Midterm Examination
Jeneil Miller
2026-03-22
Problem 3
data("Auto")
data("College")
Auto## mpg cylinders displacement horsepower weight acceleration year origin
## 1 18.0 8 307.0 130 3504 12.0 70 1
## 2 15.0 8 350.0 165 3693 11.5 70 1
## 3 18.0 8 318.0 150 3436 11.0 70 1
## 4 16.0 8 304.0 150 3433 12.0 70 1
## 5 17.0 8 302.0 140 3449 10.5 70 1
## 6 15.0 8 429.0 198 4341 10.0 70 1
## 7 14.0 8 454.0 220 4354 9.0 70 1
## 8 14.0 8 440.0 215 4312 8.5 70 1
## 9 14.0 8 455.0 225 4425 10.0 70 1
## 10 15.0 8 390.0 190 3850 8.5 70 1
## 11 15.0 8 383.0 170 3563 10.0 70 1
## 12 14.0 8 340.0 160 3609 8.0 70 1
## 13 15.0 8 400.0 150 3761 9.5 70 1
## 14 14.0 8 455.0 225 3086 10.0 70 1
## 15 24.0 4 113.0 95 2372 15.0 70 3
## 16 22.0 6 198.0 95 2833 15.5 70 1
## 17 18.0 6 199.0 97 2774 15.5 70 1
## 18 21.0 6 200.0 85 2587 16.0 70 1
## 19 27.0 4 97.0 88 2130 14.5 70 3
## 20 26.0 4 97.0 46 1835 20.5 70 2
## 21 25.0 4 110.0 87 2672 17.5 70 2
## 22 24.0 4 107.0 90 2430 14.5 70 2
## 23 25.0 4 104.0 95 2375 17.5 70 2
## 24 26.0 4 121.0 113 2234 12.5 70 2
## 25 21.0 6 199.0 90 2648 15.0 70 1
## 26 10.0 8 360.0 215 4615 14.0 70 1
## 27 10.0 8 307.0 200 4376 15.0 70 1
## 28 11.0 8 318.0 210 4382 13.5 70 1
## 29 9.0 8 304.0 193 4732 18.5 70 1
## 30 27.0 4 97.0 88 2130 14.5 71 3
## 31 28.0 4 140.0 90 2264 15.5 71 1
## 32 25.0 4 113.0 95 2228 14.0 71 3
## 34 19.0 6 232.0 100 2634 13.0 71 1
## 35 16.0 6 225.0 105 3439 15.5 71 1
## 36 17.0 6 250.0 100 3329 15.5 71 1
## 37 19.0 6 250.0 88 3302 15.5 71 1
## 38 18.0 6 232.0 100 3288 15.5 71 1
## 39 14.0 8 350.0 165 4209 12.0 71 1
## 40 14.0 8 400.0 175 4464 11.5 71 1
## 41 14.0 8 351.0 153 4154 13.5 71 1
## 42 14.0 8 318.0 150 4096 13.0 71 1
## 43 12.0 8 383.0 180 4955 11.5 71 1
## 44 13.0 8 400.0 170 4746 12.0 71 1
## 45 13.0 8 400.0 175 5140 12.0 71 1
## 46 18.0 6 258.0 110 2962 13.5 71 1
## 47 22.0 4 140.0 72 2408 19.0 71 1
## 48 19.0 6 250.0 100 3282 15.0 71 1
## 49 18.0 6 250.0 88 3139 14.5 71 1
## 50 23.0 4 122.0 86 2220 14.0 71 1
## 51 28.0 4 116.0 90 2123 14.0 71 2
## 52 30.0 4 79.0 70 2074 19.5 71 2
## 53 30.0 4 88.0 76 2065 14.5 71 2
## 54 31.0 4 71.0 65 1773 19.0 71 3
## 55 35.0 4 72.0 69 1613 18.0 71 3
## 56 27.0 4 97.0 60 1834 19.0 71 2
## 57 26.0 4 91.0 70 1955 20.5 71 1
## 58 24.0 4 113.0 95 2278 15.5 72 3
## 59 25.0 4 97.5 80 2126 17.0 72 1
## 60 23.0 4 97.0 54 2254 23.5 72 2
## 61 20.0 4 140.0 90 2408 19.5 72 1
## 62 21.0 4 122.0 86 2226 16.5 72 1
## 63 13.0 8 350.0 165 4274 12.0 72 1
## 64 14.0 8 400.0 175 4385 12.0 72 1
## 65 15.0 8 318.0 150 4135 13.5 72 1
## 66 14.0 8 351.0 153 4129 13.0 72 1
## 67 17.0 8 304.0 150 3672 11.5 72 1
## 68 11.0 8 429.0 208 4633 11.0 72 1
## 69 13.0 8 350.0 155 4502 13.5 72 1
## 70 12.0 8 350.0 160 4456 13.5 72 1
## 71 13.0 8 400.0 190 4422 12.5 72 1
## 72 19.0 3 70.0 97 2330 13.5 72 3
## 73 15.0 8 304.0 150 3892 12.5 72 1
## 74 13.0 8 307.0 130 4098 14.0 72 1
## 75 13.0 8 302.0 140 4294 16.0 72 1
## 76 14.0 8 318.0 150 4077 14.0 72 1
## 77 18.0 4 121.0 112 2933 14.5 72 2
## 78 22.0 4 121.0 76 2511 18.0 72 2
## 79 21.0 4 120.0 87 2979 19.5 72 2
## 80 26.0 4 96.0 69 2189 18.0 72 2
## 81 22.0 4 122.0 86 2395 16.0 72 1
## 82 28.0 4 97.0 92 2288 17.0 72 3
## 83 23.0 4 120.0 97 2506 14.5 72 3
## 84 28.0 4 98.0 80 2164 15.0 72 1
## 85 27.0 4 97.0 88 2100 16.5 72 3
## 86 13.0 8 350.0 175 4100 13.0 73 1
## 87 14.0 8 304.0 150 3672 11.5 73 1
## 88 13.0 8 350.0 145 3988 13.0 73 1
## 89 14.0 8 302.0 137 4042 14.5 73 1
## 90 15.0 8 318.0 150 3777 12.5 73 1
## 91 12.0 8 429.0 198 4952 11.5 73 1
## 92 13.0 8 400.0 150 4464 12.0 73 1
## 93 13.0 8 351.0 158 4363 13.0 73 1
## 94 14.0 8 318.0 150 4237 14.5 73 1
## 95 13.0 8 440.0 215 4735 11.0 73 1
## 96 12.0 8 455.0 225 4951 11.0 73 1
## 97 13.0 8 360.0 175 3821 11.0 73 1
## 98 18.0 6 225.0 105 3121 16.5 73 1
## 99 16.0 6 250.0 100 3278 18.0 73 1
## 100 18.0 6 232.0 100 2945 16.0 73 1
## 101 18.0 6 250.0 88 3021 16.5 73 1
## 102 23.0 6 198.0 95 2904 16.0 73 1
## 103 26.0 4 97.0 46 1950 21.0 73 2
## 104 11.0 8 400.0 150 4997 14.0 73 1
## 105 12.0 8 400.0 167 4906 12.5 73 1
## 106 13.0 8 360.0 170 4654 13.0 73 1
## 107 12.0 8 350.0 180 4499 12.5 73 1
## 108 18.0 6 232.0 100 2789 15.0 73 1
## 109 20.0 4 97.0 88 2279 19.0 73 3
## 110 21.0 4 140.0 72 2401 19.5 73 1
## 111 22.0 4 108.0 94 2379 16.5 73 3
## 112 18.0 3 70.0 90 2124 13.5 73 3
## 113 19.0 4 122.0 85 2310 18.5 73 1
## 114 21.0 6 155.0 107 2472 14.0 73 1
## 115 26.0 4 98.0 90 2265 15.5 73 2
## 116 15.0 8 350.0 145 4082 13.0 73 1
## 117 16.0 8 400.0 230 4278 9.5 73 1
## 118 29.0 4 68.0 49 1867 19.5 73 2
## 119 24.0 4 116.0 75 2158 15.5 73 2
## 120 20.0 4 114.0 91 2582 14.0 73 2
## 121 19.0 4 121.0 112 2868 15.5 73 2
## 122 15.0 8 318.0 150 3399 11.0 73 1
## 123 24.0 4 121.0 110 2660 14.0 73 2
## 124 20.0 6 