- Introduction
- 1. Chapter 2. Statistical Learning
- 2. Chapter 3. Linear Regression
- 3. Chapter 4. Classification
- 4. Chapter 5. Resampling Methods
- 5. Chapter 6. Linear Model Selection and Regularization
- 6. Chapter 7. Moving Beyond Linearity
- 7. Chapter 8. Tree-Based Methods
- 8. Chapter 9. Support Vector Machines
- 9. Chapter 10. Unsupervised Learning
- 10. References
- Published with GitBook
3.7 Exercises
library(ISLR)
Exercise 8
attach(Auto)
qualitative_columns <- c(2, 8, 9)
fit1 <- lm(mpg ~ horsepower, data = Auto)
plot(mpg ~ horsepower, Auto)
abline(fit1, col = "red")
plot(fit1)
Exercise 9
qualitative_columns <- c(2, 8, 9)
pairs(Auto) # almost too complicated to work with
fit <- lm(mpg ~ ., data = Auto)
summary(fit)
##
## Call:
## lm(formula = mpg ~ ., data = Auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.646 0.000 0.000 0.000 5.646
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) 0.187305 12.773943 0.015
## cylinders -0.918096 0.616653 -1.489
## displacement 0.003041 0.015621 0.195
## horsepower -0.042342 0.029070 -1.457
## weight -0.004193 0.001209 -3.467
## acceleration -0.481449 0.171537 -2.807
## year 0.636498 0.112195 5.673
## origin 1.324264 4.243221 0.312
## nameamc ambassador dpl 3.371358 3.245610 1.039
## nameamc ambassador sst 3.364264 3.270924 1.029
## nameamc concord -0.122500 3.275058 -0.037
## nameamc concord d/l -1.686548 3.422955 -0.493
## nameamc concord dl 6 -0.529687 3.514452 -0.151
## nameamc gremlin -0.426606 2.958293 -0.144
## nameamc hornet 0.269026 2.902972 0.093
## nameamc hornet sportabout (sw) -0.403111 3.527112 -0.114
## nameamc matador 0.462233 2.667735 0.173
## nameamc matador (sw) 3.118929 2.894160 1.078
## nameamc pacer 0.012163 3.519402 0.003
## nameamc pacer d/l -1.682001 3.517154 -0.478
## nameamc rebel sst 2.875941 3.284138 0.876
## nameamc spirit dl 0.713000 4.063462 0.175
## nameaudi 100 ls 0.936254 3.449074 0.271
## nameaudi 100ls -3.133448 2.984726 -1.050
## nameaudi 4000 4.004843 3.244193 1.234
## nameaudi 5000 -4.109082 3.450859 -1.191
## nameaudi 5000s (diesel) 11.652927 3.494256 3.335
## nameaudi fox 3.199486 3.328970 0.961
## namebmw 2002 2.082893 3.429803 0.607
## namebmw 320i -5.320674 3.378167 -1.575
## namebuick century 2.213275 3.073805 0.720
## namebuick century 350 2.163058 3.250910 0.665
## namebuick century limited 1.154506 3.653147 0.316
## namebuick century luxus (sw) 3.701574 3.397404 1.090
## namebuick century special 0.471663 3.468124 0.136
## namebuick electra 225 custom 5.565899 3.481596 1.599
## namebuick estate wagon (sw) 2.288361 2.883255 0.794
## namebuick lesabre custom 3.878880 3.350669 1.158
## namebuick opel isuzu deluxe 2.360903 4.090583 0.577
## namebuick regal sport coupe (turbo) -0.770758 3.673221 -0.210
## namebuick skyhawk 1.178015 3.453774 0.341
## namebuick skylark 0.485925 3.292621 0.148
## namebuick skylark 320 3.220548 3.239745 0.994
## namebuick skylark limited 2.526638 3.945353 0.640
## namecadillac eldorado 7.506805 3.434596 2.186
## namecadillac seville 4.705913 3.307504 1.423
## namecapri ii 0.213795 3.974233 0.054
## namechevroelt chevelle malibu 