PROBLEM 2

auto <- read.table("http://faculty.marshall.usc.edu/gareth-james/ISL/Auto.data", 
                   header=TRUE,
                   na.strings = "?")
auto=na.omit(auto)
attach(auto)
names(auto)
## [1] "mpg"          "cylinders"    "displacement" "horsepower"  
## [5] "weight"       "acceleration" "year"         "origin"      
## [9] "name"
library(tidyverse)
## ── Attaching packages ──────────── tidyverse 1.2.1 ──
## ✔ ggplot2 2.2.1     ✔ purrr   0.2.5
## ✔ tibble  1.4.2     ✔ dplyr   0.7.5
## ✔ tidyr   0.8.1     ✔ stringr 1.3.1
## ✔ readr   1.1.1     ✔ forcats 0.3.0
## ── Conflicts ─────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
ggplot(auto, aes(x=horsepower, y=mpg))+
  geom_point()+
  theme_bw()

mod<-lm(auto$mpg~auto$horsepower)
mod
## 
## Call:
## lm(formula = auto$mpg ~ auto$horsepower)
## 
## Coefficients:
##     (Intercept)  auto$horsepower  
##         39.9359          -0.1578
summary(mod)
## 
## Call:
## lm(formula = auto$mpg ~ auto$horsepower)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.5710  -3.2592  -0.3435   2.7630  16.9240 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     39.935861   0.717499   55.66   <2e-16 ***
## auto$horsepower -0.157845   0.006446  -24.49   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.906 on 390 degrees of freedom
## Multiple R-squared:  0.6059, Adjusted R-squared:  0.6049 
## F-statistic: 599.7 on 1 and 390 DF,  p-value: < 2.2e-16
names(mod)
##  [1] "coefficients"  "residuals"     "effects"       "rank"         
##  [5] "fitted.values" "assign"        "qr"            "df.residual"  
##  [9] "xlevels"       "call"          "terms"         "model"
# in tidyverse add a line
ggplot(auto, aes(x=horsepower, y=mpg))+
  geom_point()+
  geom_abline(slope=mod$coefficients[2], intercept=mod$coefficients[1],
              color="red", lty=2, lwd=1)+ #is this  used to answer question b? 
  theme_bw()

confint(mod)
##                     2.5 %     97.5 %
## (Intercept)     38.525212 41.3465103
## auto$horsepower -0.170517 -0.1451725
newdata<-data.frame(horsepower=c(98)) #this is the value you want to find for 
#confidence intervals for a given value
predict(mod, newdata, 
        interval="confidence")
## Warning: 'newdata' had 1 row but variables found have 392 rows
##           fit       lwr       upr
## 1   19.416046 18.831250 20.000841
## 2   13.891480 12.982802 14.800158
## 3   16.259151 15.504025 17.014277
## 4   16.259151 15.504025 17.014277
## 5   17.837598 17.174242 18.500955
## 6    8.682604  7.401151  9.964056
## 7    5.210020  3.667064  6.752976
## 8    5.999243  4.516273  7.482214
## 9    4.420796  2.817595  6.023998
## 10   9.945362  8.757051 11.133672
## 11  13.102256 12.139493 14.065020
## 12  14.680704 13.824838 15.536569
## 13  16.259151 15.504025 17.014277
## 14   4.420796  2.817595  6.023998
## 15  24.940611 24.438901 25.442321
## 16  24.940611 24.438901 25.442321
## 17  24.624922 24.128663 25.121180
## 18  26.519059 25.972996 27.065122
## 19  26.045524 25.515552 26.575497
## 20  32.675003 31.788265 33.561742
## 21  26.203369 25.668280 26.738459
## 22  25.729835 25.209322 26.250348
## 23  24.940611 24.438901 25.442321
## 24  22.099406 21.600408 22.598404
## 25  25.729835 25.209322 26.250348
## 26   5.999243  4.516273  7.482214
## 27   8.366914  7.061985  9.671844
## 28   6.788467  5.365189  8.211745
## 29   9.471827  8.248742 10.694913
## 30  26.045524 25.515552 26.575497
## 31  25.729835 25.209322 26.250348
## 32  24.940611 24.438901 25.442321
## 33  24.151388 23.660958 24.641817
## 34  23.362164 22.874970 23.849358
## 35  24.151388 23.660958 24.641817
## 36  26.045524 25.515552 26.575497
## 37  24.151388 23.660958 24.641817
## 38  13.891480 12.982802 14.800158
## 39  12.313033 11.295112 13.330953
## 40  15.785617 15.001060 16.570174
## 41  16.259151 15.504025 17.014277
## 42  11.523809 10.449826 12.597792
## 43  13.102256 12.139493 14.065020
## 44  12.313033 11.295112 13.330953
## 45  22.572940 22.080777 23.065104
## 46  28.571040 27.933378 29.208703
## 47  24.151388 23.660958 24.641817
## 48  26.045524 25.515552 26.575497
