Homework Week 1
Problem 1
Prepare “Auto” data set
auto <- read.csv("Auto.csv", TRUE, na.strings = "?")
auto <- na.omit(auto)Which of the predictors are quantitative, and which are qualitative?
str(auto)## 'data.frame': 392 obs. of 9 variables:
## $ mpg : num 18 15 18 16 17 15 14 14 14 15 ...
## $ cylinders : int 8 8 8 8 8 8 8 8 8 8 ...
## $ displacement: num 307 350 318 304 302 429 454 440 455 390 ...
## $ horsepower : int 130 165 150 150 140 198 220 215 225 190 ...
## $ weight : int 3504 3693 3436 3433 3449 4341 4354 4312 4425 3850 ...
## $ acceleration: num 12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
## $ year : int 70 70 70 70 70 70 70 70 70 70 ...
## $ origin : int 1 1 1 1 1 1 1 1 1 1 ...
## $ name : Factor w/ 304 levels "amc ambassador brougham",..: 49 36 231 14 161 141 54 223 241 2 ...
## - attr(*, "na.action")= 'omit' Named int 33 127 331 337 355
## ..- attr(*, "names")= chr "33" "127" "331" "337" ...The variables mpg, cylinders, displacement, weight, acceleration, year, and origin are quantitative. Name is qualitative.
What is the range of each quantitative predictor
range(auto$mpg)## [1] 9.0 46.6range(auto$cylinders)## [1] 3 8range(auto$displacement)## [1] 68 455range(auto$weight)## [1] 1613 5140range(auto$acceleration)## [1] 8.0 24.8range(auto$year)## [1] 70 82range(auto$origin)## [1] 1 3What is the mean and standard deviation of each quantitative predictor?
Mean
mean(auto$mpg)## [1] 23.44592mean(auto$cylinders)## [1] 5.471939mean(auto$displacement)## [1] 194.412mean(auto$weight)## [1] 2977.584mean(auto$acceleration)## [1] 15.54133mean(auto$year)## [1] 75.97959mean(auto$origin)## [1] 1.576531Standard Deviation
sd(auto$mpg)## [1] 7.805007sd(auto$cylinders)## [1] 1.705783sd(auto$displacement)## [1] 104.644sd(auto$weight)## [1] 849.4026sd(auto$acceleration)## [1] 2.758864sd(auto$year)## [1] 3.683737sd(auto$origin)## [1] 0.8055182Now remove the 10th through 85th observations. What is the range, mean, and standard deviation of each predictor in the subset of the data that remains?
Omit Values
auto_new <- auto[-c(10:84),-9]
print(auto_new)## mpg cylinders displacement horsepower weight acceleration year origin
## 1 18.0 8 307 130 3504 12.0 70 1
## 2 15.0 8 350 165 3693 11.5 70 1
## 3 18.0 8 318 150 3436 11.0 70 1
## 4 16.0 8 304 150 3433 12.0 70 1
## 5 17.0 8 302 140 3449 10.5 70 1
## 6 15.0 8 429 198 4341 10.0 70 1
## 7 14.0 8 454 220 4354 9.0 70 1
## 8 14.0 8 440 215 4312 8.5 70 1
## 9 14.0 8 455 225 4425 10.0 70 1
## 86 13.0 8 350 175 4100 13.0 73 1
## 87 14.0 8 304 150 3672 11.5 73 1
## 88 13.0 8 350 145 3988 13.0 73 1
## 89 14.0 8 302 137 4042 14.5 73 1
## 90 15.0 8 318 150 3777 12.5 73 1
## 91 