Data analysis; regression
Kushan De Silva
August 21, 2017
library(datasets)
data(iris)
head(iris)## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosadata(iris)
summary(iris)## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100
## 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300
## Median :5.800 Median :3.000 Median :4.350 Median :1.300
## Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199
## 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800
## Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500
## Species
## setosa :50
## versicolor:50
## virginica :50
##
##
## plot(iris)
cor(iris$Petal.Length, iris$Petal.Width)## [1] 0.9628654fit <- lm(iris$Petal.Length ~ iris$Petal.Width)
fit##
## Call:
## lm(formula = iris$Petal.Length ~ iris$Petal.Width)
##
## Coefficients:
## (Intercept) iris$Petal.Width
## 1.084 2.230par(mfrow=c(2,2))
plot(fit)
residuals(fit)## 1 2 3 4 5
## -0.129546132 -0.129546132 -0.229546132 -0.029546132 -0.129546132
## 6 7 8 9 10
## -0.275534231 -0.352540181 -0.029546132 -0.129546132 0.193447918
## 11 12 13 14 15
## -0.029546132 0.070453868 0.093447918 -0.206552082 -0.329546132
## 16 17 18 19 20
## -0.475534231 -0.675534231 -0.352540181 -0.052540181 -0.252540181
## 21 22 23 24 25
## 0.170453868 -0.475534231 -0.529546132 -0.498528280 0.370453868
## 26 27 28 29 30
## 0.070453868 -0.375534231 -0.029546132 -0.129546132 0.070453868
## 31 32 33 34 35
## 0.070453868 -0.475534231 0.193447918 -0.129546132 -0.029546132
## 36 37 38 39 40
## -0.329546132 -0.229546132 0.093447918 -0.229546132 -0.029546132
## 41 42 43 44 45
## -0.452540181 -0.452540181 -0.229546132 -0.821522330 -0.075534231
## 46 47 48 49 50
## -0.352540181 0.070453868 -0.129546132 -0.029546132 -0.129546132
## 51 52 53 54 55
## 0.494525274 0.071531224 0.471531224 0.017519323 0.171531224
## 56 57 58 59 60
## 0.517519323 0.048537175 -0.013498528 0.617519323 -0.305474726
## 61 62 63 64 65
## 0.186501472 -0.228468776 0.686501472 0.494525274 -0.382480677
## 66 67 68 69 70
## 0.194525274 0.071531224 0.786501472 0.071531224 0.363507423
## 71 72 73 74 75
## -0.297450924 0.017519323 0.471531224 0.940513373 0.317519323
## 76 77 78 79 80
## 0.194525274 0.594525274 0.125543125 0.071531224 0.186501472
## 81 82 83 84 85
## 0.263507423 0.386501472 0.140513373 0.448537175 0.071531224
## 86 87 88 89 90
## -0.151462825 0.271531224 0.417519323 0.117519323 0.017519323
## 91 92 93 94 95
## 0.640513373 0.394525274 0.240513373 -0.013498528 0.217519323
## 96 97 98 99 100
## 0.440513373 0.217519323 0.317519323 -0.536492577 0.117519323
## 101 102 103 104 105
## -0.658409271 -0.220444974 0.133566927 0.502549076 -0.189427122
## 106 107 108 109 110
## 0.833566927 -0.374456875 1.202549076 0.702549076 -0.558409271
## 111 112 113 114 115
## -0.443439023 -0.020444974 -0.266433073 -0.543439023 -1.335415221
## 116 117 118 119 120
## -0.912421172 0.402549076 0.710572878 0.687578828 0.571531224
## 121 122 123 124 125
## -0.512421172 -0.643439023 1.156560977 -0.197450924 -0.066433073
## 126 127 128 129 130
## 0.902549076 -0.297450924 -0.197450924 -0.166433073 1.148537175
## 131 132 133 134 135
## 0.779555026 0.856560977 -0.389427122 0.671531224 1.394525274
## 136 137 138 139 140
## -0.112421172 -0.835415221 0.402549076 -0.297450924 -0.366433073
## 141 142 143 144 145
## -0.835415221 -1.112421172 -0.220444974 -0.312421172 -0.958409271
## 146 147 148 149 150
## -1.012421172 -0.320444974 -0.343439023 -0.812421172 0.002549076summary(fit)##
## Call:
## lm(formula = iris$Petal.Length ~ iris$Petal.Width)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.33542 -0.30347 -0.02955 0.25776 1.39453
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.08356 0.07297 14.85 <2e-16 ***
## iris$Petal.Width 2.22994 0.05140 43.39 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4782 on 148 degrees of freedom
## Multiple R-squared: 0.9271, Adjusted R-squared: 0.9266
## F-statistic: 1882 on 1 and 148 DF, p-value: < 2.2e-16data2<- subset(iris, iris$Species!="setosa")
plot(data2)
cor(data2$Petal.Length,data2$Petal.Width)## [1] 0.8233476fit <- lm(data2$Petal.Length ~ data2$Petal.Width)
summary(fit)##
## Call:
## lm(formula = data2$Petal.Length ~ data2$Petal.Width)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.9842 -0.3043 -0.1043 0.2407 1.2755
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.2240 0.1926 11.55 <2e-16 ***