156.0 122 2807 13.5 73 3
## 125 11.0 8 350.0 180 3664 11.0 73 1
## 126 20.0 6 198.0 95 3102 16.5 74 1
## 128 19.0 6 232.0 100 2901 16.0 74 1
## 129 15.0 6 250.0 100 3336 17.0 74 1
## 130 31.0 4 79.0 67 1950 19.0 74 3
## 131 26.0 4 122.0 80 2451 16.5 74 1
## 132 32.0 4 71.0 65 1836 21.0 74 3
## 133 25.0 4 140.0 75 2542 17.0 74 1
## 134 16.0 6 250.0 100 3781 17.0 74 1
## 135 16.0 6 258.0 110 3632 18.0 74 1
## 136 18.0 6 225.0 105 3613 16.5 74 1
## 137 16.0 8 302.0 140 4141 14.0 74 1
## 138 13.0 8 350.0 150 4699 14.5 74 1
## 139 14.0 8 318.0 150 4457 13.5 74 1
## 140 14.0 8 302.0 140 4638 16.0 74 1
## 141 14.0 8 304.0 150 4257 15.5 74 1
## 142 29.0 4 98.0 83 2219 16.5 74 2
## 143 26.0 4 79.0 67 1963 15.5 74 2
## 144 26.0 4 97.0 78 2300 14.5 74 2
## 145 31.0 4 76.0 52 1649 16.5 74 3
## 146 32.0 4 83.0 61 2003 19.0 74 3
## 147 28.0 4 90.0 75 2125 14.5 74 1
## 148 24.0 4 90.0 75 2108 15.5 74 2
## 149 26.0 4 116.0 75 2246 14.0 74 2
## 150 24.0 4 120.0 97 2489 15.0 74 3
## 151 26.0 4 108.0 93 2391 15.5 74 3
## 152 31.0 4 79.0 67 2000 16.0 74 2
## 153 19.0 6 225.0 95 3264 16.0 75 1
## 154 18.0 6 250.0 105 3459 16.0 75 1
## 155 15.0 6 250.0 72 3432 21.0 75 1
## 156 15.0 6 250.0 72 3158 19.5 75 1
## 157 16.0 8 400.0 170 4668 11.5 75 1
## 158 15.0 8 350.0 145 4440 14.0 75 1
## 159 16.0 8 318.0 150 4498 14.5 75 1
## 160 14.0 8 351.0 148 4657 13.5 75 1
## 161 17.0 6 231.0 110 3907 21.0 75 1
## 162 16.0 6 250.0 105 3897 18.5 75 1
## 163 15.0 6 258.0 110 3730 19.0 75 1
## 164 18.0 6 225.0 95 3785 19.0 75 1
## 165 21.0 6 231.0 110 3039 15.0 75 1
## 166 20.0 8 262.0 110 3221 13.5 75 1
## 167 13.0 8 302.0 129 3169 12.0 75 1
## 168 29.0 4 97.0 75 2171 16.0 75 3
## 169 23.0 4 140.0 83 2639 17.0 75 1
## 170 20.0 6 232.0 100 2914 16.0 75 1
## 171 23.0 4 140.0 78 2592 18.5 75 1
## 172 24.0 4 134.0 96 2702 13.5 75 3
## 173 25.0 4 90.0 71 2223 16.5 75 2
## 174 24.0 4 119.0 97 2545 17.0 75 3
## 175 18.0 6 171.0 97 2984 14.5 75 1
## 176 29.0 4 90.0 70 1937 14.0 75 2
## 177 19.0 6 232.0 90 3211 17.0 75 1
## 178 23.0 4 115.0 95 2694 15.0 75 2
## 179 23.0 4 120.0 88 2957 17.0 75 2
## 180 22.0 4 121.0 98 2945 14.5 75 2
## 181 25.0 4 121.0 115 2671 13.5 75 2
## 182 33.0 4 91.0 53 1795 17.5 75 3
## 183 28.0 4 107.0 86 2464 15.5 76 2
## 184 25.0 4 116.0 81 2220 16.9 76 2
## 185 25.0 4 140.0 92 2572 14.9 76 1
## 186 26.0 4 98.0 79 2255 17.7 76 1
## 187 27.0 4 101.0 83 2202 15.3 76 2
## 188 17.5 8 305.0 140 4215 13.0 76 1
## 189 16.0 8 318.0 150 4190 13.0 76 1
## 190 15.5 8 304.0 120 3962 13.9 76 1
## 191 14.5 8 351.0 152 4215 12.8 76 1
## 192 22.0 6 225.0 100 3233 15.4 76 1
## 193 22.0 6 250.0 105 3353 14.5 76 1
## 194 24.0 6 200.0 81 3012 17.6 76 1
## 195 22.5 6 232.0 90 3085 17.6 76 1
## 196 29.0 4 85.0 52 2035 22.2 76 1
## 197 24.5 4 98.0 60 2164 22.1 76 1
## 198 29.0 4 90.0 70 1937 14.2 76 2
## 199 33.0 4 91.0 53 1795 17.4 76 3
## 200 20.0 6 225.0 100 3651 17.7 76 1
## 201 18.0 6 250.0 78 3574 21.0 76 1
## 202 18.5 6 250.0 110 3645 16.2 76 1
## 203 17.5 6 258.0 95 3193 17.8 76 1
## 204 29.5 4 97.0 71 1825 12.2 76 2
## 205 32.0 4 85.0 70 1990 17.0 76 3
## 206 28.0 4 97.0 75 2155 16.4 76 3
## 207 26.5 4 140.0 72 2565 13.6 76 1
## 208 20.0 4 130.0 102 3150 15.7 76 2
## 209 13.0 8 318.0 150 3940 13.2 76 1
## 210 19.0 4 120.0 88 3270 21.9 76 2
## 211 19.0 6 156.0 108 2930 15.5 76 3
## 212 16.5 6 168.0 120 3820 16.7 76 2
## 213 16.5 8 350.0 180 4380 12.1 76 1
## 214 13.0 8 350.0 145 4055 12.0 76 1
## 215 13.0 8 302.0 130 3870 15.0 76 1
## 216 13.0 8 318.0 150 3755 14.0 76 1
## 217 31.5 4 98.0 68 2045 18.5 77 3
## 218 30.0 4 111.0 80 2155 14.8 77 1
## 219 36.0 4 79.0 58 1825 18.6 77 2
## 220 25.5 4 122.0 96 2300 15.5 77 1
## 221 33.5 4 85.0 70 1945 16.8 77 3
## 222 17.5 8 305.0 145 3880 12.5 77 1
## 223 17.0 8 260.0 110 4060 19.0 77 1
## 224 15.5 8 318.0 145 4140 13.7 77 1
## 225 15.0 8 302.0 130 4295 14.9 77 1
## 226 17.5 6 250.0 110 3520 16.4 77 1
## 227 20.5 6 231.0 105 3425 16.9 77 1
## 228 19.0 6 225.0 100 3630 17.7 77 1
## 229 18.5 6 250.0 98 3525 19.0 77 1
## 230 16.0 8 400.0 180 4220 11.1 77 1
## 231 15.5 8 350.0 170 4165 11.4 77 1
## 232 15.5 8 400.0 190 4325 12.2 77 1
## 233 16.0 8 351.0 149 4335 14.5 77 1
## 234 29.0 4 97.0 78 1940 14.5 77 2
## 235 24.5 4 151.0 88 2740 16.0 77 1
## 236 26.0 4 97.0 75 2265 18.2 77 3
## 237 25.5 4 140.0 89 2755 15.8 77 1
## 238 30.5 4 98.0 63 2051 17.0 77 1
## 239 33.5 4 98.0 83 2075 15.9 77 1
## 240 30.0 4 97.0 67 1985 16.4 77 3
## 241 30.5 4 97.0 78 2190 14.1 77 2
## 242 22.0 6 146.0 97 2815 14.5 77 3
## 243 21.5 4 121.0 110 2600 12.8 77 2
## 244 21.5 3 80.0 110 2720 13.5 77 3
## 245 43.1 4 90.0 48 1985 21.5 78 2
## 246 36.1 4 98.0 66 1800 14.4 78 1
## 247 32.8 4 78.0 52 1985 19.4 78 3
## 248 39.4 4 85.0 70 2070 18.6 78 3
## 249 36.1 4 91.0 60 1800 16.4 78 