12.0 8 429 198 4952 11.5 73 1
## 92 13.0 8 400 150 4464 12.0 73 1
## 93 13.0 8 351 158 4363 13.0 73 1
## 94 14.0 8 318 150 4237 14.5 73 1
## 95 13.0 8 440 215 4735 11.0 73 1
## 96 12.0 8 455 225 4951 11.0 73 1
## 97 13.0 8 360 175 3821 11.0 73 1
## 98 18.0 6 225 105 3121 16.5 73 1
## 99 16.0 6 250 100 3278 18.0 73 1
## 100 18.0 6 232 100 2945 16.0 73 1
## 101 18.0 6 250 88 3021 16.5 73 1
## 102 23.0 6 198 95 2904 16.0 73 1
## 103 26.0 4 97 46 1950 21.0 73 2
## 104 11.0 8 400 150 4997 14.0 73 1
## 105 12.0 8 400 167 4906 12.5 73 1
## 106 13.0 8 360 170 4654 13.0 73 1
## 107 12.0 8 350 180 4499 12.5 73 1
## 108 18.0 6 232 100 2789 15.0 73 1
## 109 20.0 4 97 88 2279 19.0 73 3
## 110 21.0 4 140 72 2401 19.5 73 1
## 111 22.0 4 108 94 2379 16.5 73 3
## 112 18.0 3 70 90 2124 13.5 73 3
## 113 19.0 4 122 85 2310 18.5 73 1
## 114 21.0 6 155 107 2472 14.0 73 1
## 115 26.0 4 98 90 2265 15.5 73 2
## 116 15.0 8 350 145 4082 13.0 73 1
## 117 16.0 8 400 230 4278 9.5 73 1
## 118 29.0 4 68 49 1867 19.5 73 2
## 119 24.0 4 116 75 2158 15.5 73 2
## 120 20.0 4 114 91 2582 14.0 73 2
## 121 19.0 4 121 112 2868 15.5 73 2
## 122 15.0 8 318 150 3399 11.0 73 1
## 123 24.0 4 121 110 2660 14.0 73 2
## 124 20.0 6 156 122 2807 13.5 73 3
## 125 11.0 8 350 180 3664 11.0 73 1
## 126 20.0 6 198 95 3102 16.5 74 1
## 128 19.0 6 232 100 2901 16.0 74 1
## 129 15.0 6 250 100 3336 17.0 74 1
## 130 31.0 4 79 67 1950 19.0 74 3
## 131 26.0 4 122 80 2451 16.5 74 1
## 132 32.0 4 71 65 1836 21.0 74 3
## 133 25.0 4 140 75 2542 17.0 74 1
## 134 16.0 6 250 100 3781 17.0 74 1
## 135 16.0 6 258 110 3632 18.0 74 1
## 136 18.0 6 225 105 3613 16.5 74 1
## 137 16.0 8 302 140 4141 14.0 74 1
## 138 13.0 8 350 150 4699 14.5 74 1
## 139 14.0 8 318 150 4457 13.5 74 1
## 140 14.0 8 302 140 4638 16.0 74 1
## 141 14.0 8 304 150 4257 15.5 74 1
## 142 29.0 4 98 83 2219 16.5 74 2
## 143 26.0 4 79 67 1963 15.5 74 2
## 144 26.0 4 97 78 2300 14.5 74 2
## 145 31.0 4 76 52 1649 16.5 74 3
## 146 32.0 4 83 61 2003 19.0 74 3
## 147 28.0 4 90 75 2125 14.5 74 1
## 148 24.0 4 90 75 2108 15.5 74 2
## 149 26.0 4 116 75 2246 14.0 74 2
## 150 24.0 4 120 97 2489 15.0 74 3
## 151 26.0 4 108 93 2391 15.5 74 3
## 152 31.0 4 79 67 2000 16.0 74 2
## 153 19.0 6 225 95 3264 16.0 75 1
## 154 18.0 6 250 105 3459 16.0 75 1
## 155 15.0 6 250 72 3432 21.0 75 1
## 156 15.0 6 250 72 3158 19.5 75 1
## 157 16.0 8 400 170 4668 11.5 75 1
## 158 15.0 8 350 145 4440 14.0 75 1
## 159 16.0 8 318 150 4498 14.5 75 1
## 160 14.0 8 351 148 4657 13.5 75 1
## 161 17.0 6 231 110 3907 21.0 75 1
## 162 16.0 6 250 105 3897 18.5 75 1
## 163 15.0 6 258 110 3730 19.0 75 1
## 164 18.0 6 225 95 3785 19.0 75 1
## 165 21.0 6 231 110 3039 