1.190886 3.501889 0.340
## namechevrolet bel air 3.526745 3.332996 1.058
## namechevrolet camaro 1.016970 3.965053 0.256
## namechevrolet caprice classic 1.486191 2.705678 0.549
## namechevrolet cavalier 1.711757 4.062490 0.421
## namechevrolet cavalier 2-door 6.060983 4.085007 1.484
## namechevrolet cavalier wagon 0.377051 4.065117 0.093
## namechevrolet chevelle concours (sw) 1.497987 3.363217 0.445
## namechevrolet chevelle malibu 2.508523 3.012061 0.833
## namechevrolet chevelle malibu classic 2.148872 2.973671 0.723
## namechevrolet chevette 2.796588 3.583400 0.780
## namechevrolet citation 0.835024 3.277093 0.255
## namechevrolet concours -0.962069 3.436400 -0.280
## namechevrolet impala 3.901975 2.655000 1.470
## namechevrolet malibu 0.338930 2.908792 0.117
## namechevrolet malibu classic (sw) 1.566909 3.369001 0.465
## namechevrolet monte carlo 1.755561 3.510683 0.500
## namechevrolet monte carlo landau 1.360482 2.830125 0.481
## namechevrolet monte carlo s 2.817323 3.294556 0.855
## namechevrolet monza 2+2 1.960822 3.418832 0.574
## namechevrolet nova 0.013367 2.932203 0.005
## namechevrolet nova custom -0.583803 3.483183 -0.168
## namechevrolet vega -0.123809 3.451390 -0.036
## namechevrolet vega (sw) 0.835785 3.957409 0.211
## namechevrolet vega 2300 5.309133 3.978383 1.334
## namechevrolet woody 0.242401 4.035002 0.060
## namechevy c10 -1.686820 3.292205 -0.512
## namechevy c20 4.381943 3.755983 1.167
## namechevy s-10 4.822281 4.016031 1.201
## namechrysler cordoba 3.158331 3.288955 0.960
## namechrysler lebaron medallion -2.791925 4.039754 -0.691
## namechrysler lebaron salon -4.524894 3.582800 -1.263
## namechrysler lebaron town @ country (sw) 2.084281 3.302393 0.631
## namechrysler new yorker brougham 5.282481 3.390324 1.558
## namechrysler newport royal 4.391942 3.291715 1.334
## namedatsun 1200 7.452422 6.449055 1.156
## namedatsun 200-sx -5.232326 6.424023 -0.814
## namedatsun 200sx 2.817519 6.441163 0.437
## namedatsun 210 5.606103 6.195917 0.905
## namedatsun 210 mpg 5.070308 6.390048 0.793
## namedatsun 280-zx 5.896050 6.830585 0.863
## namedatsun 310 4.643895 6.277737 0.740
## namedatsun 310 gx 4.043465 6.266014 0.645
## namedatsun 510 -2.468844 6.400190 -0.386
## namedatsun 510 (sw) 3.062356 6.557580 0.467
## namedatsun 510 hatchback 6.552699 6.395446 1.025
## namedatsun 610 -3.382103 6.545652 -0.517
## namedatsun 710 1.331250 6.306882 0.211
## namedatsun 810 -3.215340 6.816828 -0.472
## namedatsun 810 maxima -2.442319 6.860787 -0.356
## namedatsun b-210 2.371920 6.357360 0.373
## namedatsun b210 3.331328 6.462449 0.515
## namedatsun b210 gx 9.604655 6.404554 1.500
## namedatsun f-10 hatchback 2.950464 6.329051 0.466
## namedatsun pl510 0.981674 6.254240 0.157
## namedodge aries se 0.403815 4.041675 0.100
## namedodge aries wagon (sw) -2.256829 4.019898 -0.561
## namedodge aspen -0.206883 3.088343 -0.067
## namedodge aspen 6 0.366429 3.465245 0.106
## namedodge aspen se 3.002155 3.493627 0.859
## namedodge challenger se 2.064684 3.290611 0.627
## namedodge charger 2.2 5.309608 4.166685 1.274
## namedodge colt 1.482396 3.584355 0.414
## namedodge