3
## 250 19.9 8 260.0 110 3365 15.5 78 1
## 251 19.4 8 318.0 140 3735 13.2 78 1
## 252 20.2 8 302.0 139 3570 12.8 78 1
## 253 19.2 6 231.0 105 3535 19.2 78 1
## 254 20.5 6 200.0 95 3155 18.2 78 1
## 255 20.2 6 200.0 85 2965 15.8 78 1
## 256 25.1 4 140.0 88 2720 15.4 78 1
## 257 20.5 6 225.0 100 3430 17.2 78 1
## 258 19.4 6 232.0 90 3210 17.2 78 1
## 259 20.6 6 231.0 105 3380 15.8 78 1
## 260 20.8 6 200.0 85 3070 16.7 78 1
## 261 18.6 6 225.0 110 3620 18.7 78 1
## 262 18.1 6 258.0 120 3410 15.1 78 1
## 263 19.2 8 305.0 145 3425 13.2 78 1
## 264 17.7 6 231.0 165 3445 13.4 78 1
## 265 18.1 8 302.0 139 3205 11.2 78 1
## 266 17.5 8 318.0 140 4080 13.7 78 1
## 267 30.0 4 98.0 68 2155 16.5 78 1
## 268 27.5 4 134.0 95 2560 14.2 78 3
## 269 27.2 4 119.0 97 2300 14.7 78 3
## 270 30.9 4 105.0 75 2230 14.5 78 1
## 271 21.1 4 134.0 95 2515 14.8 78 3
## 272 23.2 4 156.0 105 2745 16.7 78 1
## 273 23.8 4 151.0 85 2855 17.6 78 1
## 274 23.9 4 119.0 97 2405 14.9 78 3
## 275 20.3 5 131.0 103 2830 15.9 78 2
## 276 17.0 6 163.0 125 3140 13.6 78 2
## 277 21.6 4 121.0 115 2795 15.7 78 2
## 278 16.2 6 163.0 133 3410 15.8 78 2
## 279 31.5 4 89.0 71 1990 14.9 78 2
## 280 29.5 4 98.0 68 2135 16.6 78 3
## 281 21.5 6 231.0 115 3245 15.4 79 1
## 282 19.8 6 200.0 85 2990 18.2 79 1
## 283 22.3 4 140.0 88 2890 17.3 79 1
## 284 20.2 6 232.0 90 3265 18.2 79 1
## 285 20.6 6 225.0 110 3360 16.6 79 1
## 286 17.0 8 305.0 130 3840 15.4 79 1
## 287 17.6 8 302.0 129 3725 13.4 79 1
## 288 16.5 8 351.0 138 3955 13.2 79 1
## 289 18.2 8 318.0 135 3830 15.2 79 1
## 290 16.9 8 350.0 155 4360 14.9 79 1
## 291 15.5 8 351.0 142 4054 14.3 79 1
## 292 19.2 8 267.0 125 3605 15.0 79 1
## 293 18.5 8 360.0 150 3940 13.0 79 1
## 294 31.9 4 89.0 71 1925 14.0 79 2
## 295 34.1 4 86.0 65 1975 15.2 79 3
## 296 35.7 4 98.0 80 1915 14.4 79 1
## 297 27.4 4 121.0 80 2670 15.0 79 1
## 298 25.4 5 183.0 77 3530 20.1 79 2
## 299 23.0 8 350.0 125 3900 17.4 79 1
## 300 27.2 4 141.0 71 3190 24.8 79 2
## 301 23.9 8 260.0 90 3420 22.2 79 1
## 302 34.2 4 105.0 70 2200 13.2 79 1
## 303 34.5 4 105.0 70 2150 14.9 79 1
## 304 31.8 4 85.0 65 2020 19.2 79 3
## 305 37.3 4 91.0 69 2130 14.7 79 2
## 306 28.4 4 151.0 90 2670 16.0 79 1
## 307 28.8 6 173.0 115 2595 11.3 79 1
## 308 26.8 6 173.0 115 2700 12.9 79 1
## 309 33.5 4 151.0 90 2556 13.2 79 1
## 310 41.5 4 98.0 76 2144 14.7 80 2
## 311 38.1 4 89.0 60 1968 18.8 80 3
## 312 32.1 4 98.0 70 2120 15.5 80 1
## 313 37.2 4 86.0 65 2019 16.4 80 3
## 314 28.0 4 151.0 90 2678 16.5 80 1
## 315 26.4 4 140.0 88 2870 18.1 80 1
## 316 24.3 4 151.0 90 3003 20.1 80 1
## 317 19.1 6 225.0 90 3381 18.7 80 1
## 318 34.3 4 97.0 78 2188 15.8 80 2
## 319 29.8 4 134.0 90 2711 15.5 80 3
## 320 31.3 4 120.0 75 2542 17.5 80 3
## 321 37.0 4 119.0 92 2434 15.0 80 3
## 322 32.2 4 108.0 75 2265 15.2 80 3
## 323 46.6 4 86.0 65 2110 17.9 80 3
## 324 27.9 4 156.0 105 2800 14.4 80 1
## 325 40.8 4 85.0 65 2110 19.2 80 3
## 326 44.3 4 90.0 48 2085 21.7 80 2
## 327 43.4 4 90.0 48 2335 23.7 80 2
## 328 36.4 5 121.0 67 2950 19.9 80 2
## 329 30.0 4 146.0 67 3250 21.8 80 2
## 330 44.6 4 91.0 67 1850 13.8 80 3
## 332 33.8 4 97.0 67 2145 18.0 80 3
## 333 29.8 4 89.0 62 1845 15.3 80 2
## 334 32.7 6 168.0 132 2910 11.4 80 3
## 335 23.7 3 70.0 100 2420 12.5 80 3
## 336 35.0 4 122.0 88 2500 15.1 80 2
## 338 32.4 4 107.0 72 2290 17.0 80 3
## 339 27.2 4 135.0 84 2490 15.7 81 1
## 340 26.6 4 151.0 84 2635 16.4 81 1
## 341 25.8 4 156.0 92 2620 14.4 81 1
## 342 23.5 6 173.0 110 2725 12.6 81 1
## 343 30.0 4 135.0 84 2385 12.9 81 1
## 344 39.1 4 79.0 58 1755 16.9 81 3
## 345 39.0 4 86.0 64 1875 16.4 81 1
## 346 35.1 4 81.0 60 1760 16.1 81 3
## 347 32.3 4 97.0 67 2065 17.8 81 3
## 348 37.0 4 85.0 65 1975 19.4 81 3
## 349 37.7 4 89.0 62 2050 17.3 81 3
## 350 34.1 4 91.0 68 1985 16.0 81 3
## 351 34.7 4 105.0 63 2215 14.9 81 1
## 352 34.4 4 98.0 65 2045 16.2 81 1
## 353 29.9 4 98.0 65 2380 20.7 81 1
## 354 33.0 4 105.0 74 2190 14.2 81 2
## 356 33.7 4 107.0 75 2210 14.4 81 3
## 357 32.4 4 108.0 75 2350 16.8 81 3
## 358 32.9 4 119.0 100 2615 14.8 81 3
## 359 31.6 4 120.0 74 2635 18.3 81 3
## 360 28.1 4 141.0 80 3230 20.4 81 2
## 361 30.7 6 145.0 76 3160 19.6 81 2
## 362 25.4 6 168.0 116 2900 12.6 81 3
## 363 24.2 6 146.0 120 2930 13.8 81 3
## 364 22.4 6 231.0 110 3415 15.8 81 1
## 365 26.6 8 350.0 105 3725 19.0 81 1
## 366 20.2 6 200.0 88 3060 17.1 81 1
## 367 17.6 6 225.0 85 3465 16.6 81 1
## 368 28.0 4 112.0 88 2605 19.6 82 1
## 369 27.0 4 112.0 88 2640 18.6 82 1
## 370 34.0 4 112.0 88 2395 18.0 82 1
## 371 31.0 4 112.0 85 2575 16.2 82 1
## 372 29.0 4 135.0 84 2525 16.0 82 1
## 373 27.0 4 151.0 90 2735 18.0 82 1
## 374 24.0 4 140.0 92 2865 16.4 82 1
## 375 36.0 4 105.0 74 1980 15.3 82 2
## 376 37.0 4 91.0 68 2025 18.2 82 3
## 377 31.0 4 91.0 68 1970 