## 49  26.361214 25.820758 26.901669
## 50  25.729835 25.209322 26.250348
## 51  28.886730 28.232427 29.541033
## 52  27.939661 27.333469 28.545854
## 53  29.675953 28.977756 30.374151
## 54  29.044574 28.381744 29.707404
## 55  30.465177 29.720276 31.210078
## 56  28.886730 28.232427 29.541033
## 57  24.940611 24.438901 25.442321
## 58  27.308282 26.730818 27.885746
## 59  31.412245 30.608285 32.216206
## 60  25.729835 25.209322 26.250348
## 61  26.361214 25.820758 26.901669
## 62  13.891480 12.982802 14.800158
## 63  12.313033 11.295112 13.330953
## 64  16.259151 15.504025 17.014277
## 65  15.785617 15.001060 16.570174
## 66  16.259151 15.504025 17.014277
## 67   7.104156  5.704666  8.503647
## 68  15.469927 14.665349 16.274505
## 69  14.680704 13.824838 15.536569
## 70   9.945362  8.757051 11.133672
## 71  24.624922 24.128663 25.121180
## 72  16.259151 15.504025 17.014277
## 73  19.416046 18.831250 20.000841
## 74  17.837598 17.174242 18.500955
## 75  16.259151 15.504025 17.014277
## 76  22.257251 21.760844 22.753658
## 77  27.939661 27.333469 28.545854
## 78  26.203369 25.668280 26.738459
## 79  29.044574 28.381744 29.707404
## 80  26.361214 25.820758 26.901669
## 81  25.414146 24.902011 25.926280
## 82  24.624922 24.128663 25.121180
## 83  27.308282 26.730818 27.885746
## 84  26.045524 25.515552 26.575497
## 85  12.313033 11.295112 13.330953
## 86  16.259151 15.504025 17.014277
## 87  17.048375 16.340481 17.756268
## 88  18.311133 17.672969 18.949296
## 89  16.259151 15.504025 17.014277
## 90   8.682604  7.401151  9.964056
## 91  16.259151 15.504025 17.014277
## 92  14.996393 14.161242 15.831545
## 93  16.259151 15.504025 17.014277
## 94   5.999243  4.516273  7.482214
## 95   4.420796  2.817595  6.023998
## 96  12.313033 11.295112 13.330953
## 97  23.362164 22.874970 23.849358
## 98  24.151388 23.660958 24.641817
## 99  24.151388 23.660958 24.641817
## 100 26.045524 25.515552 26.575497
## 101 24.940611 24.438901 25.442321
## 102 32.675003 31.788265 33.561742
## 103 16.259151 15.504025 17.014277
## 104 13.575791 12.645619 14.505962
## 105 13.102256 12.139493 14.065020
## 106 11.523809 10.449826 12.597792
## 107 24.151388 23.660958 24.641817
## 108 26.045524 25.515552 26.575497
## 109 28.571040 27.933378 29.208703
## 110 25.098456 24.593565 25.603347
## 111 25.729835 25.209322 26.250348
## 112 26.519059 25.972996 27.065122
## 113 23.046475 22.558272 23.534677
## 114 25.729835 25.209322 26.250348
## 115 17.048375 16.340481 17.756268
## 116  3.631572  1.967894  5.295251
## 117 32.201469 31.346241 33.056697
## 118 28.097506 27.483687 28.711325
## 119 25.571990 25.055805 26.088176
## 120 22.257251 21.760844 22.753658
## 121 16.259151 15.504025 17.014277
## 122 22.572940 22.080777 23.065104
## 123 20.678804 20.143392 21.214215
## 124 11.523809 10.449826 12.597792
## 125 24.940611 24.438901 25.442321
## 126 24.151388 23.660958 24.641817
## 127 24.151388 23.660958 24.641817
## 128 29.360264 28.679992 30.040536
## 129 27.308282 26.730818 27.885746
## 130 29.675953 28.977756 30.374151
## 131 28.097506 27.483687 28.711325
## 132 24.151388 23.660958 24.641817
## 133 22.572940 22.080777 23.065104
## 134 23.362164 22.874970 23.849358
## 135 17.837598 17.174242 18.500955
## 136 16.259151 15.504025 17.014277
## 137 16.259151 15.504025 17.014277
## 138 17.837598 17.174242 18.500955
## 139 16.259151 15.504025 17.014277
## 140 26.834748 26.276776 27.392720
## 141 29.360264 28.679992 30.040536
## 142 27.623972 27.032512 28.215432
## 143 31.727935 30.903669 32.552201
## 144 30.307332 29.571971 31.042693
## 145 28.097506 27.483687 28.711325
## 146 28.097506 27.483687 28.711325
## 147 28.097506 27.483687 28.711325
## 148 24.624922 24.128663 25.121180
## 149 25.256301 24.747933 25.764669
## 150 29.360264 28.679992 30.040536
## 151 24.940611 24.438901 25.442321
## 152 23.362164 22.874970 23.849358
## 153 28.571040 27.933378 29.208703
## 154 28.571040 27.933378 29.208703
## 155 13.102256 12.139493 14.065020
## 156 17.048375 16.340481 17.756268
## 157 16.259151 15.504025 17.014277
## 158 16.574840 15.838898 17.310783
## 159 22.572940 