## data2$Petal.Width 1.6003 0.1114 14.36 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4709 on 98 degrees of freedom
## Multiple R-squared: 0.6779, Adjusted R-squared: 0.6746
## F-statistic: 206.3 on 1 and 98 DF, p-value: < 2.2e-16library(mlbench)
data(BostonHousing)
dim(BostonHousing)## [1] 506 14str(BostonHousing)## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : num 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ b : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...summary(BostonHousing)## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 0:471
## 1st Qu.: 0.08204 1st Qu.: 0.00 1st Qu.: 5.19 1: 35
## Median : 0.25651 Median : 0.00 Median : 9.69
## Mean : 3.61352 Mean : 11.36 Mean :11.14
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10
## Max. :88.97620 Max. :100.00 Max. :27.74
## nox rm age dis
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## rad tax ptratio b
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 0.32
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.:375.38
## Median : 5.000 Median :330.0 Median :19.05 Median :391.44
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :356.67
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:396.23
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :396.90
## lstat medv
## Min. : 1.73 Min. : 5.00
## 1st Qu.: 6.95 1st Qu.:17.02
## Median :11.36 Median :21.20
## Mean :12.65 Mean :22.53
## 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :37.97 Max. :50.00model <- lm(medv ~ ., data = BostonHousing)
summary(model)##
## Call:
## lm(formula = medv ~ ., data = BostonHousing)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.595 -2.730 -0.518 1.777 26.199
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.646e+01 5.103e+00 7.144 3.28e-12 ***
## crim -1.080e-01 3.286e-02 -3.287 0.001087 **
## zn 4.642e-02 1.373e-02 3.382 0.000778 ***
## indus 2.056e-02 6.150e-02 0.334 0.738288
## chas1 2.687e+00 8.616e-01 3.118 0.001925 **
## nox -1.777e+01 3.820e+00 -4.651 4.25e-06 ***
## rm 3.810e+00 4.179e-01 9.116 < 2e-16 ***
## age 6.922e-04 1.321e-02 0.052 0.958229
## dis -1.476e+00 1.995e-01 -7.398 6.01e-13 ***
## rad 3.060e-01 6.635e-02 4.613 5.07e-06 ***
## tax -1.233e-02 3.760e-03 -3.280 0.001112 **
## ptratio -9.527e-01 1.308e-01 -7.283 1.31e-12 ***
## b 9.312e-03 2.686e-03 3.467 0.000573 ***
## lstat -5.248e-01 5.072e-02 -10.347 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.745 on 492 degrees of freedom
## Multiple R-squared: 0.7406, Adjusted R-squared: 0.7338
## F-statistic: 108.1 on 13 and 492 DF, p-value: < 2.2e-16plot(model)
plot(BostonHousing)
resid(model)## 1 2 3 4 5
## -6.003843377 -3.425562379 4.132403281 4.792963511 8.256475767
## 6 7 8 9 10
## 3.443715538 -0.101808268 7.564011571 4.976363147 -0.020262107
## 11 12 13 14 15
## -3.999496511 -2.686795681 0.793478472 0.847097189 -1.083482050
## 16 17 18 19 20
## 0.602516792 2.572490209 0.588598653 4.021988943 -0.206136033
## 21 22 23 24 25
## 1.076142473 1.928963305 -0.632881292 0.693714654 -0.078338315
## 26 27 28 29 30
## 0.513314391 1.136023454 0.091525719 -1.147372851 0.123571798
## 31 32 33 34 35
## 1.244882410 -3.559232946 4.388942638 -1.182758141 -0.206758913
## 36 37 38 39 40
## -4.914635265 -2.341937076 -2.108911425 1.784973884 -0.557625688
## 41 42 43 44 45
## 0.684897746 -1.420564139 0.096133720 0.090207275 -1.741491757
## 46 47 48 49 50
## -2.796698175 -0.423200323 -1.436550884 5.293446228 2.193922486
## 51 52 53 54 55
## -1.581525353 -3.472222849 -2.655850802 -0.649018091 3.538152299
## 56 57 58 59 60
## 4.247350534 -0.156869782 -1.509198062 1.524620129 -1.484935551
## 61 62 63 64 65
## 0.827419603 -2.511102080 -1.787428565 2.445911311 9.626913558
## 66 67 68 69 70
## -6.861483581 -6.130565115 0.886614358 -0.021537857 0.115163673
## 71 72 73 74 75
## -1.001488594 -0.042657705 -1.757449572 -0.642957120 -1.404997164
## 76 77 78 79 80
## -2.566930200 -2.945454031 -2.556998184 -0.061982662 -2.128173732
## 81 82 83 84 85
## -0.405769682 -3.094860862 -1.235762968 -2.158734819 -0.884566738
## 86 87 88 89 90
## -1.190491951 0.331465769 -3.692764153 -7.074618272 -2.131106227
## 91 92 93 94 95
## -4.519019396 -5.412667341 -6.041227624 -4.081055463 -6.439773649
## 96 97 98 99 100
## -0.224599485 -3.327449776 2.918404819 8.685454127 0.948971987
## 101 102 103 104 105
## 2.919779811 0.905865254 -1.190136835 -1.011671288 -1.334825911
## 106 107 108 109 110
## 0.960059918 2.312440082 -0.350490259 -2.848291146 -0.372036695
## 111 112 113 114 115
## 1.050341357 -3.725867438 -1.973236377 -2.015483150 -6.672088813
## 116 117 118 119 120
## -2.130255909 -2.177246257 -4.490432606 0.064216357 -1.491808732
## 121 122 123 124 125
## 0.083679289 -2.171077767 -0.057385558 0.933380226 -1.760998192
## 126 127 128 129 130
## -1.081784462 1.082933672 1.021233160 -0.938685924 0.244267149
## 131 132 133 134 135
## -0.835273989 0.189865979 2.938084338 2.641923269 2.343547618
## 136 137 138 139 140
## 0.837222650 1.521581166 -2.261639540 -0.514838967 1.351185252
## 141 142 143 144 145
## 0.428580681 10.411144917 -1.194954780 3.451185197 3.071776377
## 146 147 148 149 150
## 1.764146573 -0.220820580 6.085009797 8.081558607 0.595486263
## 151 152 153 154 155
## 0.661418471 1.298988306 -4.822825579 2.113981064 -5.366002281
## 156 157 158 159 160
## -4.503759227 -0.521258907 8.040173031 -4.730172680 -2.267527694
## 161 162 163 164 165
## -5.708276658 13.225329854 9.442341555 8.152718323 -2.088673791
## 166 167 168 169 170
## -0.378892378 12.796525454 0.712512527 -2.602739553 -4.353821137
## 171 172 173 174 175
## -5.155146605 -5.190828118 0.123427810 -5.471943077 -3.921943396
## 176 177 178 179 180
## -1.322090555 -2.416693069 -4.537409794 -1.535719677 4.277684320
## 181 182 183 184 185
## 5.075595356 8.434478893 4.012126787 1.507619640 3.681799919
## 186 187 188 189 190
## 4.833521901 14.115027738 -1.424767220 -2.611991466 0.384900507
## 191 192 193 194 195
## 6.238905148 0.210658593 3.480812857 -1.012607714 -2.458710043
## 196 197 198 199 200
## 9.154442786 -2.827700792 -2.369208100 -0.104691164 4.806548382
## 201 202 203 204 205
## 2.256060935 -5.187195014 5.228516080 6.468068762 6.810501563
## 206 207 208 209 210
## -0.090347964 0.717152885 4.645527863 0.905710080 2.994122821
## 211 212 213 214 215
## -0.692510964 2.239572462 -0.338929215 2.880574461 12.580832628
## 216 217 218 219 220
## 0.489508521 -3.303347748 0.344812873 -3.415254636 -6.686527678
## 221 222 223 224 225
## -6.484197456 -2.074566560 -4.640519579 0.354180104 6.428975473
## 226 227 228 229 230
## 10.185381330 0.013942450 -0.799532503 11.243347580 0.265884883
## 231 232 233 234 235
## -0.184492269 -1.588372916 3.651895196 11.136713685 -2.713835225
## 236 237 238 239 240
## -1.267055713 -5.000107449 -1.219871558 -4.727170566 -5.129406781
## 241 242 243 244 245
## -5.293759384 -3.642624783 -1.920078909 -3.702084138 1.271424399
## 246 247 248 249 250
## 5.101087387 4.283612248 0.638155722 3.211686902 2.120108504
## 251 252 253 254 255
## 0.193664530 -0.242158213 4.680359930 12.854366255 -2.072283165
## 256 257 258 259 260
## -0.795808866 6.488907610 6.697609573 -0.483614206 -4.889885936
## 261 262 263 264 265
## -1.012115081 5.933686692 7.810714991 -3.446340893 0.666024531
## 266 267 268 269 270
## -5.445742999 -0.526735926 9.160442504 4.182076069 -5.008179052
## 271 272 273 274 275
## -1.202955330 -2.003409719 -4.111694720 -0.276765982 -3.706391643
## 276 277 278 279 280
## -1.796682735 -2.410858579 -1.739933819 -1.251926558 -0.209807009
## 281 282 283 284 285
## 6.602430340 1.068768140 5.660369252 5.326916613 0.603109145
## 286 287 288 289 290
## -5.356592298 -0.001741541 -3.842066736 -4.913645804 -2.113958394
## 291 292 293 294 295
## -4.935633106 2.896503670 -3.933398201 -1.917832369 -2.729823483
## 296 297 298 299 300
## 0.142356632 -0.262669985 0.760712419 -6.613098441 -2.910546108
## 301 302 303 304 305
## -5.971594485 -6.942758713 -2.481910224 0.301127681 2.890945441
## 306 307 308 309 310
## -2.368317923 -2.162268570 -4.509051237 -5.842442366 -3.289658271
## 311 312 313 314 315
## -2.442668968 -4.778898429 -3.881339788 -3.945802461 -1.681200571
## 316 317 318 319 320
## -4.339099011 0.184274272 1.424183136 -1.190702769 -0.325290392
## 321 322 323 324 325
## -1.086822441 -1.769372815 -2.469524474 -0.951237906 -0.117834011
## 326 327 328 329 330
## -0.067869132 -0.680761771 2.859103837 -1.874181054 -1.652490735
## 331 332 333 334 335
## -1.792608939 -2.884466054 -3.938879998 0.059393075 -0.855099290
## 336 337 338 339 340
## 0.481270932 -0.660971763 -0.784903873 -1.566723204 -2.249657744
## 341 342 343 344 345
## -2.729393054 2.372112040 -5.547349751 -3.806479125 2.652058832
## 346 347 348 349 350
## 0.954988786 2.416403590 -2.173800817 -3.042051174 4.451624376
## 351 352 353 354 355
## 2.440559053 3.553945773 1.719361734 4.697464942 3.875133681
## 356 357 358 359 360
## 4.005115383 -1.837046913 -1.018066075 0.497811132 3.394519426
## 361 362 363 364 365
## 2.333838949 0.968073818 2.571531957 -3.431508114 -15.594473900
## 366 367 368 369 370
## 13.218092659 6.357137517 12.268376759 26.199270978 17.355926399
## 371 372 373 374 375
## 15.393159576 25.056686675 24.000190899 7.673675004 13.022201940
## 376 377 378 379 380
## -10.307130642 -3.840610645 -6.932744140 -2.733313008 -6.635125872
## 381 382 383 384 385
## -3.969948255 -7.576828331 -2.127682805 -0.761775118 5.520818839
## 386 387 388 389 390
## -0.860221708 4.371578036 1.781351900 3.748014302 -2.707647352
## 391 392 393 394 395
## -2.112251831 5.901127348 -0.191166432 -6.421241935 -5.241811753
## 396 397 398 399 400
## -7.204457827 -6.795590755 -7.836327793 -1.551623191 -4.590167781
## 401 402 403 404 405
## -6.281458707 -10.611745068 -6.161265872 -4.679487807 1.121836393
## 406 407 408 409 410
## -3.211158614 3.833738070 7.917052140 3.492436308 7.647315455
## 411 412 413 414 415
## -0.223082977 0.239280190 16.181481932 4.494216128 11.281310709
## 416 417 418 419 420
## -2.383767369 -5.866608110 3.504376374 2.652201480 -6.206617942
## 421 422 423 424 425
## -2.900026702 -3.924274759 2.278228678 0.224713895 -2.926176242
## 426 427 428 429 430
## -1.623749760 -6.145906467 -3.175194255 -3.257562426 -3.542347875
## 431 432 433 434 435
## -3.659556934 -4.595543541 -5.427283002 -2.731418609 -4.260904353
## 436 437 438 439 440
## 0.038583893 -4.920793839 -0.119760054 3.532488977 -0.265913130
## 441 442 443 444 445
## -2.206096993 -0.195580592 -0.340485002 -2.659010295 -0.714746834
## 446 447 448 449 450
## -0.174003587 -2.783446185 -5.526952390 -3.418346504 -4.227425073
## 451 452 453 454 455
## -3.122716313 -4.212910951 -2.482152362 -4.689447908 -0.380001330
## 456 457 458 459 460
## -1.720893352 0.012744187 0.623662098 -2.286685309 1.487523907
## 461 462 463 464 465
## -2.648605332 -2.472089273 -0.274073197 -2.229407679 1.080881457
## 466 467 468 469 470
## 2.013837468 4.625214772 2.152231493 2.115942378 1.511616032
## 471 472 473 474 475
## -0.267194411 -3.377180317 0.744192736 4.221753735 -2.591476316
## 476 477 478 479 480
## -2.811462804 -3.834815996 0.457272618 -4.604963045 -0.462763906
## 481 482 483 484 485
## -0.468788663 -3.398873155 -3.569943017 0.716012169 1.144838044
## 486 487 488 489 490
## -1.022259141 -0.555919608 -0.725361044 3.344162834 -1.223866868
## 491 492 493 494 495
## 4.436003280 -0.159085382 4.168814549 1.173379456 3.887505860
## 496 497 498 499 500
## 6.214580361 5.686792129 -0.808541439 -0.098051744 -0.954988409
## 501 502 503 504 505
## -3.668708470 -1.133340547 -1.775718920 -3.727426095 -4.127966807
## 506
## -10.444212293fitted(model)## 1 2 3 4 5 6
## 30.0038434 25.0255624 30.5675967 28.6070365 27.9435242 25.2562845
## 7 8 9 10 11 12
## 23.0018083 19.5359884 11.5236369 18.9202621 18.9994965 21.5867957
## 13 14 15 16 17 18
## 20.9065215 19.5529028 19.2834821 19.2974832 20.5275098 16.9114013
## 19 20 21 22 23 24
## 16.1780111 18.4061360 12.5238575 17.6710367 15.8328813 13.8062853
## 25 26 27 28 29 30
## 15.6783383 13.3866856 15.4639765 14.7084743 19.5473729 20.8764282
## 31 32 33 34 35 36
## 11.4551176 18.0592329 8.8110574 14.2827581 13.7067589 23.8146353
## 37 38 39 40 41 42
## 22.3419371 23.1089114 22.9150261 31.3576257 34.2151023 28.0205641
## 43 44 45 46 47 48
## 25.2038663 24.6097927 22.9414918 22.0966982 20.4232003 18.0365509
## 49 50 51 52 53 54
## 9.1065538 17.2060775 21.2815254 23.9722228 27.6558508 24.0490181
## 55 56 57 58 59 60
## 15.3618477 31.1526495 24.8568698 33.1091981 21.7753799 21.0849356
## 61 62 63 64 65 66
## 17.8725804 18.5111021 23.9874286 22.5540887 23.3730864 30.3614836
## 67 68 69 70 71 72
## 25.5305651 21.1133856 17.4215379 20.7848363 25.2014886 21.7426577
## 73 74 75 76 77 78
## 24.5574496 24.0429571 25.5049972 23.9669302 22.9454540 23.3569982
## 79 80 81 82 83 84
## 21.2619827 22.4281737 28.4057697 26.9948609 26.0357630 25.0587348
## 85 86 87 88 89 90
## 24.7845667 27.7904920 22.1685342 25.8927642 30.6746183 30.8311062
## 91 92 93 94 95 96
## 27.1190194 27.4126673 28.9412276 29.0810555 27.0397736 28.6245995
## 97 98 99 100 101 102
## 24.7274498 35.7815952 35.1145459 32.2510280 24.5802202 25.5941347
## 103 104 105 106 107 108
## 19.7901368 20.3116713 21.4348259 18.5399401 17.1875599 20.7504903
## 109 110 111 112 113 114
## 22.6482911 19.7720367 20.6496586 26.5258674 20.7732364 20.7154831
## 115 116 117 118 119 120
## 25.1720888 20.4302559 23.3772463 23.6904326 20.3357836 20.7918087
## 121 122 123 124 125 126
## 21.9163207 22.4710778 20.5573856 16.3666198 