15.0 75 1
## 166 20.0 8 262 110 3221 13.5 75 1
## 167 13.0 8 302 129 3169 12.0 75 1
## 168 29.0 4 97 75 2171 16.0 75 3
## 169 23.0 4 140 83 2639 17.0 75 1
## 170 20.0 6 232 100 2914 16.0 75 1
## 171 23.0 4 140 78 2592 18.5 75 1
## 172 24.0 4 134 96 2702 13.5 75 3
## 173 25.0 4 90 71 2223 16.5 75 2
## 174 24.0 4 119 97 2545 17.0 75 3
## 175 18.0 6 171 97 2984 14.5 75 1
## 176 29.0 4 90 70 1937 14.0 75 2
## 177 19.0 6 232 90 3211 17.0 75 1
## 178 23.0 4 115 95 2694 15.0 75 2
## 179 23.0 4 120 88 2957 17.0 75 2
## 180 22.0 4 121 98 2945 14.5 75 2
## 181 25.0 4 121 115 2671 13.5 75 2
## 182 33.0 4 91 53 1795 17.5 75 3
## 183 28.0 4 107 86 2464 15.5 76 2
## 184 25.0 4 116 81 2220 16.9 76 2
## 185 25.0 4 140 92 2572 14.9 76 1
## 186 26.0 4 98 79 2255 17.7 76 1
## 187 27.0 4 101 83 2202 15.3 76 2
## 188 17.5 8 305 140 4215 13.0 76 1
## 189 16.0 8 318 150 4190 13.0 76 1
## 190 15.5 8 304 120 3962 13.9 76 1
## 191 14.5 8 351 152 4215 12.8 76 1
## 192 22.0 6 225 100 3233 15.4 76 1
## 193 22.0 6 250 105 3353 14.5 76 1
## 194 24.0 6 200 81 3012 17.6 76 1
## 195 22.5 6 232 90 3085 17.6 76 1
## 196 29.0 4 85 52 2035 22.2 76 1
## 197 24.5 4 98 60 2164 22.1 76 1
## 198 29.0 4 90 70 1937 14.2 76 2
## 199 33.0 4 91 53 1795 17.4 76 3
## 200 20.0 6 225 100 3651 17.7 76 1
## 201 18.0 6 250 78 3574 21.0 76 1
## 202 18.5 6 250 110 3645 16.2 76 1
## 203 17.5 6 258 95 3193 17.8 76 1
## 204 29.5 4 97 71 1825 12.2 76 2
## 205 32.0 4 85 70 1990 17.0 76 3
## 206 28.0 4 97 75 2155 16.4 76 3
## 207 26.5 4 140 72 2565 13.6 76 1
## 208 20.0 4 130 102 3150 15.7 76 2
## 209 13.0 8 318 150 3940 13.2 76 1
## 210 19.0 4 120 88 3270 21.9 76 2
## 211 19.0 6 156 108 2930 15.5 76 3
## 212 16.5 6 168 120 3820 16.7 76 2
## 213 16.5 8 350 180 4380 12.1 76 1
## 214 13.0 8 350 145 4055 12.0 76 1
## 215 13.0 8 302 130 3870 15.0 76 1
## 216 13.0 8 318 150 3755 14.0 76 1
## 217 31.5 4 98 68 2045 18.5 77 3
## 218 30.0 4 111 80 2155 14.8 77 1
## 219 36.0 4 79 58 1825 18.6 77 2
## 220 25.5 4 122 96 2300 15.5 77 1
## 221 33.5 4 85 70 1945 16.8 77 3
## 222 17.5 8 305 145 3880 12.5 77 1
## 223 17.0 8 260 110 4060 19.0 77 1
## 224 15.5 8 318 145 4140 13.7 77 1
## 225 15.0 8 302 130 4295 14.9 77 1
## 226 17.5 6 250 110 3520 16.4 77 1
## 227 20.5 6 231 105 3425 16.9 77 1
## 228 19.0 6 225 100 3630 17.7 77 1
## 229 18.5 6 250 98 3525 19.0 77 1
## 230 16.0 8 400 180 4220 11.1 77 1
## 231 15.5 8 350 170 4165 11.4 77 1
## 232 15.5 8 400 190 4325 12.2 77 1
## 233 16.0 8 351 149 4335 14.5 77 1
## 234 29.0 4 97 78 1940 14.5 77 2
## 235 24.5 4 151 88 2740 16.0 77 1
## 236 26.0 4 97 75 2265 18.2 77 3
## 237 25.5 4 140 89 2755 15.8 77 1
## 238 30.5 4 98 63 2051 17.0 77 1
## 239 33.5 4 98 