22.080777 23.065104
## 160 23.362164 22.874970 23.849358
## 161 22.572940 22.080777 23.065104
## 162 24.940611 24.438901 25.442321
## 163 22.572940 22.080777 23.065104
## 164 22.572940 22.080777 23.065104
## 165 19.573890 18.996010 20.151771
## 166 28.097506 27.483687 28.711325
## 167 26.834748 26.276776 27.392720
## 168 24.151388 23.660958 24.641817
## 169 27.623972 27.032512 28.215432
## 170 24.782767 24.283936 25.281597
## 171 28.728885 28.082973 29.374797
## 172 24.624922 24.128663 25.121180
## 173 24.624922 24.128663 25.121180
## 174 28.886730 28.232427 29.541033
## 175 25.729835 25.209322 26.250348
## 176 24.940611 24.438901 25.442321
## 177 26.045524 25.515552 26.575497
## 178 24.467077 23.973079 24.961075
## 179 21.783717 21.278621 22.288812
## 180 31.570090 30.756012 32.384168
## 181 26.361214 25.820758 26.901669
## 182 27.150438 26.579678 27.721197
## 183 25.414146 24.902011 25.926280
## 184 27.466127 26.881761 28.050493
## 185 26.834748 26.276776 27.392720
## 186 17.837598 17.174242 18.500955
## 187 16.259151 15.504025 17.014277
## 188 20.994493 20.469092 21.519894
## 189 15.943462 15.168798 16.718125
## 190 24.151388 23.660958 24.641817
## 191 23.362164 22.874970 23.849358
## 192 27.150438 26.579678 27.721197
## 193 25.729835 25.209322 26.250348
## 194 31.727935 30.903669 32.552201
## 195 30.465177 29.720276 31.210078
## 196 28.886730 28.232427 29.541033
## 197 31.570090 30.756012 32.384168
## 198 24.151388 23.660958 24.641817
## 199 27.623972 27.032512 28.215432
## 200 22.572940 22.080777 23.065104
## 201 24.940611 24.438901 25.442321
## 202 28.728885 28.082973 29.374797
## 203 28.886730 28.232427 29.541033
## 204 28.097506 27.483687 28.711325
## 205 28.571040 27.933378 29.208703
## 206 23.835698 23.347546 24.323850
## 207 16.259151 15.504025 17.014277
## 208 26.045524 25.515552 26.575497
## 209 22.888630 22.399432 23.377828
## 210 20.994493 20.469092 21.519894
## 211 11.523809 10.449826 12.597792
## 212 17.048375 16.340481 17.756268
## 213 19.416046 18.831250 20.000841
## 214 16.259151 15.504025 17.014277
## 215 29.202419 28.530931 29.873907
## 216 27.308282 26.730818 27.885746
## 217 30.780866 30.016612 31.545121
## 218 24.782767 24.283936 25.281597
## 219 28.886730 28.232427 29.541033
## 220 17.048375 16.340481 17.756268
## 221 22.572940 22.080777 23.065104
## 222 17.048375 16.340481 17.756268
## 223 19.416046 18.831250 20.000841
## 224 22.572940 22.080777 23.065104
## 225 23.362164 22.874970 23.849358
## 226 24.151388 23.660958 24.641817
## 227 24.467077 23.973079 24.961075
## 228 11.523809 10.449826 12.597792
## 229 13.102256 12.139493 14.065020
## 230  9.945362  8.757051 11.133672
## 231 16.416996 15.671508 17.162484
## 232 27.623972 27.032512 28.215432
## 233 26.045524 25.515552 26.575497
## 234 28.097506 27.483687 28.711325
## 235 25.887680 25.362568 26.412791
## 236 29.991643 29.275071 30.708215
## 237 26.834748 26.276776 27.392720
## 238 29.360264 28.679992 30.040536
## 239 27.623972 27.032512 28.215432
## 240 24.624922 24.128663 25.121180
## 241 22.572940 22.080777 23.065104
## 242 22.572940 22.080777 23.065104
## 243 32.359314 31.493641 33.224987
## 244 29.518109 28.828932 30.207285
## 245 31.727935 30.903669 32.552201
## 246 28.886730 28.232427 29.541033
## 247 30.465177 29.720276 31.210078
## 248 22.572940 22.080777 23.065104
## 249 17.837598 17.174242 18.500955
## 250 17.995443 17.340622 18.650264
## 251 23.362164 22.874970 23.849358
## 252 24.940611 24.438901 25.442321
## 253 26.519059 25.972996 27.065122
## 254 26.045524 25.515552 26.575497
## 255 24.151388 23.660958 24.641817
## 256 25.729835 25.209322 26.250348
## 257 23.362164 22.874970 23.849358
## 258 26.519059 25.972996 27.065122
## 259 22.572940 22.080777 23.065104
## 260 20.994493 20.469092 21.519894
## 261 17.048375 16.340481 17.756268
## 262 13.891480 12.982802 14.800158
## 263 17.995443 17.340622 18.650264
## 264 17.837598 17.174242 18.500955
## 265 29.202419 28.530931 29.873907
## 266 24.940611 24.438901 25.442321
## 267 24.624922 24.128663 25.121180
## 268 28.097506 27.483687 28.711325
## 269 24.940611 24.438901 25.442321
