, "\n")
}
dataAll = cbind(GCV = GCV, Rsq = Rsq, komb_ke = 1:nkomb, knotmat)
colnames(dataAll)[4:ncol(dataAll)] = nama.knot
file.out = paste0("dataknot",k,"_v2.csv")
write.csv(dataAll, file = file.out)
dataG = dataAll[order(GCV), -2] # GCV, komb_ke, knot...
cat("\n==============================================\n")
cat("HASIL GCV terkecil dengan", k, "knot\n")
cat("==============================================\n")
print(dataG[1, ])
cat("\nNilai GCV 10 terkecil pertama\n")
print(dataG[1:10, ])
# ---- estimasi parameter pada knot OPTIMAL ----
best = which.min(GCV)
knotopt = matrix(knotmat[best, ], nrow = k, byrow = TRUE,
dimnames = list(paste0("knot_", 1:k), paste0("x", 1:m)))
mxopt = buat_mx(X, knotopt, "gcv")
Bopt = pinv(t(mxopt) %*% mxopt) %*% t(mxopt) %*% y
rownames(Bopt) = colnames(mxopt)
cat("\nKombinasi knot optimal ke-", best, " GCV =", min(GCV), "\n")
print(knotopt)
cat("\n==============================================\n")
cat("HASIL ESTIMASI PARAMETER", k, "TITIK KNOT (OPTIMAL)\n")
cat("==============================================\n")
print(Bopt)
cat("\nFile knot tersimpan di:", file.out, "\n")
invisible(list(knotopt = knotopt, mingcv = min(GCV), B = Bopt, dataAll = dataAll))
}
# ============================================================
# BAGIAN C: UJI SIGNIFIKANSI SIMULTAN & PARSIAL (k = 2 atau 3)
# ============================================================
uji_k = function(data, k = 2, alpha = 0.1)
{
data = as.matrix(data)
y = data[, 1]
X = data[, 2:ncol(data), drop = FALSE]
n = nrow(data); m = ncol(X)
# ambil knot dengan GCV minimum dari file hasil GCVk
file.knot = paste0("dataknot",k,"_v2.csv")
knot_all = read.csv(file.knot, header = TRUE, row.names = 1)
best = which.min(knot_all$GCV)
knot = matrix(as.numeric(knot_all[best, 4:ncol(knot_all)]), nrow = k, byrow= TRUE,
dimnames = list(paste0("knot_", 1:k), paste0("x", 1:m)))
cat("Kombinasi knot optimal ke-", best, " GCV =", knot_all$GCV[best], "\n")
print(knot)
cat("\n")
mx = buat_mx(X, knot, "uji")
B = pinv(t(mx) %*% mx) %*% t(mx) %*% y
p = nrow(B)
yhat = mx %*% B
ybar = mean(y)
res = y - yhat
SSE = sum(res^2)
SSR = sum((yhat - ybar)^2)
SST = sum((y - ybar)^2)
MSE = SSE / (n - p)
MSR = SSR / (p - 1)
Rsq = SSR / (SSR + SSE) * 100
# --- Uji simultan ---
Fhit = MSR / MSE
pvalue = pf(Fhit, p - 1, n - p, lower.tail = FALSE)
cat('---------------------------------------\n')
cat('Kesimpulan hasil uji simultan\n')
cat('---------------------------------------\n')
if (pvalue <= alpha) {
cat('Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan\n\n')
} else {
cat('Gagal Tolak Ho yakni semua variabel bebas tidak berpengaruh signifikan\n\n')
}
# --- Uji parsial ---
SE = sqrt(diag(MSE * pinv(t(mx) %*% mx)))
thit = B[, 1] / SE
pval = 2 * pt(abs(thit), n - p, lower.tail = FALSE)
cat('---------------------------------------------\n')
cat('Kesimpulan hasil uji parsial\n')
cat('---------------------------------------------\n')
for (i in 1:p)
{
if (pval[i] <= alpha)
cat('Parameter', i - 1, colnames(mx)[i], ': Tolak Ho, signifikan, pvalue=', pval[i], '\n') else
cat('Parameter', i - 1, colnames(mx)[i], ': Gagal tolak Ho, tidak signifikan, pvalue =', pval[i], '\n')
}
cat('=============================================\n')