17.6 82 3
## 378 38.0 4 105.0 63 2125 14.7 82 1
## 379 36.0 4 98.0 70 2125 17.3 82 1
## 380 36.0 4 120.0 88 2160 14.5 82 3
## 381 36.0 4 107.0 75 2205 14.5 82 3
## 382 34.0 4 108.0 70 2245 16.9 82 3
## 383 38.0 4 91.0 67 1965 15.0 82 3
## 384 32.0 4 91.0 67 1965 15.7 82 3
## 385 38.0 4 91.0 67 1995 16.2 82 3
## 386 25.0 6 181.0 110 2945 16.4 82 1
## 387 38.0 6 262.0 85 3015 17.0 82 1
## 388 26.0 4 156.0 92 2585 14.5 82 1
## 389 22.0 6 232.0 112 2835 14.7 82 1
## 390 32.0 4 144.0 96 2665 13.9 82 3
## 391 36.0 4 135.0 84 2370 13.0 82 1
## 392 27.0 4 151.0 90 2950 17.3 82 1
## 393 27.0 4 140.0 86 2790 15.6 82 1
## 394 44.0 4 97.0 52 2130 24.6 82 2
## 395 32.0 4 135.0 84 2295 11.6 82 1
## 396 28.0 4 120.0 79 2625 18.6 82 1
## 397 31.0 4 119.0 82 2720 19.4 82 1
## name
## 1 chevrolet chevelle malibu
## 2 buick skylark 320
## 3 plymouth satellite
## 4 amc rebel sst
## 5 ford torino
## 6 ford galaxie 500
## 7 chevrolet impala
## 8 plymouth fury iii
## 9 pontiac catalina
## 10 amc ambassador dpl
## 11 dodge challenger se
## 12 plymouth 'cuda 340
## 13 chevrolet monte carlo
## 14 buick estate wagon (sw)
## 15 toyota corona mark ii
## 16 plymouth duster
## 17 amc hornet
## 18 ford maverick
## 19 datsun pl510
## 20 volkswagen 1131 deluxe sedan
## 21 peugeot 504
## 22 audi 100 ls
## 23 saab 99e
## 24 bmw 2002
## 25 amc gremlin
## 26 ford f250
## 27 chevy c20
## 28 dodge d200
## 29 hi 1200d
## 30 datsun pl510
## 31 chevrolet vega 2300
## 32 toyota corona
## 34 amc gremlin
## 35 plymouth satellite custom
## 36 chevrolet chevelle malibu
## 37 ford torino 500
## 38 amc matador
## 39 chevrolet impala
## 40 pontiac catalina brougham
## 41 ford galaxie 500
## 42 plymouth fury iii
## 43 dodge monaco (sw)
## 44 ford country squire (sw)
## 45 pontiac safari (sw)
## 46 amc hornet sportabout (sw)
## 47 chevrolet vega (sw)
## 48 pontiac firebird
## 49 ford mustang
## 50 mercury capri 2000
## 51 opel 1900
## 52 peugeot 304
## 53 fiat 124b
## 54 toyota corolla 1200
## 55 datsun 1200
## 56 volkswagen model 111
## 57 plymouth cricket
## 58 toyota corona hardtop
## 59 dodge colt hardtop
## 60 volkswagen type 3
## 61 chevrolet vega
## 62 ford pinto runabout
## 63 chevrolet impala
## 64 pontiac catalina
## 65 plymouth fury iii
## 66 ford galaxie 500
## 67 amc ambassador sst
## 68 mercury marquis
## 69 buick lesabre custom
## 70 oldsmobile delta 88 royale
## 71 chrysler newport royal
## 72 mazda rx2 coupe
## 73 amc matador (sw)
## 74 chevrolet chevelle concours (sw)
## 75 ford gran torino (sw)
## 76 plymouth satellite custom (sw)
## 77 volvo 145e (sw)
## 78 volkswagen 411 (sw)
## 79 peugeot 504 (sw)
## 80 renault 12 (sw)
## 81 ford pinto (sw)
## 82 datsun 510 (sw)
## 83 toyouta corona mark ii (sw)
## 84 dodge colt (sw)
## 85 toyota corolla 1600 (sw)
## 86 buick century 350
## 87 amc matador
## 88 chevrolet malibu
## 89 ford gran torino
## 90 dodge coronet custom
## 91 mercury marquis brougham
## 92 chevrolet caprice classic
## 93 ford ltd
## 94 plymouth fury gran sedan
## 95 chrysler new yorker brougham
## 96 buick electra 225 custom
## 97 amc ambassador brougham
## 98 plymouth valiant
## 99 chevrolet nova custom
## 100 amc hornet
## 101 ford maverick
## 102 plymouth duster
## 103 volkswagen super beetle
## 104 chevrolet impala
## 105 ford country
## 106 plymouth custom suburb
## 107 oldsmobile vista cruiser
## 108 amc gremlin
## 109 toyota carina
## 110 chevrolet vega
## 111 datsun 610
## 112 maxda rx3
## 113 ford pinto
## 114 mercury capri v6
## 115 fiat 124 sport coupe
## 116 chevrolet monte carlo s
## 117 pontiac grand prix
## 118 fiat 128
## 119 opel manta
## 120 audi 100ls
## 121 volvo 144ea
## 122 dodge dart custom
## 123 saab 99le
## 124 toyota mark ii
## 125 oldsmobile omega
## 126 plymouth duster
## 128 amc hornet
## 129 chevrolet nova
## 130 datsun b210
## 131 ford pinto
## 132 toyota corolla 1200
## 133 chevrolet vega
## 134 chevrolet chevelle malibu classic
## 135 amc matador
## 136 plymouth satellite sebring
## 137 ford gran torino
## 138 buick century luxus (sw)
## 139 dodge coronet custom (sw)
## 140 ford gran torino (sw)
## 141 amc matador (sw)
## 142 audi fox
## 143 volkswagen dasher
## 144 opel manta
## 145 toyota corona
## 146 datsun 710
## 147 dodge colt
## 148 fiat 128
## 149 fiat 124 tc
## 150 honda civic
## 151 subaru
## 152 fiat x1.9
## 153 plymouth valiant custom
## 154 chevrolet nova
## 155 mercury monarch
## 156 ford maverick
## 157 pontiac catalina
## 158 chevrolet bel air
## 159 plymouth grand fury
## 160 ford ltd
## 161 buick century
## 162 chevroelt chevelle malibu
## 163 amc matador
## 164 plymouth fury
## 165 buick skyhawk
## 166 chevrolet monza 2+2
## 167 ford mustang ii
## 168 toyota corolla
## 169 ford pinto
## 170 amc gremlin
## 171 pontiac astro
## 172 