## 270 23.362164 22.874970 23.849358
## 271 26.519059 25.972996 27.065122
## 272 24.624922 24.128663 25.121180
## 273 23.677853 23.190350 24.165357
## 274 20.205269 19.653000 20.757539
## 275 21.783717 21.278621 22.288812
## 276 18.942511 18.335857 19.549166
## 277 28.728885 28.082973 29.374797
## 278 29.202419 28.530931 29.873907
## 279 21.783717 21.278621 22.288812
## 280 26.519059 25.972996 27.065122
## 281 26.045524 25.515552 26.575497
## 282 25.729835 25.209322 26.250348
## 283 22.572940 22.080777 23.065104
## 284 19.416046 18.831250 20.000841
## 285 19.573890 18.996010 20.151771
## 286 18.153288 17.506866 18.799709
## 287 18.626822 18.004730 19.248914
## 288 15.469927 14.665349 16.274505
## 289 17.521909 16.841095 18.202722
## 290 20.205269 19.653000 20.757539
## 291 16.259151 15.504025 17.014277
## 292 28.728885 28.082973 29.374797
## 293 29.675953 28.977756 30.374151
## 294 27.308282 26.730818 27.885746
## 295 27.308282 26.730818 27.885746
## 296 27.781817 27.183079 28.380554
## 297 20.205269 19.653000 20.757539
## 298 28.728885 28.082973 29.374797
## 299 25.729835 25.209322 26.250348
## 300 28.886730 28.232427 29.541033
## 301 28.886730 28.232427 29.541033
## 302 29.675953 28.977756 30.374151
## 303 29.044574 28.381744 29.707404
## 304 25.729835 25.209322 26.250348
## 305 21.783717 21.278621 22.288812
## 306 21.783717 21.278621 22.288812
## 307 25.729835 25.209322 26.250348
## 308 27.939661 27.333469 28.545854
## 309 30.465177 29.720276 31.210078
## 310 28.886730 28.232427 29.541033
## 311 29.675953 28.977756 30.374151
## 312 25.729835 25.209322 26.250348
## 313 26.045524 25.515552 26.575497
## 314 25.729835 25.209322 26.250348
## 315 25.729835 25.209322 26.250348
## 316 27.623972 27.032512 28.215432
## 317 25.729835 25.209322 26.250348
## 318 28.097506 27.483687 28.711325
## 319 25.414146 24.902011 25.926280
## 320 28.097506 27.483687 28.711325
## 321 29.675953 28.977756 30.374151
## 322 23.362164 22.874970 23.849358
## 323 29.675953 28.977756 30.374151
## 324 32.359314 31.493641 33.224987
## 325 32.359314 31.493641 33.224987
## 326 29.360264 28.679992 30.040536
## 327 29.360264 28.679992 30.040536
## 328 29.360264 28.679992 30.040536
## 329 29.360264 28.679992 30.040536
## 330 30.149488 29.423571 30.875404
## 331 19.100356 18.501167 19.699545
## 332 24.151388 23.660958 24.641817
## 333 26.045524 25.515552 26.575497
## 334 28.571040 27.933378 29.208703
## 335 26.676903 26.124999 27.228808
## 336 26.676903 26.124999 27.228808
## 337 25.414146 24.902011 25.926280
## 338 22.572940 22.080777 23.065104
## 339 26.676903 26.124999 27.228808
## 340 30.780866 30.016612 31.545121
## 341 29.833798 29.126467 30.541129
## 342 30.465177 29.720276 31.210078
## 343 29.360264 28.679992 30.040536
## 344 29.675953 28.977756 30.374151
## 345 30.149488 29.423571 30.875404
## 346 29.202419 28.530931 29.873907
## 347 29.991643 29.275071 30.708215
## 348 29.675953 28.977756 30.374151
## 349 29.675953 28.977756 30.374151
## 350 28.255351 27.633741 28.876961
## 351 28.097506 27.483687 28.711325
## 352 28.097506 27.483687 28.711325
## 353 24.151388 23.660958 24.641817
## 354 28.255351 27.633741 28.876961
## 355 27.308282 26.730818 27.885746
## 356 27.939661 27.333469 28.545854
## 357 21.625872 21.117282 22.134462
## 358 20.994493 20.469092 21.519894
## 359 22.572940 22.080777 23.065104
## 360 23.362164 22.874970 23.849358
## 361 26.045524 25.515552 26.575497
## 362 26.519059 25.972996 27.065122
## 363 26.045524 25.515552 26.575497
## 364 26.045524 25.515552 26.575497
## 365 26.045524 25.515552 26.575497
## 366 26.519059 25.972996 27.065122
## 367 26.676903 26.124999 27.228808
## 368 25.729835 25.209322 26.250348
## 369 25.414146 24.902011 25.926280
## 370 28.255351 27.633741 28.876961
## 371 29.202419 28.530931 29.873907
## 372 29.202419 28.530931 29.873907
## 373 29.991643 29.275071 30.708215
## 374 28.886730 28.232427 29.541033
## 375 26.045524 25.515552 26.575497
## 376 28.097506 27.483687 28.711325
## 377 28.886730 28.232427 29.541033
## 378 29.360264 28.679992 30.040536
## 379 29.360264 28.679992 30.040536
## 380 29.360264 28.679992 30.040536
## 381 22.572940 22.080777 23.065104
## 382 26.519059 25.972996 27.065122
## 383 25.414146 24.902011 25.926280
## 384 22.257251 21.760844 22.753658
## 385 24.782767 24.283936 25.281597
## 386 26.676903 26.124999 27.228808
## 387 25.729835 25.209322 26.250348
## 388 26.361214 25.820758 26.901669
## 389 31.727935 30.903669 32.552201
## 390 26.676903 26.124999 27.228808
## 391 27.466127 26.881761 28.050493
## 392 26.992593 26.428333 27.556853
# prediction interval 
predict(mod, newdata, 