cat('Estimasi parameter, t hitung, p-value\n')
cat('=============================================\n')
tab = cbind(Beta = B[, 1], SE = SE, t_hitung = thit, p_value = pval)
rownames(tab) = colnames(mx)
print(tab)
cat('\nAnalysis of Variance\n')
cat('=============================================\n')
cat('Sumber df SS MS Fhit\n')
cat('Regresi ', p - 1, ' ', SSR, ' ', MSR, ' ', Fhit, '\n')
cat('Error ', n - p, ' ', SSE, ' ', MSE, '\n')
cat('Total ', n - 1, ' ', SST, '\n')
cat('=============================================\n')
cat('s =', sqrt(MSE), ' Rsq =', Rsq, '\n')
cat('pvalue(F) =', pvalue, '\n')
write.csv(res, file = paste0('output_uji_residual_knot', k, '_v2.csv'))
write.csv(mx, file = paste0('output_uji_mx_knot', k, '_v2.csv'))
write.csv(yhat, file = paste0('output_uji_yhat_knot', k, '_v2.csv'))
invisible(list(B = B, tab = tab, Rsq = Rsq))
}
hasil2 = GCVk(data, k = 2)
## Jumlah kombinasi knot: 1128
##
## ==============================================
## HASIL GCV terkecil dengan 2 knot
## ==============================================
## GCV komb_ke k1_x1 k1_x2 k1_x3 k1_x4 k1_x5
## 18.985476 921.000000 56.925714 7.828571 49.611429 68.411429 28.685714
## k1_x6 k2_x1 k2_x2 k2_x3 k2_x4 k2_x5 k2_x6
## 61.128571 63.024898 8.530204 54.926939 69.771224 31.759184 66.163061
##
## Nilai GCV 10 terkecil pertama
## GCV komb_ke k1_x1 k1_x2 k1_x3 k1_x4 k1_x5 k1_x6
## [1,] 18.98548 921 56.92571 7.828571 49.61143 68.41143 28.68571 61.12857
## [2,] 18.98686 920 56.92571 7.828571 49.61143 68.41143 28.68571 61.12857
## [3,] 19.04751 901 54.89265 7.594694 47.83959 67.95816 27.66122 59.45041
## [4,] 19.10503 939 58.95878 8.062449 51.38327 68.86469 29.71020 62.80673
## [5,] 19.12689 919 56.92571 7.828571 49.61143 68.41143 28.68571 61.12857
## [6,] 19.12877 900 54.89265 7.594694 47.83959 67.95816 27.66122 59.45041
## [7,] 19.13558 940 58.95878 8.062449 51.38327 68.86469 29.71020 62.80673
## [8,] 19.15718 880 52.85959 7.360816 46.06776 67.50490 26.63673 57.77224
## [9,] 19.19519 902 54.89265 7.594694 47.83959 67.95816 27.66122 59.45041
## [10,] 19.21913 922 56.92571 7.828571 49.61143 68.41143 28.68571 61.12857
## k2_x1 k2_x2 k2_x3 k2_x4 k2_x5 k2_x6
## [1,] 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306
## [2,] 60.99184 8.296327 53.15510 69.31796 30.73469 64.48490
## [3,] 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306
## [4,] 60.99184 8.296327 53.15510 69.31796 30.73469 64.48490
## [5,] 58.95878 8.062449 51.38327 68.86469 29.71020 62.80673
## [6,] 60.99184 8.296327 53.15510 69.31796 30.73469 64.48490
## [7,] 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306
## [8,] 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306
## [9,] 65.05796 8.764082 56.69878 70.22449 32.78367 67.84122
## [10,] 65.05796 8.764082 56.69878 70.22449 32.78367 67.84122
##
## Kombinasi knot optimal ke- 921 GCV = 18.98548
## x1 x2 x3 x4 x5 x6
## knot_1 56.92571 7.828571 49.61143 68.41143 28.68571 61.12857
## knot_2 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306
##
## ==============================================
## HASIL ESTIMASI PARAMETER 2 TITIK KNOT (OPTIMAL)
## ==============================================
## [,1]
## b0 91.36884401
## x1 -0.01679699
## x2 -0.92744459
## x3 -0.03116134
## x4 -0.52954211
## x5 0.02368497
## x6 -0.62717611
## (x1-k1)+\n 0.47186143
## (x2-k1)+\n -0.40340313
## (x3-k1)+\n 1.06073557
## (x4-k1)+\n -0.59686929
## (x5-k1)+\n 0.45300042
## (x6-k1)+\n 1.73075599
## (x1-k2)+\n -0.68801713
## (x2-k2)+\n 0.81801155
## (x3-k2)+\n -1.35431420
## (x4-k2)+\n 1.14374483
## (x5-k2)+\n -0.18233420
## (x6-k2)+\n -1.34946890
##
## File knot tersimpan di: dataknot2_v2.csv
uji_k(data,k=2,alpha=0.1)
## Kombinasi knot optimal ke- 921 GCV = 18.98548
## x1 x2 x3 x4 x5 x6
## knot_1 56.92571 7.828571 49.61143 68.41143 28.68571 61.12857
## knot_2 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306
##
## ---------------------------------------
## Kesimpulan hasil uji simultan
## ---------------------------------------
## Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan
##
## ---------------------------------------------
## Kesimpulan hasil uji parsial
## ---------------------------------------------
## Parameter 0 b0 : Tolak Ho, signifikan, pvalue= 2.934602e-13
## Parameter 1 x1 : Gagal tolak Ho, tidak signifikan, pvalue = 0.3502805
## Parameter 2 (x1-k1)+ : Tolak Ho, signifikan, pvalue= 0.0441384
## Parameter 3 (x1-k2)+ : Tolak Ho, signifikan, pvalue= 0.01264274
## Parameter 4 x2 : Tolak Ho, signifikan, pvalue= 0.08261912
## Parameter 5 (x2-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.7452275
## Parameter 6 (x2-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.4479317
## Parameter 7 x3 : Gagal tolak Ho, tidak signifikan, pvalue = 0.3704973
## Parameter 8 (x3-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.1270509
## Parameter 9 (x3-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.1019149
## Parameter 10 x4 : Tolak Ho, signifikan, pvalue= 0.002675393
## Parameter 11 (x4-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.3062695
## Parameter 12 (x4-k2)+ : Tolak Ho, signifikan, pvalue= 0.04111677
## Parameter 13 x5 : Gagal tolak Ho, tidak signifikan, pvalue = 0.4835666
## Parameter 14 (x5-k1)+ : Tolak Ho, signifikan, pvalue= 0.09056891
## Parameter 15 (x5-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.5746511
## Parameter 16 x6 : Tolak Ho, signifikan, pvalue= 5.160811e-18
## Parameter 17 (x6-k1)+ : Tolak Ho, signifikan, pvalue= 1.390408e-11
## Parameter 18 (x6-k2)+ : Tolak Ho, signifikan, pvalue= 1.330151e-08
## =============================================
## Estimasi parameter, t hitung, p-value
## =============================================
## Beta SE t_hitung p_value
## b0 91.36884402 12.17917641 7.5020544 2.934602e-13
## x1 -0.01679699 0.01796605 -0.9349295 3.502805e-01
## (x1-k1)+ 0.47186143 0.23383534 2.0179218 4.413840e-02
## (x1-k2)+ -0.68801713 0.27489897 -2.5027999 1.264274e-02
## x2 -0.92744459 0.53325561 -1.7392121 8.261912e-02
## (x2-k1)+ -0.40340312 1.24078168 -0.3251201 7.452275e-01
## (x2-k2)+ 0.81801155 1.07707909 0.7594721 4.479317e-01
## x3 -0.03116134 0.03476439 -0.8963581 3.704973e-01
## (x3-k1)+ 1.06073557 0.69401497 1.5284044 1.270509e-01
## (x3-k2)+ -1.35431420 0.82646559 -1.6386819 1.019149e-01
## x4 -0.52954211 0.17545975 -3.0180261 2.675393e-03
## (x4-k1)+ -0.59686929 0.58280060 -1.0241398 3.062695e-01
## (x4-k2)+ 1.14374483 0.55855145 2.0476983 4.111677e-02
## x5 0.02368497 0.03378232 0.7011055 4.835666e-01
## (x5-k1)+ 0.45300042 0.26714439 1.6957137 9.056891e-02
## (x5-k2)+ -0.18233420 0.32467625 -0.5615877 5.746511e-01
## x6 -0.62717611 0.06974848 -8.9919681 5.160811e-18
## (x6-k1)+ 1.73075599 0.25005449 6.9215153 1.390408e-11
## (x6-k2)+ -1.34946890 0.23350967 -5.7790708 1.330151e-08
##
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 18 17208.01 956.0008 52.28711