colt (sw) 3.716950 4.113570 0.904
## namedodge colt hardtop 1.522048 4.067987 0.374
## namedodge colt hatchback custom 5.628627 4.197231 1.341
## namedodge colt m/m 6.221646 4.105872 1.515
## namedodge coronet brougham 2.669663 3.290052 0.811
## namedodge coronet custom 1.606868 3.247032 0.495
## namedodge coronet custom (sw) 3.302820 3.364562 0.982
## namedodge d100 -1.672691 3.254823 -0.514
## namedodge d200 5.074896 3.746461 1.355
## namedodge dart custom -0.700127 3.265096 -0.214
## namedodge diplomat 2.561880 3.282848 0.780
## namedodge magnum xe 2.349068 3.293521 0.713
## namedodge monaco (sw) 5.409949 3.475789 1.556
## namedodge monaco brougham 1.448836 3.286662 0.441
## namedodge omni 2.600955 4.128988 0.630
## namedodge rampage 0.321131 4.244538 0.076
## namedodge st. regis 1.874870 3.310142 0.566
## namefiat 124 sport coupe 0.843793 3.356728 0.251
## namefiat 124 tc -1.284412 3.299112 -0.389
## namefiat 124b 4.234430 3.350724 1.264
## namefiat 128 -0.302820 2.911282 -0.104
## namefiat 131 1.571897 3.313206 0.474
## namefiat strada custom 6.505740 3.221602 2.019
## namefiat x1.9 3.420877 3.286517 1.041
## nameford country 3.810815 3.447980 1.105
## nameford country squire (sw) 2.588023 2.891203 0.895
## nameford escort 2h 2.903207 4.052921 0.716
## nameford escort 4w 3.832150 4.172436 0.918
## nameford f108 -1.507274 3.300893 -0.457
## nameford f250 5.376492 3.649336 1.473
## nameford fairmont 1.688480 3.942005 0.428
## nameford fairmont (auto) -2.420856 3.577091 -0.677
## nameford fairmont (man) -0.267333 3.979340 -0.067
## nameford fairmont 4 -2.076328 3.945762 -0.526
## nameford fairmont futura -2.654573 4.013149 -0.661
## nameford fiesta 5.590179 4.227911 1.322
## nameford futura -1.916806 3.362257 -0.570
## nameford galaxie 500 4.442480 2.696732 1.647
## nameford gran torino 2.395149 2.717190 0.881
## nameford gran torino (sw) 4.305909 3.032697 1.420
## nameford granada 0.802555 3.476415 0.231
## nameford granada ghia 1.260545 3.617154 0.348
## nameford granada gl -3.179138 3.572976 -0.890
## nameford granada l -3.195561 3.585987 -0.891
## nameford ltd 2.931338 2.921112 1.004
## nameford ltd landau -0.237362 3.326697 -0.071
## nameford maverick 0.203527 3.006394 0.068
## nameford mustang -0.086763 3.673287 -0.024
## nameford mustang gl -0.608234 4.034452 -0.151
## nameford mustang ii -5.296511 3.364527 -1.574
## nameford mustang ii 2+2 1.150829 3.960070 0.291
## nameford pinto -0.775120 3.301082 -0.235
## nameford pinto (sw) -0.652033 4.001814 -0.163
## nameford pinto runabout -2.119866 3.996017 -0.530
## nameford ranger 0.908753 4.018900 0.226
## nameford thunderbird 3.220573 3.297455 0.977
## nameford torino 2.803510 3.333644 0.841
## nameford torino 500 2.078087 3.646390 0.570
## namehi 1200d 6.272325 3.984511 1.574
## namehonda accord 1.948521 6.116848 0.319
## namehonda accord cvcc 2.063973 6.429582 0.321
## namehonda accord lx -1.109939 6.347929 -0.175
## namehonda civic 1.053256 6.055926 0.174
## namehonda civic (auto) -2.323039 6.246699 -0.372
## namehonda civic 1300 0.480561 6.224808 0.077
## namehonda civic 1500 gl 10.153049 6.196347 1.639