83 2075 15.9 77 1
## 240 30.0 4 97 67 1985 16.4 77 3
## 241 30.5 4 97 78 2190 14.1 77 2
## 242 22.0 6 146 97 2815 14.5 77 3
## 243 21.5 4 121 110 2600 12.8 77 2
## 244 21.5 3 80 110 2720 13.5 77 3
## 245 43.1 4 90 48 1985 21.5 78 2
## 246 36.1 4 98 66 1800 14.4 78 1
## 247 32.8 4 78 52 1985 19.4 78 3
## 248 39.4 4 85 70 2070 18.6 78 3
## 249 36.1 4 91 60 1800 16.4 78 3
## 250 19.9 8 260 110 3365 15.5 78 1
## 251 19.4 8 318 140 3735 13.2 78 1
## 252 20.2 8 302 139 3570 12.8 78 1
## 253 19.2 6 231 105 3535 19.2 78 1
## 254 20.5 6 200 95 3155 18.2 78 1
## 255 20.2 6 200 85 2965 15.8 78 1
## 256 25.1 4 140 88 2720 15.4 78 1
## 257 20.5 6 225 100 3430 17.2 78 1
## 258 19.4 6 232 90 3210 17.2 78 1
## 259 20.6 6 231 105 3380 15.8 78 1
## 260 20.8 6 200 85 3070 16.7 78 1
## 261 18.6 6 225 110 3620 18.7 78 1
## 262 18.1 6 258 120 3410 15.1 78 1
## 263 19.2 8 305 145 3425 13.2 78 1
## 264 17.7 6 231 165 3445 13.4 78 1
## 265 18.1 8 302 139 3205 11.2 78 1
## 266 17.5 8 318 140 4080 13.7 78 1
## 267 30.0 4 98 68 2155 16.5 78 1
## 268 27.5 4 134 95 2560 14.2 78 3
## 269 27.2 4 119 97 2300 14.7 78 3
## 270 30.9 4 105 75 2230 14.5 78 1
## 271 21.1 4 134 95 2515 14.8 78 3
## 272 23.2 4 156 105 2745 16.7 78 1
## 273 23.8 4 151 85 2855 17.6 78 1
## 274 23.9 4 119 97 2405 14.9 78 3
## 275 20.3 5 131 103 2830 15.9 78 2
## 276 17.0 6 163 125 3140 13.6 78 2
## 277 21.6 4 121 115 2795 15.7 78 2
## 278 16.2 6 163 133 3410 15.8 78 2
## 279 31.5 4 89 71 1990 14.9 78 2
## 280 29.5 4 98 68 2135 16.6 78 3
## 281 21.5 6 231 115 3245 15.4 79 1
## 282 19.8 6 200 85 2990 18.2 79 1
## 283 22.3 4 140 88 2890 17.3 79 1
## 284 20.2 6 232 90 3265 18.2 79 1
## 285 20.6 6 225 110 3360 16.6 79 1
## 286 17.0 8 305 130 3840 15.4 79 1
## 287 17.6 8 302 129 3725 13.4 79 1
## 288 16.5 8 351 138 3955 13.2 79 1
## 289 18.2 8 318 135 3830 15.2 79 1
## 290 16.9 8 350 155 4360 14.9 79 1
## 291 15.5 8 351 142 4054 14.3 79 1
## 292 19.2 8 267 125 3605 15.0 79 1
## 293 18.5 8 360 150 3940 13.0 79 1
## 294 31.9 4 89 71 1925 14.0 79 2
## 295 34.1 4 86 65 1975 15.2 79 3
## 296 35.7 4 98 80 1915 14.4 79 1
## 297 27.4 4 121 80 2670 15.0 79 1
## 298 25.4 5 183 77 3530 20.1 79 2
## 299 23.0 8 350 125 3900 17.4 79 1
## 300 27.2 4 141 71 3190 24.8 79 2
## 301 23.9 8 260 90 3420 22.2 79 1
## 302 34.2 4 105 70 2200 13.2 79 1
## 303 34.5 4 105 70 2150 14.9 79 1
## 304 31.8 4 85 65 2020 19.2 79 3
## 305 37.3 4 91 69 2130 14.7 79 2
## 306 28.4 4 151 90 2670 16.0 79 1
## 307 28.8 6 173 115 2595 11.3 79 1
## 308 26.8 6 173 115 2700 12.9 79 1
## 309 33.5 4 151 90 2556 13.2 79 1
## 310 41.5 4 98 76 2144 14.7 80 2
## 311 38.1 4 89 60 1968 18.8 80 3
## 312 32.1 4 98 70 2120 15.5 80 1
## 