## Error 495 9050.421 18.28368
## Total 513 26258.43
## =============================================
## s = 4.275942 Rsq = 65.53328
## pvalue(F) = 4.47837e-102
#PEMILIHAN TIGA TITIK KNOT#
hasil3=GCVk(data, k=3)
## Jumlah kombinasi knot: 17296
## selesai 2000 dari 17296
## selesai 4000 dari 17296
## selesai 6000 dari 17296
## selesai 8000 dari 17296
## selesai 10000 dari 17296
## selesai 12000 dari 17296
## selesai 14000 dari 17296
## selesai 16000 dari 17296
##
## ==============================================
## HASIL GCV terkecil dengan 3 knot
## ==============================================
## GCV komb_ke k1_x1 k1_x2 k1_x3 k1_x4
## 18.636070 14057.000000 42.694286 6.191429 37.208571 65.238571
## k1_x5 k1_x6 k2_x1 k2_x2 k2_x3 k2_x4
## 21.514286 49.381429 46.760408 6.659184 40.752245 66.145102
## k2_x5 k2_x6 k3_x1 k3_x2 k3_x3 k3_x4
## 23.563265 52.737755 69.124082 9.231837 60.242449 71.131020
## k3_x5 k3_x6
## 34.832653 71.197551
##
## Nilai GCV 10 terkecil pertama
## GCV komb_ke k1_x1 k1_x2 k1_x3 k1_x4 k1_x5 k1_x6
## [1,] 18.63607 14057 42.69429 6.191429 37.20857 65.23857 21.51429 49.38143
## [2,] 18.63904 16006 56.92571 7.828571 49.61143 68.41143 28.68571 61.12857
## [3,] 18.64996 14058 42.69429 6.191429 37.20857 65.23857 21.51429 49.38143
## [4,] 18.65976 16005 56.92571 7.828571 49.61143 68.41143 28.68571 61.12857
## [5,] 18.66287 13706 40.66122 5.957551 35.43673 64.78531 20.48980 47.70327
## [6,] 18.66361 13707 40.66122 5.957551 35.43673 64.78531 20.48980 47.70327
## [7,] 18.67131 16007 56.92571 7.828571 49.61143 68.41143 28.68571 61.12857
## [8,] 18.69623 15816 54.89265 7.594694 47.83959 67.95816 27.66122 59.45041
## [9,] 18.69868 14382 44.72735 6.425306 38.98041 65.69184 22.53878 51.05959
## [10,] 18.70235 15831 54.89265 7.594694 47.83959 67.95816 27.66122 59.45041
## k2_x1 k2_x2 k2_x3 k2_x4 k2_x5 k2_x6 k3_x1 k3_x2
## [1,] 46.76041 6.659184 40.75224 66.14510 23.56327 52.73776 69.12408 9.231837
## [2,] 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306 69.12408 9.231837
## [3,] 46.76041 6.659184 40.75224 66.14510 23.56327 52.73776 71.15714 9.465714
## [4,] 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306 67.09102 8.997959
## [5,] 46.76041 6.659184 40.75224 66.14510 23.56327 52.73776 69.12408 9.231837
## [6,] 46.76041 6.659184 40.75224 66.14510 23.56327 52.73776 71.15714 9.465714
## [7,] 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306 71.15714 9.465714
## [8,] 63.02490 8.530204 54.92694 69.77122 31.75918 66.16306 69.12408 9.231837
## [9,] 46.76041 6.659184 40.75224 66.14510 23.56327 52.73776 69.12408 9.231837
## [10,] 65.05796 8.764082 56.69878 70.22449 32.78367 67.84122 67.09102 8.997959
## k3_x3 k3_x4 k3_x5 k3_x6
## [1,] 60.24245 71.13102 34.83265 