        interval="predict")
## Warning: 'newdata' had 1 row but variables found have 392 rows
##           fit        lwr      upr
## 1   19.416046  9.7532948 29.07880
## 2   13.891480  4.2037318 23.57923
## 3   16.259151  6.5845976 25.93370
## 4   16.259151  6.5845976 25.93370
## 5   17.837598  8.1697749 27.50542
## 6    8.682604 -1.0471901 18.41240
## 7    5.210020 -4.5576558 14.97770
## 8    5.999243 -3.7591362 15.75762
## 9    4.420796 -5.3565771 14.19817
## 10   9.945362  0.2273963 19.66333
## 11  13.102256  3.4092855 22.79523
## 12  14.680704  4.9977664 24.36364
## 13  16.259151  6.5845976 25.93370
## 14   4.420796 -5.3565771 14.19817
## 15  24.940611 15.2825327 34.59869
## 16  24.940611 15.2825327 34.59869
## 17  24.624922 14.9671249 34.28272
## 18  26.519059 16.8585745 36.17954
## 19  26.045524 16.3859365 35.70511
## 20  32.675003 22.9892883 42.36072
## 21  26.203369 16.5434991 35.86324
## 22  25.729835 16.0707614 35.38891
## 23  24.940611 15.2825327 34.59869
## 24  22.099406 12.4414680 31.75734
## 25  25.729835 16.0707614 35.38891
## 26   5.999243 -3.7591362 15.75762
## 27   8.366914 -1.3659995 18.09983
## 28   6.788467 -2.9610196 16.53795
## 29   9.471827 -0.2504514 19.19411
## 30  26.045524 16.3859365 35.70511
## 31  25.729835 16.0707614 35.38891
## 32  24.940611 15.2825327 34.59869
## 33  24.151388 14.4938885 33.80889
## 34  23.362164 13.7048286 33.01950
## 35  24.151388 14.4938885 33.80889
## 36  26.045524 16.3859365 35.70511
## 37  24.151388 14.4938885 33.80889
## 38  13.891480  4.2037318 23.57923
## 39  12.313033  2.6144281 22.01164
## 40  15.785617  6.1087217 25.46251
## 41  16.259151  6.5845976 25.93370
## 42  11.523809  1.8191602 21.22846
## 43  13.102256  3.4092855 22.79523
## 44  12.313033  2.6144281 22.01164
## 45  22.572940 12.9153529 32.23053
## 46  28.571040 18.9049457 38.23713
## 47  24.151388 14.4938885 33.80889
## 48  26.045524 16.3859365 35.70511
## 49  26.361214 16.7010451 36.02138
## 50  25.729835 16.0707614 35.38891
## 51  28.886730 19.2195232 38.55394
## 52  27.939661 18.2755918 37.60373
## 53  29.675953 20.0056767 39.34623
## 54  29.044574 19.3767870 38.71236
## 55  30.465177 20.7914163 40.13894
## 56  28.886730 19.2195232 38.55394
## 57  24.940611 15.2825327 34.59869
## 58  27.308282 17.6459724 36.97059
## 59  31.412245 21.7337578 41.09073
## 60  25.729835 16.0707614 35.38891
## 61  26.361214 16.7010451 36.02138
## 62  13.891480  4.2037318 23.57923
## 63  12.313033  2.6144281 22.01164
## 64  16.259151  6.5845976 25.93370
## 65  15.785617  6.1087217 25.46251
## 66  16.259151  6.5845976 25.93370
## 67   7.104156 -2.6418860 16.85020
## 68  15.469927  5.7913884 25.14847
## 69  14.680704  4.9977664 24.36364
## 70   9.945362  0.2273963 19.66333
## 71  24.624922 14.9671249 34.28272
## 72  16.259151  6.5845976 25.93370
## 73  19.416046  9.7532948 29.07880
## 74  17.837598  8.1697749 27.50542
## 75  16.259151  6.5845976 25.93370
## 76  22.257251 12.5994463 31.91506
## 77  27.939661 18.2755918 37.60373
## 78  26.203369 16.5434991 35.86324
## 79  29.044574 19.3767870 38.71236
## 80  26.361214 16.7010451 36.02138
## 81  25.414146 15.7555198 35.07277
## 82  24.624922 14.9671249 34.28272
## 83  27.308282 17.6459724 36.97059
## 84  26.045524 16.3859365 35.70511
## 85  12.313033  2.6144281 22.01164
## 86  16.259151  6.5845976 25.93370
## 87  17.048375  7.3773932 26.71936
## 88  18.311133  8.6450050 27.97726
## 89  16.259151  6.5845976 25.93370
## 90   8.682604 -1.0471901 18.41240
## 91  16.259151  6.5845976 25.93370
## 92  14.996393  5.3152647 24.67752
## 93  16.259151  6.5845976 25.93370
## 