toyota corona
## 173 volkswagen dasher
## 174 datsun 710
## 175 ford pinto
## 176 volkswagen rabbit
## 177 amc pacer
## 178 audi 100ls
## 179 peugeot 504
## 180 volvo 244dl
## 181 saab 99le
## 182 honda civic cvcc
## 183 fiat 131
## 184 opel 1900
## 185 capri ii
## 186 dodge colt
## 187 renault 12tl
## 188 chevrolet chevelle malibu classic
## 189 dodge coronet brougham
## 190 amc matador
## 191 ford gran torino
## 192 plymouth valiant
## 193 chevrolet nova
## 194 ford maverick
## 195 amc hornet
## 196 chevrolet chevette
## 197 chevrolet woody
## 198 vw rabbit
## 199 honda civic
## 200 dodge aspen se
## 201 ford granada ghia
## 202 pontiac ventura sj
## 203 amc pacer d/l
## 204 volkswagen rabbit
## 205 datsun b-210
## 206 toyota corolla
## 207 ford pinto
## 208 volvo 245
## 209 plymouth volare premier v8
## 210 peugeot 504
## 211 toyota mark ii
## 212 mercedes-benz 280s
## 213 cadillac seville
## 214 chevy c10
## 215 ford f108
## 216 dodge d100
## 217 honda accord cvcc
## 218 buick opel isuzu deluxe
## 219 renault 5 gtl
## 220 plymouth arrow gs
## 221 datsun f-10 hatchback
## 222 chevrolet caprice classic
## 223 oldsmobile cutlass supreme
## 224 dodge monaco brougham
## 225 mercury cougar brougham
## 226 chevrolet concours
## 227 buick skylark
## 228 plymouth volare custom
## 229 ford granada
## 230 pontiac grand prix lj
## 231 chevrolet monte carlo landau
## 232 chrysler cordoba
## 233 ford thunderbird
## 234 volkswagen rabbit custom
## 235 pontiac sunbird coupe
## 236 toyota corolla liftback
## 237 ford mustang ii 2+2
## 238 chevrolet chevette
## 239 dodge colt m/m
## 240 subaru dl
## 241 volkswagen dasher
## 242 datsun 810
## 243 bmw 320i
## 244 mazda rx-4
## 245 volkswagen rabbit custom diesel
## 246 ford fiesta
## 247 mazda glc deluxe
## 248 datsun b210 gx
## 249 honda civic cvcc
## 250 oldsmobile cutlass salon brougham
## 251 dodge diplomat
## 252 mercury monarch ghia
## 253 pontiac phoenix lj
## 254 chevrolet malibu
## 255 ford fairmont (auto)
## 256 ford fairmont (man)
## 257 plymouth volare
## 258 amc concord
## 259 buick century special
## 260 mercury zephyr
## 261 dodge aspen
## 262 amc concord d/l
## 263 chevrolet monte carlo landau
## 264 buick regal sport coupe (turbo)
## 265 ford futura
## 266 dodge magnum xe
## 267 chevrolet chevette
## 268 toyota corona
## 269 datsun 510
## 270 dodge omni
## 271 toyota celica gt liftback
## 272 plymouth sapporo
## 273 oldsmobile starfire sx
## 274 datsun 200-sx
## 275 audi 5000
## 276 volvo 264gl
## 277 saab 99gle
## 278 peugeot 604sl
## 279 volkswagen scirocco
## 280 honda accord lx
## 281 pontiac lemans v6
## 282 mercury zephyr 6
## 283 ford fairmont 4
## 284 amc concord dl 6
## 285 dodge aspen 6
## 286 chevrolet caprice classic
## 287 ford ltd landau
## 288 mercury grand marquis
## 289 dodge st. regis
## 290 buick estate wagon (sw)
## 291 ford country squire (sw)
## 292 chevrolet malibu classic (sw)
## 293 chrysler lebaron town @ country (sw)
## 294 vw rabbit custom
## 295 maxda glc deluxe
## 296 dodge colt hatchback custom
## 297 amc spirit dl
## 298 mercedes benz 300d
## 299 cadillac eldorado
## 300 peugeot 504
## 301 oldsmobile cutlass salon brougham
## 302 plymouth horizon
## 303 plymouth horizon tc3
## 304 datsun 210
## 305 fiat strada custom
## 306 buick skylark limited
## 307 chevrolet citation
## 308 oldsmobile omega brougham
## 309 pontiac phoenix
## 310 vw rabbit
## 311 toyota corolla tercel
## 312 chevrolet chevette
## 313 datsun 310
## 314 chevrolet citation
## 315 ford fairmont
## 316 amc concord
## 317 dodge aspen
## 318 audi 4000
## 319 toyota corona liftback
## 320 mazda 626
## 321 datsun 510 hatchback
## 322 toyota corolla
## 323 mazda glc
## 324 dodge colt
## 325 datsun 210
## 326 vw rabbit c (diesel)
## 327 vw dasher (diesel)
## 328 audi 5000s (diesel)
## 329 mercedes-benz 240d
## 330 honda civic 1500 gl
## 332 subaru dl
## 333 vokswagen rabbit
## 334 datsun 280-zx
## 335 mazda rx-7 gs
## 336 triumph tr7 coupe
## 338 honda accord
## 339 plymouth reliant
## 340 buick skylark
## 341 dodge aries wagon (sw)
## 342 chevrolet citation
## 343 plymouth reliant
## 344 toyota starlet
## 345 plymouth champ
## 346 honda civic 1300
## 347 subaru
## 348 datsun 210 mpg
## 349 toyota tercel
## 350 mazda glc 4
## 351 plymouth horizon 4
## 352 ford escort 4w
## 353 ford escort 2h
## 354 volkswagen jetta
## 356 honda prelude
## 357 toyota corolla
## 358 datsun 200sx
## 359 mazda 626
## 360 peugeot 505s turbo diesel
## 361 volvo diesel
## 362 toyota cressida
## 363 datsun 810 maxima
## 364 buick century
## 365 oldsmobile cutlass ls
## 366 ford granada gl
## 367 chrysler lebaron salon
## 368 chevrolet cavalier
## 369 chevrolet cavalier wagon
## 370 chevrolet cavalier 2-door
## 371 pontiac j2000 se hatchback
## 