## namehonda civic cvcc 3.182648 6.123490 0.520
## namehonda prelude 0.704854 6.280545 0.112
## namemaxda glc deluxe 1.418177 6.244770 0.227
## namemaxda rx3 -10.867477 6.267079 -1.734
## namemazda 626 1.984386 6.282271 0.316
## namemazda glc 15.147599 6.344260 2.388
## namemazda glc 4 0.684088 6.266174 0.109
## namemazda glc custom -2.344981 6.320355 -0.371
## namemazda glc custom l 4.174484 6.349602 0.657
## namemazda glc deluxe 2.292567 6.386457 0.359
## namemazda rx-4 -6.598216 6.446482 -1.024
## namemazda rx-7 gs -8.439964 6.251072 -1.350
## namemazda rx2 coupe -8.070898 6.367885 -1.267
## namemercedes-benz 240d 6.431350 3.628762 1.772
## namemercedes-benz 280s -0.574813 3.970931 -0.145
## namemercedes benz 300d 4.052324 3.714017 1.091
## namemercury capri 2000 -0.712146 4.074233 -0.175
## namemercury capri v6 -0.303572 3.691241 -0.082
## namemercury cougar brougham 1.589959 3.361893 0.473
## namemercury grand marquis -0.237277 3.337834 -0.071
## namemercury lynx l 5.872369 4.147537 1.416
## namemercury marquis 3.228385 3.350958 0.963
## namemercury marquis brougham 4.746644 3.423970 1.386
## namemercury monarch -1.952366 3.676929 -0.531
## namemercury monarch ghia 2.483829 3.298276 0.753
## namemercury zephyr -0.947324 3.554276 -0.267
## namemercury zephyr 6 -2.197060 3.553076 -0.618
## namenissan stanza xe 2.717783 6.321214 0.430
## nameoldsmobile cutlass ciera (diesel) 13.431975 3.705632 3.625
## nameoldsmobile cutlass ls 9.023570 3.661744 2.464
## nameoldsmobile cutlass salon brougham 4.510530 3.094646 1.458
## nameoldsmobile cutlass supreme 3.859509 3.468811 1.113
## nameoldsmobile delta 88 royale 2.897729 3.327483 0.871
## nameoldsmobile omega -2.416124 3.226729 -0.749
## nameoldsmobile omega brougham 2.387769 3.687973 0.647
## nameoldsmobile starfire sx -0.102617 3.905251 -0.026
## nameoldsmobile vista cruiser 2.806911 3.342458 0.840
## nameopel 1900 0.364179 2.888955 0.126
## nameopel manta -1.463586 2.886584 -0.507
## namepeugeot 304 6.452724 3.479899 1.854
## namepeugeot 504 2.256143 3.020582 0.747
## namepeugeot 504 (sw) 1.205706 3.655813 0.330
## namepeugeot 505s turbo diesel 3.702626 3.568596 1.038
## namepeugeot 604sl -3.734443 3.870878 -0.965
## nameplymouth 'cuda 340 0.001994 3.312175 0.001
## nameplymouth arrow gs -0.550125 4.028316 -0.137
## nameplymouth champ 7.809841 4.225532 1.848
## nameplymouth cricket 3.723019 4.089471 0.910
## nameplymouth custom suburb 4.243663 3.356462 1.264
## nameplymouth duster 3.100163 3.013252 1.029
## nameplymouth fury 2.614640 3.537123 0.739
## nameplymouth fury gran sedan 3.498384 3.316570 1.055
## nameplymouth fury iii 4.299562 2.679985 1.604
## nameplymouth grand fury 5.319669 3.369828 1.579
## nameplymouth horizon 4.301083 4.214230 1.021
## nameplymouth horizon 4 4.113045 4.189513 0.982
## nameplymouth horizon miser 6.302919 4.228303 1.491
## nameplymouth horizon tc3 5.209914 4.143729 1.257
## nameplymouth reliant -0.545007 3.754920 -0.145
## nameplymouth sapporo -0.765473 3.911418 -0.196
## nameplymouth satellite 4.364495 3.282401 1.330
## nameplymouth satellite custom 0.448326 3.526696 0.127
## nameplymouth