94   5.999243 -3.7591362 15.75762
## 95   4.420796 -5.3565771 14.19817
## 96  12.313033  2.6144281 22.01164
## 97  23.362164 13.7048286 33.01950
## 98  24.151388 14.4938885 33.80889
## 99  24.151388 14.4938885 33.80889
## 100 26.045524 16.3859365 35.70511
## 101 24.940611 15.2825327 34.59869
## 102 32.675003 22.9892883 42.36072
## 103 16.259151  6.5845976 25.93370
## 104 13.575791  3.8860027 23.26558
## 105 13.102256  3.4092855 22.79523
## 106 11.523809  1.8191602 21.22846
## 107 24.151388 14.4938885 33.80889
## 108 26.045524 16.3859365 35.70511
## 109 28.571040 18.9049457 38.23713
## 110 25.098456 15.4402117 34.75670
## 111 25.729835 16.0707614 35.38891
## 112 26.519059 16.8585745 36.17954
## 113 23.046475 13.3890882 32.70386
## 114 25.729835 16.0707614 35.38891
## 115 17.048375  7.3773932 26.71936
## 116  3.631572 -6.1558990 13.41904
## 117 32.201469 22.5185881 41.88435
## 118 28.097506 18.4329552 37.76206
## 119 25.571990 15.9131489 35.23083
## 120 22.257251 12.5994463 31.91506
## 121 16.259151  6.5845976 25.93370
## 122 22.572940 12.9153529 32.23053
## 123 20.678804 11.0189156 30.33869
## 124 11.523809  1.8191602 21.22846
## 125 24.940611 15.2825327 34.59869
## 126 24.151388 14.4938885 33.80889
## 127 24.151388 14.4938885 33.80889
## 128 29.360264 19.6912650 39.02926
## 129 27.308282 17.6459724 36.97059
## 130 29.675953 20.0056767 39.34623
## 131 28.097506 18.4329552 37.76206
## 132 24.151388 14.4938885 33.80889
## 133 22.572940 12.9153529 32.23053
## 134 23.362164 13.7048286 33.01950
## 135 17.837598  8.1697749 27.50542
## 136 16.259151  6.5845976 25.93370
## 137 16.259151  6.5845976 25.93370
## 138 17.837598  8.1697749 27.50542
## 139 16.259151  6.5845976 25.93370
## 140 26.834748 17.1735835 36.49591
## 141 29.360264 19.6912650 39.02926
## 142 27.623972 17.9608153 37.28713
## 143 31.727935 22.0477395 41.40813
## 144 30.307332 20.6343015 39.98036
## 145 28.097506 18.4329552 37.76206
## 146 28.097506 18.4329552 37.76206
## 147 28.097506 18.4329552 37.76206
## 148 24.624922 14.9671249 34.28272
## 149 25.256301 15.5978741 34.91473
## 150 29.360264 19.6912650 39.02926
## 151 24.940611 15.2825327 34.59869
## 152 23.362164 13.7048286 33.01950
## 153 28.571040 18.9049457 38.23713
## 154 28.571040 18.9049457 38.23713
## 155 13.102256  3.4092855 22.79523
## 156 17.048375  7.3773932 26.71936
## 157 16.259151  6.5845976 25.93370
## 158 16.574840  6.9017655 26.24792
## 159 22.572940 12.9153529 32.23053
## 160 23.362164 13.7048286 33.01950
## 161 22.572940 12.9153529 32.23053
## 162 24.940611 15.2825327 34.59869
## 163 22.572940 12.9153529 32.23053
## 164 22.572940 12.9153529 32.23053
## 165 19.573890  9.9115555 29.23623
## 166 28.097506 18.4329552 37.76206
## 167 26.834748 17.1735835 36.49591
## 168 24.151388 14.4938885 33.80889
## 169 27.623972 17.9608153 37.28713
## 170 24.782767 15.1248371 34.44070
## 171 28.728885 19.0622427 38.39553
## 172 24.624922 14.9671249 34.28272
## 173 24.624922 14.9671249 34.28272
## 174 28.886730 19.2195232 38.55394
## 175 25.729835 16.0707614 35.38891
## 176 24.940611 15.2825327 34.59869
## 177 26.045524 16.3859365 35.70511
## 178 24.467077 14.8093961 34.12476
## 179 21.783717 12.1254616 31.44197
## 180 31.570090 21.8907569 41.24942
## 181 26.361214 16.7010451 36.02138
## 182 27.150438 17.4885260 36.81235
## 183 25.414146 15.7555198 35.07277
## 184 27.466127 17.8034021 37.12885
## 185 26.834748 17.1735835 36.49591
## 186 17.837598  8.1697749 27.50542
## 187 16.259151  6.5845976 25.93370
## 188 20.994493 11.3351547 30.65383
## 189 15.943462  6.2673635 25.61956
## 190 24.151388 14.4938885 33.80889
## 191 23.362164 13.7048286 33.01950
## 192 27.150438 17.4885260 36.81235
## 193 25.729835 16.0707614 35.38891
## 194 31.727935 22.0477395 41.40813
## 195 30.465177 20.7914163 40.13894
## 196 28.886730 19.2195232 38.55394
## 197 31.570090 21.8907569 41.24942
## 198 24.151388 14.4938885 33.80889
## 199 27.623972 17.9608153 37.28713
## 200 22.572940 12.9153529 32.23053
## 201 24.940611 15.2825327 34.59869
## 202 28.728885 19.0622427 38.39553
## 203 28.886730 19.2195232 38.55394
## 204 28.097506 18.4329552 