372 dodge aries se
## 373 pontiac phoenix
## 374 ford fairmont futura
## 375 volkswagen rabbit l
## 376 mazda glc custom l
## 377 mazda glc custom
## 378 plymouth horizon miser
## 379 mercury lynx l
## 380 nissan stanza xe
## 381 honda accord
## 382 toyota corolla
## 383 honda civic
## 384 honda civic (auto)
## 385 datsun 310 gx
## 386 buick century limited
## 387 oldsmobile cutlass ciera (diesel)
## 388 chrysler lebaron medallion
## 389 ford granada l
## 390 toyota celica gt
## 391 dodge charger 2.2
## 392 chevrolet camaro
## 393 ford mustang gl
## 394 vw pickup
## 395 dodge rampage
## 396 ford ranger
## 397 chevy s-10sapply(Auto[,1:7], range)## mpg cylinders displacement horsepower weight acceleration year
## [1,] 9.0 3 68 46 1613 8.0 70
## [2,] 46.6 8 455 230 5140 24.8 82sapply(Auto[,1:7], mean)## mpg cylinders displacement horsepower weight acceleration
## 23.445918 5.471939 194.411990 104.469388 2977.584184 15.541327
## year
## 75.979592sapply(Auto[,1:7], sd)## mpg cylinders displacement horsepower weight acceleration
## 7.805007 1.705783 104.644004 38.491160 849.402560 2.758864
## year
## 3.683737Auto_sub <- Auto[-(20:80), ]
sapply(Auto_sub[,1:7], range)## mpg cylinders displacement horsepower weight acceleration year
## [1,] 11.0 3 68 46 1649 8.0 70
## [2,] 46.6 8 455 230 4997 24.8 82sapply(Auto_sub[,1:7], mean)## mpg cylinders displacement horsepower weight acceleration
## 24.216918 5.401813 189.441088 101.858006 2935.015106 15.613897
## year
## 76.854985sapply(Auto_sub[,1:7], sd)## mpg cylinders displacement horsepower weight acceleration
## 7.823191 1.665659 101.760735 36.601057 805.475115 2.758818
## year
## 3.323488pairs(Auto)
plot(Auto$horsepower, Auto$mpg)
Problem 4
set.seed(1)
train_idx <- sample(1:nrow(College), 0.8*nrow(College))
train <- College[train_idx, ]
test <- College[-train_idx, ]library(e1071)##
## Attaching package: 'e1071'## The following object is masked from 'package:ggplot2':
##
## elementsvm_model <- svm(Apps ~ ., data=train, kernel="radial")
pred_svm <- predict(svm_model, test)
mean((pred_svm - test$Apps)^2)## [1] 1188763library(nnet)
nn_model <- nnet(Apps ~ ., data=train, size=5, linout=TRUE)## # weights: 96
## initial value 14329732540.584587
## final value 6387881304.046285
## convergedpred_nn <- predict(nn_model, test)
mean((pred_nn - test$Apps)^2)## [1] 11793019mars_model <- earth(Apps ~ ., data=train)
pred_mars <- predict(mars_model, test)
mean((pred_mars - test$Apps)^2)## [1] 1354297evimp(mars_model)## nsubsets gcv rss
## Accept 12 100.0 100.0
## Top10perc 10 23.5 24.0
## Enroll 9 10.8 12.0
## Top25perc 8 7.6 9.1
## F.Undergrad 7 5.5 7.3
## Outstate 4 3.2 4.8
## Room.Board 3 2.4 3.9Problem 5
# Load packages
library(AppliedPredictiveModeling)## Warning: package 'AppliedPredictiveModeling' was built under R version 4.5.3# Load dataset
data(ChemicalManufacturingProcess)
X <- as.data.frame(ChemicalManufacturingProcess[, -1]) # all predictors
y <- ChemicalManufacturingProcess$Yield # response
# Check structure (important)
str(X)## 'data.frame': 176 obs. of 57 variables:
## $ BiologicalMaterial01 : num 6.25 8.01 8.01 8.01 7.47 6.12 7.48 6.94 6.94 6.94 ...
## $ BiologicalMaterial02 : num 49.6 61 61 61 63.3 ...
## $ BiologicalMaterial03 : num 57 67.5 67.5 67.5 72.2 ...
## $ BiologicalMaterial04 : num 12.7 14.6 14.6 14.6 14 ...
## $ BiologicalMaterial05 : num 19.5 19.4 19.4 19.4 17.9 ...
## $ BiologicalMaterial06 : num 43.7 53.1 53.1 53.1 54.7 ...
## $ BiologicalMaterial07 : num 100 100 100 100 100 100 100 100 100 100 ...
## $ BiologicalMaterial08 : num 16.7 19 19 19 18.2 ...
## $ BiologicalMaterial09 : num 11.4 12.6 12.6 12.6 12.8 ...
## $ BiologicalMaterial10 : num 3.46 3.46 3.46 3.46 3.05 3.78 3.04 3.85 3.85 3.85 ...
## $ BiologicalMaterial11 : num 138 154 154 154 148 ...
## $ BiologicalMaterial12 : num 18.8 21.1 21.1 21.1 21.1 ...
## $ ManufacturingProcess01: num NA 0 0 0 10.7 12 11.5 12 12 12 ...
## $ ManufacturingProcess02: num NA 0 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess03: num NA NA NA NA NA NA 1.56 1.55 1.56 1.55 ...
## $ ManufacturingProcess04: num NA 917 912 911 918 924 933 929 928 938 ...
## $ ManufacturingProcess05: num NA 1032 1004 1015 1028 ...
## $ ManufacturingProcess06: num NA 210 207 213 206 ...
## $ ManufacturingProcess07: num NA 177 178 177 178 178 177 178 177 177 ...
## $ ManufacturingProcess08: num NA 178 178 177 178 178 178 178 177 177 ...
## $ ManufacturingProcess09: num 43 46.6 45.1 44.9 45 ...
## $ ManufacturingProcess10: num NA NA NA NA NA NA 11.6 10.2 9.7 10.1 ...
## $ ManufacturingProcess11: num NA NA NA NA NA NA 11.5 11.3 11.1 10.2 ...
## $ ManufacturingProcess12: num NA 0 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess13: num 35.5 34 34.8 34.8 34.6 34 32.4 33.6 33.9 34.3 ...