20.5609982 22.4817845
## 127 128 129 130 131 132
## 14.6170663 15.1787668 18.9386859 14.0557329 20.0352740 19.4101340
## 133 134 135 136 137 138
## 20.0619157 15.7580767 13.2564524 17.2627773 15.8784188 19.3616395
## 139 140 141 142 143 144
## 13.8148390 16.4488147 13.5714193 3.9888551 14.5949548 12.1488148
## 145 146 147 148 149 150
## 8.7282236 12.0358534 15.8208206 8.5149902 9.7184414 14.8045137
## 151 152 153 154 155 156
## 20.8385815 18.3010117 20.1228256 17.2860189 22.3660023 20.1037592
## 157 158 159 160 161 162
## 13.6212589 33.2598270 29.0301727 25.5675277 32.7082767 36.7746701
## 163 164 165 166 167 168
## 40.5576584 41.8472817 24.7886738 25.3788924 37.2034745 23.0874875
## 169 170 171 172 173 174
## 26.4027396 26.6538211 22.5551466 24.2908281 22.9765722 29.0719431
## 175 176 177 178 179 180
## 26.5219434 30.7220906 25.6166931 29.1374098 31.4357197 32.9223157
## 181 182 183 184 185 186
## 34.7244046 27.7655211 33.8878732 30.9923804 22.7182001 24.7664781
## 187 188 189 190 191 192
## 35.8849723 33.4247672 32.4119915 34.5150995 30.7610949 30.2893414
## 193 194 195 196 197 198
## 32.9191871 32.1126077 31.5587100 40.8455572 36.1277008 32.6692081
## 199 200 201 202 203 204
## 34.7046912 30.0934516 30.6439391 29.2871950 37.0714839 42.0319312
## 205 206 207 208 209 210
## 43.1894984 22.6903480 23.6828471 17.8544721 23.4942899 17.0058772
## 211 212 213 214 215 216
## 22.3925110 17.0604275 22.7389292 25.2194255 11.1191674 24.5104915
## 217 218 219 220 221 222
## 26.6033477 28.3551871 24.9152546 29.6865277 33.1841975 23.7745666
## 223 224 225 226 227 228
## 32.1405196 29.7458199 38.3710245 39.8146187 37.5860575 32.3995325
## 229 230 231 232 233 234
## 35.4566524 31.2341151 24.4844923 33.2883729 38.0481048 37.1632863
## 235 236 237 238 239 240
## 31.7138352 25.2670557 30.1001074 32.7198716 28.4271706 28.4294068
## 241 242 243 244 245 246
## 27.2937594 23.7426248 24.1200789 27.4020841 16.3285756 13.3989126
## 247 248 249 250 251 252
## 20.0163878 19.8618443 21.2883131 24.0798915 24.2063355 25.0421582
## 253 254 255 256 257 258
## 24.9196401 29.9456337 23.9722832 21.6958089 37.5110924 43.3023904
## 259 260 261 262 263 264
## 36.4836142 34.9898859 34.8121151 37.1663133 40.9892850 34.4463409
## 265 266 267 268 269 270
## 35.8339755 28.2457430 31.2267359 40.8395575 39.3179239 25.7081791
## 271 272 273 274 275 276
## 22.3029553 27.2034097 28.5116947 35.4767660 36.1063916 33.7966827
## 277 278 279 280 281 282
## 35.6108586 34.8399338 30.3519266 35.3098070 38.7975697 34.3312319
## 283 284 285 286 287 288
## 40.3396307 44.6730834 31.5968909 27.3565923 20.1017415 27.0420667
## 289 290 291 292 293 294
## 27.2136458 26.9139584 33.4356331 34.4034963 31.8333982 25.8178324
## 295 296 297 298 299 300
## 24.4298235 28.4576434 27.3626700 19.5392876 29.1130984 31.9105461
## 301 302 303 304 305 306
## 30.7715945 28.9427587 28.8819102 32.7988723 33.2090546 30.7683179
## 307 308 309 310 311 312
## 35.5622686 32.7090512 28.6424424 23.5896583 18.5426690 26.8788984
## 313 314 315 316 317 318
## 23.2813398 25.5458025 25.4812006 20.5390990 17.6157257 18.3758169
## 319 320 321 322 323 324
## 24.2907028 21.3252904 24.8868224 24.8693728 22.8695245 19.4512379
## 325 326 327 328 329 330
## 25.1178340 24.6678691 23.6807618 19.3408962 21.1741811 24.2524907
## 331 332 333 334 335 336
## 21.5926089 19.9844661 23.3388800 22.1406069 21.5550993 20.6187291
## 337 338 339 340 341 342
## 20.1609718 19.2849039 22.1667232 21.2496577 21.4293931 30.3278880
## 343 344 345 346 347 348
## 22.0473498 27.7064791 28.5479412 16.5450112 14.7835964 25.2738008
## 349 350 351 352 353 354
## 27.5420512 22.1483756 20.4594409 20.5460542 16.8806383 25.4025351
## 355 356 357 358 359 360
## 14.3248663 16.5948846 19.6370469 22.7180661 22.2021889 19.2054806
## 361 362 363 364 365 366
## 22.6661611 18.9319262 18.2284680 20.2315081 37.4944739 14.2819073
## 367 368 369 370 371 372
## 15.5428625 10.8316232 23.8007290 32.6440736 34.6068404 24.9433133
## 373 374 375 376 377 378
## 25.9998091 6.1263250 0.7777981 25.3071306 17.7406106 20.2327441
## 379 380 381 382 383 384
## 15.8333130 16.8351259 14.3699483 18.4768283 13.4276828 13.0617751
## 385 386 387 388 389 390
## 3.2791812 8.0602217 6.1284220 5.6186481 6.4519857 14.2076474
## 391 392 393 394 395 396
## 17.2122518 17.2988727 9.8911664 20.2212419 17.9418118 20.3044578
## 397 398 399 400 401 402
## 19.2955908 16.3363278 6.5516232 10.8901678 11.8814587 17.8117451
## 403 404 405 406 407 408