313 37.2 4 86 65 2019 16.4 80 3
## 314 28.0 4 151 90 2678 16.5 80 1
## 315 26.4 4 140 88 2870 18.1 80 1
## 316 24.3 4 151 90 3003 20.1 80 1
## 317 19.1 6 225 90 3381 18.7 80 1
## 318 34.3 4 97 78 2188 15.8 80 2
## 319 29.8 4 134 90 2711 15.5 80 3
## 320 31.3 4 120 75 2542 17.5 80 3
## 321 37.0 4 119 92 2434 15.0 80 3
## 322 32.2 4 108 75 2265 15.2 80 3
## 323 46.6 4 86 65 2110 17.9 80 3
## 324 27.9 4 156 105 2800 14.4 80 1
## 325 40.8 4 85 65 2110 19.2 80 3
## 326 44.3 4 90 48 2085 21.7 80 2
## 327 43.4 4 90 48 2335 23.7 80 2
## 328 36.4 5 121 67 2950 19.9 80 2
## 329 30.0 4 146 67 3250 21.8 80 2
## 330 44.6 4 91 67 1850 13.8 80 3
## 332 33.8 4 97 67 2145 18.0 80 3
## 333 29.8 4 89 62 1845 15.3 80 2
## 334 32.7 6 168 132 2910 11.4 80 3
## 335 23.7 3 70 100 2420 12.5 80 3
## 336 35.0 4 122 88 2500 15.1 80 2
## 338 32.4 4 107 72 2290 17.0 80 3
## 339 27.2 4 135 84 2490 15.7 81 1
## 340 26.6 4 151 84 2635 16.4 81 1
## 341 25.8 4 156 92 2620 14.4 81 1
## 342 23.5 6 173 110 2725 12.6 81 1
## 343 30.0 4 135 84 2385 12.9 81 1
## 344 39.1 4 79 58 1755 16.9 81 3
## 345 39.0 4 86 64 1875 16.4 81 1
## 346 35.1 4 81 60 1760 16.1 81 3
## 347 32.3 4 97 67 2065 17.8 81 3
## 348 37.0 4 85 65 1975 19.4 81 3
## 349 37.7 4 89 62 2050 17.3 81 3
## 350 34.1 4 91 68 1985 16.0 81 3
## 351 34.7 4 105 63 2215 14.9 81 1
## 352 34.4 4 98 65 2045 16.2 81 1
## 353 29.9 4 98 65 2380 20.7 81 1
## 354 33.0 4 105 74 2190 14.2 81 2
## 356 33.7 4 107 75 2210 14.4 81 3
## 357 32.4 4 108 75 2350 16.8 81 3
## 358 32.9 4 119 100 2615 14.8 81 3
## 359 31.6 4 120 74 2635 18.3 81 3
## 360 28.1 4 141 80 3230 20.4 81 2
## 361 30.7 6 145 76 3160 19.6 81 2
## 362 25.4 6 168 116 2900 12.6 81 3
## 363 24.2 6 146 120 2930 13.8 81 3
## 364 22.4 6 231 110 3415 15.8 81 1
## 365 26.6 8 350 105 3725 19.0 81 1
## 366 20.2 6 200 88 3060 17.1 81 1
## 367 17.6 6 225 85 3465 16.6 81 1
## 368 28.0 4 112 88 2605 19.6 82 1
## 369 27.0 4 112 88 2640 18.6 82 1
## 370 34.0 4 112 88 2395 18.0 82 1
## 371 31.0 4 112 85 2575 16.2 82 1
## 372 29.0 4 135 84 2525 16.0 82 1
## 373 27.0 4 151 90 2735 18.0 82 1
## 374 24.0 4 140 92 2865 16.4 82 1
## 375 36.0 4 105 74 1980 15.3 82 2
## 376 37.0 4 91 68 2025 18.2 82 3
## 377 31.0 4 91 68 1970 17.6 82 3
## 378 38.0 4 105 63 2125 14.7 82 1
## 379 36.0 4 98 70 2125 17.3 82 1
## 380 36.0 4 120 88 2160 14.5 82 3
## 381 36.0 4 107 75 2205 14.5 82 3
## 382 34.0 4 108 70 2245 16.9 82 3
## 383 38.0 4 91 67 1965 15.0 82 3
## 384 32.0 4 91 67 1965 15.7 82 3
## 385 38.0 4 91 67 1995 16.2 82 3
## 386 25.0 6 181 110 2945 16.4 82 1
## 387 38.0 6 262 85 3015 17.0 82 1
## 388 26.0 4 156 92 2585 14.5 82 1
## 389 22.0 6 232 112 2835 14.7 82 1
## 390 32.0 4 144 96 