satellite custom (sw) 3.223333 3.292706 0.979
## nameplymouth satellite sebring 1.749802 3.497976 0.500
## nameplymouth valiant 1.232906 3.073459 0.401
## nameplymouth valiant custom -0.014077 3.503255 -0.004
## nameplymouth volare 1.061859 3.474219 0.306
## nameplymouth volare custom 1.277611 3.488038 0.366
## nameplymouth volare premier v8 -1.282210 3.255780 -0.394
## namepontiac astro 0.074570 3.909875 0.019
## namepontiac catalina 5.445037 2.738420 1.988
## namepontiac catalina brougham 5.087948 3.326698 1.529
## namepontiac firebird 2.261616 3.549778 0.637
## namepontiac grand prix 6.401045 3.428059 1.867
## namepontiac grand prix lj 2.265087 3.274738 0.692
## namepontiac j2000 se hatchback 2.822025 4.099435 0.688
## namepontiac lemans v6 0.400000 3.461834 0.116
## namepontiac phoenix 3.126592 3.641875 0.859
## namepontiac phoenix lj 1.358450 3.465997 0.392
## namepontiac safari (sw) 7.162903 3.555491 2.015
## namepontiac sunbird coupe 0.108434 3.930485 0.028
## namepontiac ventura sj 1.102220 3.450690 0.319
## namerenault 12 (sw) 1.482167 3.395489 0.437
## namerenault 12tl -0.731646 3.266427 -0.224
## namerenault 5 gtl 6.648358 3.298178 2.016
## namesaab 99e 3.370839 3.531246 0.955
## namesaab 99gle -3.431693 3.516847 -0.976
## namesaab 99le 0.426670 3.063299 0.139
## namesubaru -0.233280 6.193441 -0.038
## namesubaru dl 0.927894 6.146221 0.151
## nametoyota carina -4.818346 6.613451 -0.729
## nametoyota celica gt 0.811953 6.436095 0.126
## nametoyota celica gt liftback -7.749581 6.454951 -1.201
## nametoyota corolla 0.502682 6.023789 0.083
## nametoyota corolla 1200 4.597137 6.314043 0.728
## nametoyota corolla 1600 (sw) 0.864045 6.491090 0.133
## nametoyota corolla liftback -2.358642 6.455302 -0.365
## nametoyota corolla tercel 6.264712 6.367373 0.984
## nametoyota corona -1.217090 6.101896 -0.199
## nametoyota corona hardtop -1.623374 6.517263 -0.249
## nametoyota corona liftback 0.624486 6.480690 0.096
## nametoyota corona mark ii -0.196994 6.567408 -0.030
## nametoyota cressida -2.182111 6.794927 -0.321
## nametoyota mark ii -3.168040 6.744488 -0.470
## nametoyota starlet 4.766154 6.246630 0.763
## nametoyota tercel 4.934523 6.305873 0.783
## nametoyouta corona mark ii (sw) -2.085503 6.540427 -0.319
## nametriumph tr7 coupe 6.023330 3.279325 1.837
## namevokswagen rabbit -2.827106 3.226492 -0.876
## namevolkswagen 1131 deluxe sedan 1.497675 3.578202 0.419
## namevolkswagen 411 (sw) -0.947433 3.453190 -0.274
## namevolkswagen dasher -0.858245 2.683260 -0.320
## namevolkswagen jetta 1.112715 3.228297 0.345
## namevolkswagen model 111 1.727602 3.449948 0.501
## namevolkswagen rabbit -1.074894 2.814449 -0.382
## namevolkswagen rabbit custom -1.051324 3.224945 -0.326
## namevolkswagen rabbit custom diesel 14.722011 3.409156 4.318
## namevolkswagen rabbit l 3.125355 3.244626 0.963
## namevolkswagen scirocco 0.942324 3.219495 0.293
## namevolkswagen super beetle 0.311060 3.498963 0.089
## namevolkswagen type 3 0.764483 3.649570 0.209
## namevolvo 144ea -2.766457 3.580135 -0.773
## namevolvo 145e (sw) -3.338886 3.609192 -0.925
## namevolvo 244dl -1.790859 