37.76206
## 205 28.571040 18.9049457 38.23713
## 206 23.835698 14.1783144 33.49308
## 207 16.259151  6.5845976 25.93370
## 208 26.045524 16.3859365 35.70511
## 209 22.888630 13.2311931 32.54607
## 210 20.994493 11.3351547 30.65383
## 211 11.523809  1.8191602 21.22846
## 212 17.048375  7.3773932 26.71936
## 213 19.416046  9.7532948 29.07880
## 214 16.259151  6.5845976 25.93370
## 215 29.202419 19.5340343 38.87080
## 216 27.308282 17.6459724 36.97059
## 217 30.780866 21.1055963 40.45614
## 218 24.782767 15.1248371 34.44070
## 219 28.886730 19.2195232 38.55394
## 220 17.048375  7.3773932 26.71936
## 221 22.572940 12.9153529 32.23053
## 222 17.048375  7.3773932 26.71936
## 223 19.416046  9.7532948 29.07880
## 224 22.572940 12.9153529 32.23053
## 225 23.362164 13.7048286 33.01950
## 226 24.151388 14.4938885 33.80889
## 227 24.467077 14.8093961 34.12476
## 228 11.523809  1.8191602 21.22846
## 229 13.102256  3.4092855 22.79523
## 230  9.945362  0.2273963 19.66333
## 231 16.416996  6.7431898 26.09080
## 232 27.623972 17.9608153 37.28713
## 233 26.045524 16.3859365 35.70511
## 234 28.097506 18.4329552 37.76206
## 235 25.887680 16.2283572 35.54700
## 236 29.991643 20.3200222 39.66326
## 237 26.834748 17.1735835 36.49591
## 238 29.360264 19.6912650 39.02926
## 239 27.623972 17.9608153 37.28713
## 240 24.624922 14.9671249 34.28272
## 241 22.572940 12.9153529 32.23053
## 242 22.572940 12.9153529 32.23053
## 243 32.359314 22.6755047 42.04312
## 244 29.518109 19.8484792 39.18774
## 245 31.727935 22.0477395 41.40813
## 246 28.886730 19.2195232 38.55394
## 247 30.465177 20.7914163 40.13894
## 248 22.572940 12.9153529 32.23053
## 249 17.837598  8.1697749 27.50542
## 250 17.995443  8.3282015 27.66268
## 251 23.362164 13.7048286 33.01950
## 252 24.940611 15.2825327 34.59869
## 253 26.519059 16.8585745 36.17954
## 254 26.045524 16.3859365 35.70511
## 255 24.151388 14.4938885 33.80889
## 256 25.729835 16.0707614 35.38891
## 257 23.362164 13.7048286 33.01950
## 258 26.519059 16.8585745 36.17954
## 259 22.572940 12.9153529 32.23053
## 260 20.994493 11.3351547 30.65383
## 261 17.048375  7.3773932 26.71936
## 262 13.891480  4.2037318 23.57923
## 263 17.995443  8.3282015 27.66268
## 264 17.837598  8.1697749 27.50542
## 265 29.202419 19.5340343 38.87080
## 266 24.940611 15.2825327 34.59869
## 267 24.624922 14.9671249 34.28272
## 268 28.097506 18.4329552 37.76206
## 269 24.940611 15.2825327 34.59869
## 270 23.362164 13.7048286 33.01950
## 271 26.519059 16.8585745 36.17954
## 272 24.624922 14.9671249 34.28272
## 273 23.677853 14.0205024 33.33520
## 274 20.205269 10.5444324 29.86611
## 275 21.783717 12.1254616 31.44197
## 276 18.942511  9.2784130 28.60661
## 277 28.728885 19.0622427 38.39553
## 278 29.202419 19.5340343 38.87080
## 279 21.783717 12.1254616 31.44197
## 280 26.519059 16.8585745 36.17954
## 281 26.045524 16.3859365 35.70511
## 282 25.729835 16.0707614 35.38891
## 283 22.572940 12.9153529 32.23053
## 284 19.416046  9.7532948 29.07880
## 285 19.573890  9.9115555 29.23623
## 286 18.153288  8.4866115 27.81996
## 287 18.626822  8.9617422 28.29190
## 288 15.469927  5.7913884 25.14847
## 289 17.521909  7.8528719 27.19095
## 290 20.205269 10.5444324 29.86611
## 291 16.259151  6.5845976 25.93370
## 292 28.728885 19.0622427 38.39553
## 293 29.675953 20.0056767 39.34623
## 294 27.308282 17.6459724 36.97059
## 295 27.308282 17.6459724 36.97059
## 296 27.781817 18.1182118 37.44542
## 297 20.205269 10.5444324 29.86611
## 298 28.728885 19.0622427 38.39553
## 299 25.729835 16.0707614 35.38891
## 300 28.886730 19.2195232 38.55394
## 301 28.886730 19.2195232 38.55394
## 302 29.675953 20.0056767 39.34623
## 303 29.044574 19.3767870 38.71236
## 304 25.729835 16.0707614 35.38891
## 305 21.783717 12.1254616 31.44197
## 306 21.783717 12.1254616 31.44197
## 307 25.729835 16.0707614 35.38891
## 308 27.939661 18.2755918 37.60373
## 309 30.465177 20.7914163 40.13894
## 310 28.886730 19.2195232 38.55394
## 311 29.675953 20.0056767 39.34623
## 312 25.729835 16.0707614 35.38891
## 313 26.045524 16.3859365 35.70511
## 314 25.729835 16.0707614 35.38891
## 