## 18.2612659 12.9794878 7.3781636 8.2111586 8.0662619 19.9829479
## 409 410 411 412 413 414
## 13.7075637 19.8526845 15.2230830 16.9607198 1.7185181 11.8057839
## 415 416 417 418 419 420
## -4.2813107 9.5837674 13.3666081 6.8956236 6.1477985 14.6066179
## 421 422 423 424 425 426
## 19.6000267 18.1242748 18.5217713 13.1752861 14.6261762 9.9237498
## 427 428 429 430 431 432
## 16.3459065 14.0751943 14.2575624 13.0423479 18.1595569 18.6955435
## 433 434 435 436 437 438
## 21.5272830 17.0314186 15.9609044 13.3614161 14.5207938 8.8197601
## 439 440 441 442 443 444
## 4.8675110 13.0659131 12.7060970 17.2955806 18.7404850 18.0590103
## 445 446 447 448 449 450
## 11.5147468 11.9740036 17.6834462 18.1269524 17.5183465 17.2274251
## 451 452 453 454 455 456
## 16.5227163 19.4129110 18.5821524 22.4894479 15.2800013 15.8208934
## 457 458 459 460 461 462
## 12.6872558 12.8763379 17.1866853 18.5124761 19.0486053 20.1720893
## 463 464 465 466 467 468
## 19.7740732 22.4294077 20.3191185 17.8861625 14.3747852 16.9477685
## 469 470 471 472 473 474
## 16.9840576 18.5883840 20.1671944 22.9771803 22.4558073 25.5782463
## 475 476 477 478 479 480
## 16.3914763 16.1114628 20.5348160 11.5427274 19.2049630 21.8627639
## 481 482 483 484 485 486
## 23.4687887 27.0988732 28.5699430 21.0839878 19.4551620 22.2222591
## 487 488 489 490 491 492
## 19.6559196 21.3253610 11.8558372 8.2238669 3.6639967 13.7590854
## 493 494 495 496 497 498
## 15.9311855 20.6266205 20.6124941 16.8854196 14.0132079 19.1085414
## 499 500 501 502 503 504
## 21.2980517 18.4549884 20.4687085 23.5333405 22.3757189 27.6274261
## 505 506
## 26.1279668 22.3442123par(mfrow=c(2,2))
plot(model)
model2 <- lm(medv ~ crim + zn +indus + nox + rm + age + dis + rad, data = BostonHousing)
summary(model2)##
## Call:
## lm(formula = medv ~ crim + zn + indus + nox + rm + age + dis +
## rad, data = BostonHousing)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.808 -3.065 -0.666 2.062 38.058
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.31945 4.09090 -0.323 0.747184
## crim -0.18960 0.03877 -4.891 1.36e-06 ***
## zn 0.06209 0.01541 4.030 6.45e-05 ***
## indus -0.20164 0.06535 -3.085 0.002145 **
## nox -12.32881 4.31920 -2.854 0.004492 **
## rm 6.99462 0.41206 16.975 < 2e-16 ***
## age -0.05495 0.01493 -3.681 0.000258 ***
## dis -1.78329 0.23963 -7.442 4.40e-13 ***
## rad -0.05302 0.04445 -1.193 0.233511
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.739 on 497 degrees of freedom
## Multiple R-squared: 0.6168, Adjusted R-squared: 0.6107
## F-statistic: 100 on 8 and 497 DF, p-value: < 2.2e-16plot(model2)
library('chemometrics')## Loading required package: rpartdata("mtcars")
summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000str(mtcars)## 'data.frame': 32 obs. of 11 variables:
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ cyl : num 6 6 4 6 8 6 8 4 4 6 ...
## $ disp: num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec: num 16.5 17 18.6 19.4 17 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ am : num 1 1 1 0 0 0 0 0 0 0 ...
## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...m <- lm(cbind(mtcars$mpg,mtcars$hp) ~
mtcars$cyl + mtcars$disp + mtcars$wt)
summary(m)## Response mtcars$mpg :
##
## Call:
## lm(formula = `mtcars$mpg` ~ mtcars$cyl + mtcars$disp + mtcars$wt)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4035 -1.4028 -0.4955 1.3387 6.0722
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 41.107678 2.842426 14.462 1.62e-14 ***
## mtcars$cyl -1.784944 0.607110 -2.940 0.00651 **
## mtcars$disp 0.007473 0.011845 0.631 0.53322
## mtcars$wt -3.635677 1.040138 -3.495 0.00160 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.595 on 28 degrees of freedom
## Multiple R-squared: 0.8326, Adjusted R-squared: 0.8147
## F-statistic: 46.42 on 3 and 28 DF, p-value: 5.399e-11
##
##
## Response mtcars$hp :
##
## Call:
## lm(formula = `mtcars$hp` ~ mtcars$cyl + mtcars$disp + mtcars$wt)
##
## Residuals:
## Min 1Q Median 3Q Max
## -54.39 -22.30 -9.33 18.64 134.56
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -13.5912 42.8244 -0.317 0.7533
## mtcars$cyl 23.9368 9.1468 2.617 0.0141 *
## mtcars$disp 0.2009 0.1785 1.126 0.2698
## mtcars$wt -10.6253 15.6708 -0.678 0.5033
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 39.09 on 28 degrees of freedom
## Multiple R-squared: 0.7064, Adjusted R-squared: 0.6749
## F-statistic: 22.46 on 3 and 28 DF, p-value: 1.306e-07mm <- manova(m)
mm## Call:
## manova(m)
##
## Terms:
## mtcars$cyl mtcars$disp mtcars$wt Residuals
## resp 1 817.71 37.59 82.25 188.49
## resp 2 100984.17 1254.66 702.48 42785.56
## Deg. of Freedom 1 1 1 28
##
## Residual standard errors: 2.594585 39.09035
## Estimated effects may be unbalancedsummary(mm)## Df Pillai approx F num Df den Df Pr(>F)
## mtcars$cyl 1 0.83917 70.439 2 27 1.932e-11 ***
## mtcars$disp 1 0.16712 2.709 2 27 0.0847 .
## mtcars$wt 1 0.35841 7.542 2 27 0.0025 **
## Residuals 28
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cor(mtcars)## mpg cyl disp hp drat wt
## mpg 1.0000000 -0.8521620 -0.8475514 -0.7761684 0.68117191 -0.8676594
## cyl -0.8521620 1.0000000 0.9020329 0.8324475 -0.69993811 0.7824958
## disp -0.8475514 0.9020329 1.0000000 0.7909486 -0.71021393 0.8879799
## hp -0.7761684 0.8324475 0.7909486 1.0000000 -0.44875912 0.6587479
## drat 0.6811719 -0.6999381 -0.7102139 -0.4487591 1.00000000 -0.7124406
## wt -0.8676594 0.7824958 0.8879799 0.6587479 -0.71244065 1.0000000
## qsec 0.4186840 -0.5912421 -0.4336979 -0.7082234 0.09120476 -0.1747159
## vs 0.6640389 -0.8108118 -0.7104159 -0.7230967 0.44027846 -0.5549157
## am 0.5998324 -0.5226070 -0.5912270 -0.2432043 0.71271113 -0.6924953
## gear 0.4802848 -0.4926866 -0.5555692 -0.1257043 0.69961013 -0.5832870
## carb -0.5509251 0.5269883 0.3949769 0.7498125 -0.09078980 0.4276059
## qsec vs am gear carb
## mpg 0.41868403 0.6640389 0.59983243 0.4802848 -0.55092507
## cyl -0.59124207 -0.8108118 -0.52260705 -0.4926866 0.52698829
## disp -0.43369788 -0.7104159 -0.59122704 -0.5555692 0.39497686
## hp -0.70822339 -0.7230967 -0.24320426 -0.1257043 0.74981247
## drat 0.09120476 0.4402785 0.71271113 0.6996101 -0.09078980
## wt -0.17471588 -0.5549157 -0.69249526 -0.5832870 0.42760594
## qsec 1.00000000 0.7445354 -0.22986086 -0.2126822 -0.65624923
## vs 0.74453544 1.0000000 0.16834512 0.2060233 -0.56960714
## am -0.22986086 0.1683451 1.00000000 0.7940588 0.05753435
## gear -0.21268223 0.2060233 0.79405876 1.0000000 0.27407284
## carb -0.65624923 -0.5696071 0.05753435 0.2740728 1.00000000cov(mtcars)## mpg cyl disp hp drat
## mpg 36.324103 -9.1723790 -633.09721 -320.732056 2.19506351
## cyl -9.172379 3.1895161 199.66028 101.931452 -0.66836694
## disp -633.097208 199.6602823 15360.79983 6721.158669 -47.06401915
## hp -320.732056 101.9314516 6721.15867 4700.866935 -16.45110887
## drat 2.195064 -0.6683669 -47.06402 -16.451109 0.28588135
## wt -5.116685 1.3673710 107.68420 44.192661 -0.37272073
## qsec 4.509149 -1.8868548 -96.05168 -86.770081 0.08714073
## vs 2.017137 -0.7298387 -44.37762 -24.987903 0.11864919
## am 1.803931 -0.4657258 -36.56401 -8.320565 0.19015121
## gear 2.135685 -0.6491935 -50.80262 -6.358871 0.27598790
## carb -5.363105 1.5201613 79.06875 83.036290 -0.07840726
## wt qsec vs am gear
## mpg -5.1166847 4.50914919 2.01713710 1.80393145 2.1356855
## cyl 1.3673710 -1.88685484 -0.72983871 -0.46572581 -0.6491935
## disp 107.6842040 -96.05168145 -44.37762097 -36.56401210 -50.8026210
## hp 44.1926613 -86.77008065 -24.98790323 -8.32056452 -6.3588710
## drat -0.3727207 0.08714073 0.11864919 0.19015121 0.2759879
## wt 0.9573790 -0.30548161 -0.27366129 -0.33810484 -0.4210806
## qsec -0.3054816 3.19316613 0.67056452 -0.20495968 -0.2804032
## vs -0.2736613 0.67056452 0.25403226 0.04233871 0.0766129
## am -0.3381048 -0.20495968 0.04233871 0.24899194 0.2923387
## gear -0.4210806 -0.28040323 0.07661290 0.29233871 0.5443548
## carb 0.6757903 -1.89411290 -0.46370968 0.04637097 0.3266129
## carb
## mpg -5.36310484
## cyl 1.52016129
## disp 79.06875000
## hp 83.03629032
## drat -0.07840726
## wt 0.67579032
## qsec -1.89411290
## vs -0.46370968
## am 0.04637097
## gear 0.32661290
## carb 2.60887097Robust Regression
mtcars2 <- subset(mtcars, select = c(1:3,5:11))
prcomp(mtcars2)## Standard deviations (1, .., p=10):