## $ ManufacturingProcess14: num 4898 4869 4878 4897 4992 ...
## $ ManufacturingProcess15: num 6108 6095 6087 6102 6233 ...
## $ ManufacturingProcess16: num 4682 4617 4617 4635 4733 ...
## $ ManufacturingProcess17: num 35.5 34 34.8 34.8 33.9 33.4 33.8 33.6 33.9 35.3 ...
## $ ManufacturingProcess18: num 4865 4867 4877 4872 4886 ...
## $ ManufacturingProcess19: num 6049 6097 6078 6073 6102 ...
## $ ManufacturingProcess20: num 4665 4621 4621 4611 4659 ...
## $ ManufacturingProcess21: num 0 0 0 0 -0.7 -0.6 1.4 0 0 1 ...
## $ ManufacturingProcess22: num NA 3 4 5 8 9 1 2 3 4 ...
## $ ManufacturingProcess23: num NA 0 1 2 4 1 1 2 3 1 ...
## $ ManufacturingProcess24: num NA 3 4 5 18 1 1 2 3 4 ...
## $ ManufacturingProcess25: num 4873 4869 4897 4892 4930 ...
## $ ManufacturingProcess26: num 6074 6107 6116 6111 6151 ...
## $ ManufacturingProcess27: num 4685 4630 4637 4630 4684 ...
## $ ManufacturingProcess28: num 10.7 11.2 11.1 11.1 11.3 11.4 11.2 11.1 11.3 11.4 ...
## $ ManufacturingProcess29: num 21 21.4 21.3 21.3 21.6 21.7 21.2 21.2 21.5 21.7 ...
## $ ManufacturingProcess30: num 9.9 9.9 9.4 9.4 9 10.1 11.2 10.9 10.5 9.8 ...
## $ ManufacturingProcess31: num 69.1 68.7 69.3 69.3 69.4 68.2 67.6 67.9 68 68.5 ...
## $ ManufacturingProcess32: num 156 169 173 171 171 173 159 161 160 164 ...
## $ ManufacturingProcess33: num 66 66 66 68 70 70 65 65 65 66 ...
## $ ManufacturingProcess34: num 2.4 2.6 2.6 2.5 2.5 2.5 2.5 2.5 2.5 2.5 ...
## $ ManufacturingProcess35: num 486 508 509 496 468 490 475 478 491 488 ...
## $ ManufacturingProcess36: num 0.019 0.019 0.018 0.018 0.017 0.018 0.019 0.019 0.019 0.019 ...
## $ ManufacturingProcess37: num 0.5 2 0.7 1.2 0.2 0.4 0.8 1 1.2 1.8 ...
## $ ManufacturingProcess38: num 3 2 2 2 2 2 2 2 3 3 ...
## $ ManufacturingProcess39: num 7.2 7.2 7.2 7.2 7.3 7.2 7.3 7.3 7.4 7.1 ...
## $ ManufacturingProcess40: num NA 0.1 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess41: num NA 0.15 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess42: num 11.6 11.1 12 10.6 11 11.5 11.7 11.4 11.4 11.3 ...
## $ ManufacturingProcess43: num 3 0.9 1 1.1 1.1 2.2 0.7 0.8 0.9 0.8 ...
## $ ManufacturingProcess44: num 1.8 1.9 1.8 1.8 1.7 1.8 2 2 1.9 1.9 ...
## $ ManufacturingProcess45: num 2.4 2.2 2.3 2.1 2.1 2 2.2 2.2 2.1 2.4 ...str(y)## num [1:176] 38 42.4 42 41.4 42.5 ...# (a) Impute missing values
# Create df
df <- as.data.frame(ChemicalManufacturingProcess)
# Check structure
str(df)## 'data.frame': 176 obs. of 58 variables:
## $ Yield : num 38 42.4 42 41.4 42.5 ...
## $ BiologicalMaterial01 : num 6.25 8.01 8.01 8.01 7.47 6.12 7.48 6.94 6.94 6.94 ...
## $ BiologicalMaterial02 : num 49.6 61 61 61 63.3 ...
## $ BiologicalMaterial03 : num 57 67.5 67.5 67.5 72.2 ...
## $ BiologicalMaterial04 : num 12.7 14.6 14.6 14.6 14 ...
## $ BiologicalMaterial05 : num 19.5 19.4 19.4 19.4 17.9 ...
## $ BiologicalMaterial06 : num 43.7 53.1 53.1 53.1 54.7 ...
## $ BiologicalMaterial07 : num 100 100 100 100 100 100 100 100 100 100 ...
## $ BiologicalMaterial08 : num 16.7 19 19 19 18.2 ...
## $ BiologicalMaterial09 : num 11.4 12.6 12.6 12.6 12.8 ...
## $ BiologicalMaterial10 : num 3.46 3.46 3.46 3.46 3.05 3.78 3.04 3.85 3.85 3.85 ...
## $ BiologicalMaterial11 : num 138 154 154 154 148 ...
## $ BiologicalMaterial12 : num 18.8 21.1 21.1 21.1 21.1 ...
## $ ManufacturingProcess01: num NA 0 0 0 10.7 12 11.5 12 12 12 ...
## $ ManufacturingProcess02: num NA 0 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess03: num NA NA NA NA NA NA 1.56 1.55 1.56 1.55 ...
## $ ManufacturingProcess04: num NA 917 912 911 918 924 933 929 928 938 ...
## $ ManufacturingProcess05: num NA 1032 1004 1015 1028 ...
## $ ManufacturingProcess06: num NA 210 207 213 206 ...
## $ ManufacturingProcess07: num NA 177 178 177 178 178 177 178 177 177 ...
## $ ManufacturingProcess08: num NA 178 178 177 178 178 178 178 177 177 ...
## $ ManufacturingProcess09: num 43 46.6 45.1 44.9 45 ...
## $ ManufacturingProcess10: num NA NA NA NA NA NA 11.6 10.2 9.7 10.1 ...
## $ ManufacturingProcess11: num NA NA NA NA NA NA 11.5 11.3 11.1 10.2 ...
## $ ManufacturingProcess12: num NA 0 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess13: num 35.5 34 34.8 34.8 34.6 34 32.4 33.6 33.9 34.3 ...