3.478340 -0.515
## namevolvo 245 -2.848126 3.553844 -0.801
## namevolvo 264gl -5.464384 3.628736 -1.506
## namevolvo diesel 7.278640 3.656834 1.990
## namevw dasher (diesel) 16.275630 3.503824 4.645
## namevw pickup 15.324526 3.586036 4.273
## namevw rabbit 4.756880 2.789326 1.705
## namevw rabbit c (diesel) 15.164570 3.399743 4.461
## namevw rabbit custom NA NA NA
## Pr(>|t|)
## (Intercept) 0.988335
## cylinders 0.140231
## displacement 0.846109
## horsepower 0.148919
## weight 0.000829 ***
## acceleration 0.006206 **
## year 1.89e-07 ***
## origin 0.755737
## nameamc ambassador dpl 0.301870
## nameamc ambassador sst 0.306616
## nameamc concord 0.970251
## nameamc concord d/l 0.623483
## nameamc concord dl 6 0.880556
## nameamc gremlin 0.885679
## nameamc hornet 0.926382
## nameamc hornet sportabout (sw) 0.909278
## nameamc matador 0.862853
## nameamc matador (sw) 0.284233
## nameamc pacer 0.997251
## nameamc pacer d/l 0.633716
## nameamc rebel sst 0.383658
## nameamc spirit dl 0.861131
## nameaudi 100 ls 0.786702
## nameaudi 100ls 0.296773
## nameaudi 4000 0.220431
## nameaudi 5000 0.237070
## nameaudi 5000s (diesel) 0.001266 **
## nameaudi fox 0.339226
## namebmw 2002 0.545276
## namebmw 320i 0.118967
## namebuick century 0.473473
## namebuick century 350 0.507615
## namebuick century limited 0.752754
## namebuick century luxus (sw) 0.278999
## namebuick century special 0.892143
## namebuick electra 225 custom 0.113606
## namebuick estate wagon (sw) 0.429596
## namebuick lesabre custom 0.250252
## namebuick opel isuzu deluxe 0.565360
## namebuick regal sport coupe (turbo) 0.834301
## namebuick skyhawk 0.733885
## namebuick skylark 0.883024
## namebuick skylark 320 0.323008
## namebuick skylark limited 0.523630
## namecadillac eldorado 0.031592 *
## namecadillac seville 0.158454
## namecapri ii 0.957225
## namechevroelt chevelle malibu 0.734643
## namechevrolet bel air 0.292994
## namechevrolet camaro 0.798197
## namechevrolet caprice classic 0.584249
## namechevrolet cavalier 0.674558
## namechevrolet cavalier 2-door 0.141584
## namechevrolet cavalier wagon 0.926318
## namechevrolet chevelle concours (sw) 0.657161
## namechevrolet chevelle malibu 0.407277
## namechevrolet chevelle malibu classic 0.471889
## namechevrolet chevette 0.437307
## namechevrolet citation 0.799488
## namechevrolet concours 0.780185
## namechevrolet impala 0.145343
## namechevrolet malibu 0.907516
## namechevrolet malibu classic (sw) 0.643052
## namechevrolet monte carlo 0.618323
## namechevrolet monte carlo landau 0.631955
## namechevrolet monte carlo s 0.394875
## namechevrolet monza 2+2 0.567797
## namechevrolet nova 0.996373
## namechevrolet nova custom 0.867291
## namechevrolet vega 0.971468
## namechevrolet vega (sw) 0.833241
## namechevrolet vega 2300 0.185606
## namechevrolet woody 0.952237
## namechevy c10 0.609722
## namechevy c20 0.246612
## namechevy s-10 0.233181
## namechrysler cordoba 0.339636
## namechrysler lebaron medallion 0.491378
## namechrysler lebaron salon 0.210061
## namechrysler lebaron town @ country (sw) 0.529641
## namechrysler new yorker brougham 0.122924