2665 13.9 82 3
## 391 36.0 4 135 84 2370 13.0 82 1
## 392 27.0 4 151 90 2950 17.3 82 1
## 393 27.0 4 140 86 2790 15.6 82 1
## 394 44.0 4 97 52 2130 24.6 82 2
## 395 32.0 4 135 84 2295 11.6 82 1
## 396 28.0 4 120 79 2625 18.6 82 1
## 397 31.0 4 119 82 2720 19.4 82 1Range
range(auto_new$mpg)## [1] 11.0 46.6range(auto_new$cylinders)## [1] 3 8range(auto_new$displacement)## [1] 68 455range(auto_new$weight)## [1] 1649 4997range(auto_new$acceleration)## [1] 8.5 24.8range(auto_new$year)## [1] 70 82range(auto_new$origin)## [1] 1 3Mean
mean(auto_new$mpg)## [1] 24.36845mean(auto_new$cylinders)## [1] 5.381703mean(auto_new$displacement)## [1] 187.7539mean(auto_new$weight)## [1] 2939.644mean(auto_new$acceleration)## [1] 15.7183mean(auto_new$year)## [1] 77.13249mean(auto_new$origin)## [1] 1.599369Standard Deviation
sd(auto_new$mpg)## [1] 7.880898sd(auto_new$cylinders)## [1] 1.658135sd(auto_new$displacement)## [1] 99.93949sd(auto_new$weight)## [1] 812.6496sd(auto_new$acceleration)## [1] 2.693813sd(auto_new$year)## [1] 3.110026sd(auto_new$origin)## [1] 0.8193079Create plots highlighting the relationships among predictors
Plot 1
library(ggplot2)
auto$cylinders_factor <- as.factor(auto$cylinders)
ggplot(data = auto, aes(y = mpg, fill = cylinders_factor))+
geom_boxplot()+
theme_bw()
These boxplots show that cars with more cylinders have less mpg. However, the exception is cars with three cylinders which have low gas mileage despite being having the least amount of cylinders.
Plot 2
plot(auto$year, auto$mpg, col="blue", xlab = "YEAR", ylab = "MPG")
This scatterplot indicates that newer cars tend to get better gas mileage.
Plot 3
plot(auto$acceleration, auto$mpg, col="blue", xlab = "ACCEL", ylab = "MPG")
This scatterplot indicates that cars with greater acceleration tend to have greater gas mileage.
Do your plots suggest that any of the other variables might be useful in predicting mpg?
plot(auto$year, auto$mpg, col="blue", xlab = "YEAR", ylab = "MPG")
plot(auto$acceleration, auto$mpg, col="blue", xlab = "ACCELERATION", ylab = "MPG")
plot(auto$cylinders, auto$mpg, col="blue", xlab = "CYLINDERS", ylab = "MPG")
plot(auto$displacement, auto$mpg, col="blue", xlab = "DISPLACEMENT", ylab = "MPG")
plot(auto$horsepower, auto$mpg, col="blue", xlab = "HORSEPOWER", ylab = "MPG")
plot(auto$weight, auto$mpg, col="blue", xlab = "WEIGHT", ylab = "MPG")
plot(auto$origin, auto$mpg, col="blue", xlab = "ORIGIN", ylab = "MPG")
Year, accelleration, and origin are positively correlated with mpg. Weight, horsepower, displacement, and cylinders are negatively correlated with mpg. Therefore, all varariables may be useful in predicting mpg, but to varying degrees.