## $ ManufacturingProcess14: num 4898 4869 4878 4897 4992 ...
## $ ManufacturingProcess15: num 6108 6095 6087 6102 6233 ...
## $ ManufacturingProcess16: num 4682 4617 4617 4635 4733 ...
## $ ManufacturingProcess17: num 35.5 34 34.8 34.8 33.9 33.4 33.8 33.6 33.9 35.3 ...
## $ ManufacturingProcess18: num 4865 4867 4877 4872 4886 ...
## $ ManufacturingProcess19: num 6049 6097 6078 6073 6102 ...
## $ ManufacturingProcess20: num 4665 4621 4621 4611 4659 ...
## $ ManufacturingProcess21: num 0 0 0 0 -0.7 -0.6 1.4 0 0 1 ...
## $ ManufacturingProcess22: num NA 3 4 5 8 9 1 2 3 4 ...
## $ ManufacturingProcess23: num NA 0 1 2 4 1 1 2 3 1 ...
## $ ManufacturingProcess24: num NA 3 4 5 18 1 1 2 3 4 ...
## $ ManufacturingProcess25: num 4873 4869 4897 4892 4930 ...
## $ ManufacturingProcess26: num 6074 6107 6116 6111 6151 ...
## $ ManufacturingProcess27: num 4685 4630 4637 4630 4684 ...
## $ ManufacturingProcess28: num 10.7 11.2 11.1 11.1 11.3 11.4 11.2 11.1 11.3 11.4 ...
## $ ManufacturingProcess29: num 21 21.4 21.3 21.3 21.6 21.7 21.2 21.2 21.5 21.7 ...
## $ ManufacturingProcess30: num 9.9 9.9 9.4 9.4 9 10.1 11.2 10.9 10.5 9.8 ...
## $ ManufacturingProcess31: num 69.1 68.7 69.3 69.3 69.4 68.2 67.6 67.9 68 68.5 ...
## $ ManufacturingProcess32: num 156 169 173 171 171 173 159 161 160 164 ...
## $ ManufacturingProcess33: num 66 66 66 68 70 70 65 65 65 66 ...
## $ ManufacturingProcess34: num 2.4 2.6 2.6 2.5 2.5 2.5 2.5 2.5 2.5 2.5 ...
## $ ManufacturingProcess35: num 486 508 509 496 468 490 475 478 491 488 ...
## $ ManufacturingProcess36: num 0.019 0.019 0.018 0.018 0.017 0.018 0.019 0.019 0.019 0.019 ...
## $ ManufacturingProcess37: num 0.5 2 0.7 1.2 0.2 0.4 0.8 1 1.2 1.8 ...
## $ ManufacturingProcess38: num 3 2 2 2 2 2 2 2 3 3 ...
## $ ManufacturingProcess39: num 7.2 7.2 7.2 7.2 7.3 7.2 7.3 7.3 7.4 7.1 ...
## $ ManufacturingProcess40: num NA 0.1 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess41: num NA 0.15 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess42: num 11.6 11.1 12 10.6 11 11.5 11.7 11.4 11.4 11.3 ...
## $ ManufacturingProcess43: num 3 0.9 1 1.1 1.1 2.2 0.7 0.8 0.9 0.8 ...
## $ ManufacturingProcess44: num 1.8 1.9 1.8 1.8 1.7 1.8 2 2 1.9 1.9 ...
## $ ManufacturingProcess45: num 2.4 2.2 2.3 2.1 2.1 2 2.2 2.2 2.1 2.4 ...preProc <- preProcess(df, method = "medianImpute")
df <- predict(preProc, df)
# Scale numeric predictors (exclude response)
numeric_vars <- setdiff(names(df), "Yield")
df[numeric_vars] <- scale(df[numeric_vars])# (b) Train-test split (80/20)
trainIndex <- createDataPartition(df$Yield, p = 0.8, list = FALSE)
trainData <- df[trainIndex, ]
testData <- df[-trainIndex, ]# Cross-validation setup
control <- trainControl(method = "cv", number = 5)
formula <- Yield ~ .
# Train models
lm_model <- train(formula, data = trainData, method = "lm", trControl = control)## Warning in predict.lm(modelFit, newdata): prediction from rank-deficient fit;
## attr(*, "non-estim") has doubtful casesridge_model <- train(formula, data = trainData, method = "glmnet",
trControl = control,
tuneGrid = expand.grid(alpha = 0, lambda = seq(0.001, 1, length = 10)))
lasso_model <- train(formula, data = trainData, method = "glmnet",
trControl = control,
tuneGrid = expand.grid(alpha = 1, lambda = seq(0.001, 1, length = 10)))
enet_model <- train(formula, data = trainData, method = "glmnet",
trControl = control,
tuneLength = 10)
# Show best tuning parameters
ridge_model$bestTune## alpha lambda
## 10 0 1lasso_model$bestTune## alpha lambda
## 2 1 0.112enet_model$bestTune## alpha lambda
## 97 1 0.07758802# (c) Compare models
results <- resamples(list(
LM = lm_model,
Ridge = ridge_model,
Lasso = lasso_model,
ENET = enet_model
))
summary(results)##
## Call:
## summary.resamples(object = results)
##
## Models: LM, Ridge, Lasso, ENET
## Number of resamples: 5
##
## MAE
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## LM 1.1569852 1.2811446 2.5722833 3.1861152 4.9747624 5.9454004 0
## Ridge 0.8837748 0.9391611 0.9548600 1.0826445 1.0803394 1.5550871 0
## Lasso 0.8047478 0.8334269 1.0054266 0.9483970 1.0365544 1.0618294 0
## ENET 0.8311569 0.8696135 0.8701004 0.8960332 0.9382661 0.9710293 0
##
## RMSE
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## LM 1.3936548 1.748762 6.959025 10.020866 19.062492 20.940395 0
## Ridge 1.0782612 1.194793 1.280354 1.543592 1.466862 2.697690 0
## Lasso 0.9825905 1.058715 1.228523 1.177783 1.287353 1.331736 0
## ENET 1.0420772 1.060283 1.094077 1.126386 1.163196 1.272297 0
##
## Rsquared
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## LM 0.01131565 0.01943617 0.09279589 0.1607647 0.3250457 0.3552302 0
## Ridge 0.18848609 0.40681220 0.41896641 0.4897641 0.7110236 0.7235322 0
## Lasso 0.48791470 0.51808957 0.61494823 0.5840811 0.6264617 0.6729915 0
## ENET 0.54544269 0.61406080 0.61465018 0.6304020 0.6662081 0.7116482 0# (c) Test set performance
pred_lm <- predict(lm_model, newdata = testData)
pred_ridge <- predict(ridge_model, newdata = testData)
pred_lasso <- predict(lasso_model, newdata = testData)
pred_enet <- predict(enet_model, newdata = testData)
postResample(pred_lm, testData$Yield)## RMSE Rsquared MAE
## 1.4069374 0.5239431 0.9938425postResample(pred_ridge, testData$Yield)## RMSE Rsquared MAE
## 1.2272269 0.6301739 0.9604219postResample(pred_lasso, testData$Yield)## RMSE Rsquared MAE
## 1.2271240 0.6389607 0.9854725postResample(pred_enet, testData$Yield)## RMSE Rsquared MAE
## 1.2158635 0.6388860 0.9694533# (d) Variable importance (Elastic Net)
var_imp <- varImp(enet_model)
top_vars <- rownames(var_imp$importance)[order(var_imp$importance$Overall, decreasing = TRUE)][1:5]
top_vars## [1] "ManufacturingProcess32" "ManufacturingProcess09" "ManufacturingProcess17"
## [4] "ManufacturingProcess45" "ManufacturingProcess06"# (e) Plot relationships of top predictors
top_vars <- varImp(enet_model)$importance
top_vars <- rownames(top_vars)[order(top_vars$Overall, decreasing = TRUE)][1:5]
for (var in top_vars) {
plot(df[[var]], df$Yield,
main = paste("Yield vs", var),
xlab = var,
ylab = "Yield")
}