315 25.729835 16.0707614 35.38891
## 316 27.623972 17.9608153 37.28713
## 317 25.729835 16.0707614 35.38891
## 318 28.097506 18.4329552 37.76206
## 319 25.414146 15.7555198 35.07277
## 320 28.097506 18.4329552 37.76206
## 321 29.675953 20.0056767 39.34623
## 322 23.362164 13.7048286 33.01950
## 323 29.675953 20.0056767 39.34623
## 324 32.359314 22.6755047 42.04312
## 325 32.359314 22.6755047 42.04312
## 326 29.360264 19.6912650 39.02926
## 327 29.360264 19.6912650 39.02926
## 328 29.360264 19.6912650 39.02926
## 329 29.360264 19.6912650 39.02926
## 330 30.149488 20.4771701 39.82180
## 331 19.100356  9.4367235 28.76399
## 332 24.151388 14.4938885 33.80889
## 333 26.045524 16.3859365 35.70511
## 334 28.571040 18.9049457 38.23713
## 335 26.676903 17.0160873 36.33772
## 336 26.676903 17.0160873 36.33772
## 337 25.414146 15.7555198 35.07277
## 338 22.572940 12.9153529 32.23053
## 339 26.676903 17.0160873 36.33772
## 340 30.780866 21.1055963 40.45614
## 341 29.833798 20.1628578 39.50474
## 342 30.465177 20.7914163 40.13894
## 343 29.360264 19.6912650 39.02926
## 344 29.675953 20.0056767 39.34623
## 345 30.149488 20.4771701 39.82180
## 346 29.202419 19.5340343 38.87080
## 347 29.991643 20.3200222 39.66326
## 348 29.675953 20.0056767 39.34623
## 349 29.675953 20.0056767 39.34623
## 350 28.255351 18.5903019 37.92040
## 351 28.097506 18.4329552 37.76206
## 352 28.097506 18.4329552 37.76206
## 353 24.151388 14.4938885 33.80889
## 354 28.255351 18.5903019 37.92040
## 355 27.308282 17.6459724 36.97059
## 356 27.939661 18.2755918 37.60373
## 357 21.625872 11.9674335 31.28431
## 358 20.994493 11.3351547 30.65383
## 359 22.572940 12.9153529 32.23053
## 360 23.362164 13.7048286 33.01950
## 361 26.045524 16.3859365 35.70511
## 362 26.519059 16.8585745 36.17954
## 363 26.045524 16.3859365 35.70511
## 364 26.045524 16.3859365 35.70511
## 365 26.045524 16.3859365 35.70511
## 366 26.519059 16.8585745 36.17954
## 367 26.676903 17.0160873 36.33772
## 368 25.729835 16.0707614 35.38891
## 369 25.414146 15.7555198 35.07277
## 370 28.255351 18.5903019 37.92040
## 371 29.202419 19.5340343 38.87080
## 372 29.202419 19.5340343 38.87080
## 373 29.991643 20.3200222 39.66326
## 374 28.886730 19.2195232 38.55394
## 375 26.045524 16.3859365 35.70511
## 376 28.097506 18.4329552 37.76206
## 377 28.886730 19.2195232 38.55394
## 378 29.360264 19.6912650 39.02926
## 379 29.360264 19.6912650 39.02926
## 380 29.360264 19.6912650 39.02926
## 381 22.572940 12.9153529 32.23053
## 382 26.519059 16.8585745 36.17954
## 383 25.414146 15.7555198 35.07277
## 384 22.257251 12.5994463 31.91506
## 385 24.782767 15.1248371 34.44070
## 386 26.676903 17.0160873 36.33772
## 387 25.729835 16.0707614 35.38891
## 388 26.361214 16.7010451 36.02138
## 389 31.727935 22.0477395 41.40813
## 390 26.676903 17.0160873 36.33772
## 391 27.466127 17.8034021 37.12885
## 392 26.992593 17.3310631 36.65412
detach(auto) #Essential to do at the end of the code

PROBLEM 3

auto<-read.csv("http://faculty.marshall.usc.edu/gareth-james/ISL/Auto.csv",
               header=TRUE,
               na.strings = "?")
auto=na.omit(auto)

# TAKE OUT COLUMNS FOR ORIGIN AND NAME
auto<-auto[,-c(8:9)]
names(auto)
## [1] "mpg"          "cylinders"    "displacement" "horsepower"  
## [5] "weight"       "acceleration" "year"
head(auto)
##   mpg cylinders displacement horsepower weight acceleration year
## 1  18         8          307        130   3504         12.0   70
## 2  15         8          350        165   3693         11.5   70
## 3  18         8          318        150   3436         11.0   70
## 4  16         8          304        150   3433         12.0   70
## 5  17         8          302        140   3449         10.5   70
## 6  15         8          429        198   4341         10.0   70
autodf<-data.frame(mpg=auto$mpg, 
                   cylinders=auto$cylinders,
                   displacement=auto$displacement,
                   horsepower=auto$horsepower,
                   weight=auto$weight,
                   acceleration=auto$acceleration,
                   year=auto$year)
pairs(autodf)