## [1] 124.0636883 3.3156055 1.9727388 0.9707287 0.6644391
## [6] 0.3146818 0.2859604 0.2664605 0.2147193 0.2018027
##
## Rotation (n x k) = (10 x 10):
## PC1 PC2 PC3 PC4 PC5
## mpg -0.041203129 0.95183084 0.232722413 0.12056369 0.143485224
## cyl 0.012988407 -0.10484001 0.159076414 -0.27289350 0.798327666
## disp 0.998991829 0.04314172 0.002130588 0.00748304 -0.007924665
## drat -0.003061490 0.01699931 0.088999116 0.09937560 -0.233250086
## wt 0.007005058 -0.05829569 -0.112386522 0.24558785 0.115318084
## qsec -0.006249938 0.11072226 -0.751430367 0.49520763 0.201798940
## vs -0.002886954 0.02708815 -0.112674747 0.09517980 -0.093584346
## am -0.002378581 0.01613746 0.154271439 0.01337939 -0.209439675
## gear -0.003303766 -0.01612221 0.229043235 0.22570301 -0.342547528
## carb 0.005149505 -0.25291208 0.496361949 0.73166795 0.252257083
## PC6 PC7 PC8 PC9 PC10
## mpg -0.0400228143 0.0226924552 -0.0003540778 0.030095664 -0.003790957
## cyl 0.4190888426 -0.1887906595 0.0462382810 0.111047902 0.161213070
## disp 0.0007329425 -0.0005858438 -0.0031957826 -0.004212149 -0.001395423
## drat 0.0103913419 -0.9384812124 0.0682470382 0.201427862 -0.037601701
## wt -0.3056261176 0.1565490515 0.4696441895 0.704420274 0.274993899
## qsec 0.2684368135 -0.1027094089 0.0808239868 -0.215306288 -0.040045667
## vs 0.0672285498 -0.0027898119 -0.7236644285 0.236611153 0.620114966
## am 0.1456280922 -0.0223283455 0.4653387762 -0.458049655 0.695582133
## gear 0.7765594813 0.2179864535 0.0755825359 0.312507017 -0.158277041
## carb -0.1685725522 0.0038144361 -0.1419603525 -0.200379664 -0.043887856d1<- cooks.distance(m)
d1## [,1] [,2]
## 1 3.510367e-03 1.822065e+00
## 2 2.936643e-07 6.897965e-03
## 3 4.573918e-02 6.946566e-01
## 4 6.069887e-06 1.483451e-02
## 5 2.019247e-02 1.059792e+01
## 6 1.555998e-05 8.893810e-03
## 7 2.741556e-02 5.848365e+00
## 8 3.007257e-05 8.541479e-03
## 9 4.381135e-03 2.415355e+00
## 10 9.802341e-08 5.337843e-04
## 11 1.269762e-02 1.211628e-01
## 12 2.253562e-04 4.288834e-03
## 13 2.438907e-02 1.174039e+00
## 14 8.343661e-08 5.004033e-03
## 15 1.330855e-02 2.521798e+00
## 16 1.670128e-06 4.196937e-04
## 17 2.291895e-01 5.964357e+00
## 18 5.467712e-04 1.182479e-03
## 19 1.880896e-02 4.953478e+00
## 20 7.185953e-04 2.779920e-03
## 21 7.567035e-02 1.115400e+00
## 22 1.349353e-05 4.853181e-02
## 23 8.324926e-03 1.151130e+01
## 24 6.436269e-05 1.908001e-02
## 25 9.003823e-02 1.432997e+01
## 26 8.935852e-07 2.358305e-03
## 27 5.855017e-03 2.725187e-01
## 28 6.365207e-05 3.296419e-02
## 29 4.807696e-02 2.581010e+01
## 30 5.910588e-05 4.138886e-02
## 31 4.662546e-03 7.000564e+01
## 32 2.330744e-04 2.117389e-02library(MASS)
m <- rlm(mpg ~ cyl + disp + wt + gear, data = mtcars)
m## Call:
## rlm(formula = mpg ~ cyl + disp + wt + gear, data = mtcars)
## Converged in 8 iterations
##
## Coefficients:
## (Intercept) cyl disp wt gear
## 43.193813720 -1.746917038 0.007003493 -3.767535205 -0.535293330
##
## Degrees of freedom: 32 total; 27 residual
## Scale estimate: 2.11m2<- ltsreg(mpg ~ cyl + disp + wt + qsec,
data = mtcars)
m2## Call:
## lqs.formula(formula = mpg ~ cyl + disp + wt + qsec, data = mtcars,
## method = "lts")
##
## Coefficients:
## (Intercept) cyl disp wt qsec
## 22.23042 -0.11731 -0.01894 -1.48761 0.33662
##
## Scale estimates 1.440 1.565ltsreg(mpg ~ cyl + disp + wt + qsec,
data = mtcars)## Call:
## lqs.formula(formula = mpg ~ cyl + disp + wt + qsec, data = mtcars,
## method = "lts")
##
## Coefficients:
## (Intercept) cyl disp wt qsec
## 28.91579 -0.41783 -0.01722 -1.44949 0.02073
##
## Scale estimates 1.3830 0.9423ltsreg(mpg ~ cyl + disp + wt + qsec,
data = mtcars)## Call:
## lqs.formula(formula = mpg ~ cyl + disp + wt + qsec, data = mtcars,
## method = "lts")
##
## Coefficients:
## (Intercept) cyl disp wt qsec
## 27.23779 -0.26495 -0.01926 -1.27250 0.06052
##
## Scale estimates 1.4092 0.9238