71.19755
## [2,] 60.24245 71.13102 34.83265 71.19755
## [3,] 62.01429 71.58429 35.85714 72.87571
## [4,] 58.47061 70.67776 33.80816 69.51939
## [5,] 60.24245 71.13102 34.83265 71.19755
## [6,] 62.01429 71.58429 35.85714 72.87571
## [7,] 62.01429 71.58429 35.85714 72.87571
## [8,] 60.24245 71.13102 34.83265 71.19755
## [9,] 60.24245 71.13102 34.83265 71.19755
## [10,] 58.47061 70.67776 33.80816 69.51939
##
## Kombinasi knot optimal ke- 14057 GCV = 18.63607
## x1 x2 x3 x4 x5 x6
## knot_1 42.69429 6.191429 37.20857 65.23857 21.51429 49.38143
## knot_2 46.76041 6.659184 40.75224 66.14510 23.56327 52.73776
## knot_3 69.12408 9.231837 60.24245 71.13102 34.83265 71.19755
##
## ==============================================
## HASIL ESTIMASI PARAMETER 3 TITIK KNOT (OPTIMAL)
## ==============================================
## [,1]
## b0 95.37246210
## x1 -0.03266317
## x2 0.78251791
## x3 -0.06708851
## x4 -0.84045363
## x5 0.01901839
## x6 -0.37636772
## (x1-k1)+\n 0.25879501
## (x2-k1)+\n -12.11865938
## (x3-k1)+\n -0.07747172
## (x4-k1)+\n 3.19168414
## (x5-k1)+\n -0.20262179
## (x6-k1)+\n -2.53034180
## (x1-k2)+\n -0.21956394
## (x2-k2)+\n 10.65241559
## (x3-k2)+\n 0.64210012
## (x4-k2)+\n -3.26669072
## (x5-k2)+\n 0.39611079
## (x6-k2)+\n 3.09616317
## (x1-k3)+\n -0.12011621
## (x2-k3)+\n -0.05039049
## (x3-k3)+\n -1.01592956
## (x4-k3)+\n 1.23141797
## (x5-k3)+\n 0.22850765
## (x6-k3)+\n -0.44966092
##
## File knot tersimpan di: dataknot3_v2.csv
uji_k(data,k=3,alpha=0.1)
## Kombinasi knot optimal ke- 14057 GCV = 18.63607
## x1 x2 x3 x4 x5 x6
## knot_1 42.69429 6.191429 37.20857 65.23857 21.51429 49.38143
## knot_2 46.76041 6.659184 40.75224 66.14510 23.56327 52.73776
## knot_3 69.12408 9.231837 60.24245 71.13102 34.83265 71.19755
##
## ---------------------------------------
## Kesimpulan hasil uji simultan
## ---------------------------------------
## Tolak Ho yakni minimal terdapat 1 variabel bebas yang signifikan
##
## ---------------------------------------------
## Kesimpulan hasil uji parsial
## ---------------------------------------------
## Parameter 0 b0 : Tolak Ho, signifikan, pvalue= 0.0001122409
## Parameter 1 x1 : Gagal tolak Ho, tidak signifikan, pvalue = 0.1535764
## Parameter 2 (x1-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.3086953
## Parameter 3 (x1-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.4645934
## Parameter 4 (x1-k3)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.3856544
## Parameter 5 x2 : Gagal tolak Ho, tidak signifikan, pvalue = 0.426021
## Parameter 6 (x2-k1)+ : Tolak Ho, signifikan, pvalue= 0.008077313
## Parameter 7 (x2-k2)+ : Tolak Ho, signifikan, pvalue= 0.01250061
## Parameter 8 (x2-k3)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.932627
## Parameter 9 x3 : Gagal tolak Ho, tidak signifikan, pvalue = 0.1359782
## Parameter 10 (x3-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.9266264
## Parameter 11 (x3-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.5261923
## Parameter 12 (x3-k3)+ : Tolak Ho, signifikan, pvalue= 0.02254717
## Parameter 13 x4 : Tolak Ho, signifikan, pvalue= 0.02231408
## Parameter 14 (x4-k1)+ : Tolak Ho, signifikan, pvalue= 0.03891771
## Parameter 15 (x4-k2)+ : Tolak Ho, signifikan, pvalue= 0.01849356
## Parameter 16 (x4-k3)+ : Tolak Ho, signifikan, pvalue= 1.02792e-05
## Parameter 17 x5 : Gagal tolak Ho, tidak signifikan, pvalue = 0.7139656
## Parameter 18 (x5-k1)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.5686832
## Parameter 19 (x5-k2)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.2990122
## Parameter 20 (x5-k3)+ : Gagal tolak Ho, tidak signifikan, pvalue = 0.2192119
## Parameter 21 x6 : Tolak Ho, signifikan, pvalue= 0.00378706
## Parameter 22 (x6-k1)+ : Tolak Ho, signifikan, pvalue= 3.842611e-06
## Parameter 23 (x6-k2)+ : Tolak Ho, signifikan, pvalue= 1.299459e-09
## Parameter 24 (x6-k3)+ : Tolak Ho, signifikan, pvalue= 2.698957e-06
## =============================================
## Estimasi parameter, t hitung, p-value
## =============================================
## Beta SE t_hitung p_value
## b0 95.37246205 24.49124168 3.89414564 1.122409e-04
## x1 -0.03266317 0.02285367 -1.42923080 1.535764e-01
## (x1-k1)+ 0.25879501 0.25396353 1.01902434 3.086953e-01
## (x1-k2)+ -0.21956394 0.30000058 -0.73187839 4.645934e-01
## (x1-k3)+ -0.12011621 0.13833444 -0.86830296 3.856544e-01
## x2 0.78251791 0.98221827 0.79668434 4.260210e-01
## (x2-k1)+ -12.11865938 4.55636943 -2.65971835 8.077313e-03
## (x2-k2)+ 10.65241559 4.24913068 2.50696352 1.250061e-02
## (x2-k3)+ -0.05039049 0.59574772 -0.08458361 9.326270e-01
## x3 -0.06708851 0.04492342 -1.49339729 1.359782e-01
## (x3-k1)+ -0.07747172 0.84082546 -0.09213770 9.266264e-01
## (x3-k2)+ 0.64210012 1.01232311 0.63428377 5.261923e-01
## (x3-k3)+ -1.01592956 0.44397132 -2.28827744 2.254717e-02
## x4 -0.84045363 0.36664714 -2.29226836 2.231408e-02
## (x4-k1)+ 3.19168414 1.54140835 2.07062855 3.891771e-02
## (x4-k2)+ -3.26669072 1.38214295 -2.36349700 1.849356e-02
## (x4-k3)+ 1.23141797 0.27624008 4.45778173 1.027920e-05
## x5 0.01901839 0.05185683 0.36674800 7.139656e-01
## (x5-k1)+ -0.20262179 0.35524109 -0.57037825 5.686832e-01
## (x5-k2)+ 0.39611079 0.38100074 1.03965885 2.990122e-01
## (x5-k3)+ 0.22850765 0.18574765 1.23020481 2.192119e-01
## x6 -0.37636772 0.12936594 -2.90932616 3.787060e-03
## (x6-k1)+ -2.53034180 0.54147923 -4.67301731 3.842611e-06
## (x6-k2)+ 3.09616317 0.50045198 6.18673376 1.299459e-09
## (x6-k3)+ -0.44966092 0.09469955 -4.74828995 2.698957e-06
##
## Analysis of Variance
## =============================================
## Sumber df SS MS Fhit
## Regresi 24 17588.64 732.8599 41.33528
## Error 489 8669.797 17.72965
## Total 513 26258.43
## =============================================
## s = 4.210659 Rsq = 66.98281
## pvalue(F) = 1.631479e-101
r = read.csv("dataknot2_v2.csv", row.names = 1)
k.last = matrix(as.numeric(r[nrow(r), 4:ncol(r)]), nrow = 2, byrow = TRUE)
X = as.matrix(data[, 2:5]); y = data[, 1]
mx = buat_mx(X, k.last, "gcv")
print(pinv(t(mx) %*% mx) %*% t(mx) %*% y)
## [,1]
## [1,] 71.76466169
## [2,] 0.04093318
## [3,] -1.15731143
## [4,] 0.13598784
## [5,] -0.73903390
## [6,] 2.28729327
## [7,] 5.53938584
## [8,] -3.45397031
## [9,] 20.51459460
## [10,] 1.92008027
## [11,] 2.76969292
## [12,] -1.72698515
## [13,] -35.59306849
getwd()
## [1] "D:/DOKUMEN KULIAH/REGRESI NONPAR- SEM 5/TUGAS PERTEMUAN 6"