## namechrysler newport royal 0.185688
## namedatsun 1200 0.251090
## namedatsun 200-sx 0.417638
## namedatsun 200sx 0.662913
## namedatsun 210 0.368126
## namedatsun 210 mpg 0.429714
## namedatsun 280-zx 0.390466
## namedatsun 310 0.461496
## namedatsun 310 gx 0.520470
## namedatsun 510 0.700649
## namedatsun 510 (sw) 0.641698
## namedatsun 510 hatchback 0.308465
## namedatsun 610 0.606711
## namedatsun 710 0.833331
## namedatsun 810 0.638366
## namedatsun 810 maxima 0.722736
## namedatsun b-210 0.710004
## namedatsun b210 0.607549
## namedatsun b210 gx 0.137408
## namedatsun f-10 hatchback 0.642281
## namedatsun pl510 0.875648
## namedodge aries se 0.920649
## namedodge aries wagon (sw) 0.575992
## namedodge aspen 0.946748
## namedodge aspen 6 0.916035
## namedodge aspen se 0.392579
## namedodge challenger se 0.532048
## namedodge charger 2.2 0.206030
## namedodge colt 0.680228
## namedodge colt (sw) 0.368771
## namedodge colt hardtop 0.709223
## namedodge colt hatchback custom 0.183482
## namedodge colt m/m 0.133405
## namedodge coronet brougham 0.419382
## namedodge coronet custom 0.621967
## namedodge coronet custom (sw) 0.329059
## namedodge d100 0.608647
## namedodge d200 0.179140
## namedodge dart custom 0.830727
## namedodge diplomat 0.437333
## namedodge magnum xe 0.477652
## namedodge monaco (sw) 0.123313
## namedodge monaco brougham 0.660460
## namedodge omni 0.530433
## namedodge rampage 0.939869
## namedodge st. regis 0.572613
## namefiat 124 sport coupe 0.802132
## namefiat 124 tc 0.698013
## namefiat 124b 0.209780
## namefiat 128 0.917402
## namefiat 131 0.636407
## namefiat strada custom 0.046595 *
## namefiat x1.9 0.300882
## nameford country 0.272178
## nameford country squire (sw) 0.373242
## nameford escort 2h 0.475754
## nameford escort 4w 0.360985
## nameford f108 0.649105
## nameford f250 0.144369
## nameford fairmont 0.669494
## nameford fairmont (auto) 0.500392
## nameford fairmont (man) 0.946596
## nameford fairmont 4 0.600108
## nameford fairmont futura 0.510101
## nameford fiesta 0.189646
## nameford futura 0.570117
## nameford galaxie 500 0.103177
## nameford gran torino 0.380544
## nameford gran torino (sw) 0.159315
## nameford granada 0.817981
## nameford granada ghia 0.728333
## nameford granada gl 0.376099
## nameford granada l 0.375378
## nameford ltd 0.318467
## nameford ltd landau 0.943286
## nameford maverick 0.946185
## nameford mustang 0.981211
## nameford mustang gl 0.880522
## nameford mustang ii 0.119151
## nameford mustang ii 2+2 0.772059
## nameford pinto 0.814923
## nameford pinto (sw) 0.870957
## nameford pinto runabout 0.597152
## nameford ranger 0.821651
## nameford thunderbird 0.331497
## nameford torino 0.402722
## nameford torino 500 0.570247
## namehi 1200d 0.119162
## namehonda accord 0.750849
## namehonda accord cvcc 0.748989
## namehonda accord lx 0.861613
## namehonda civic 0.862341
## namehonda civic (auto) 0.710906
## namehonda civic 1300 0.938645
## namehonda civic 1500 gl 0.105003
## namehonda civic cvcc 0.604593
## namehonda prelude 0.910907
## namemaxda glc deluxe 0.820893
## namemaxda rx3 0.086533 .
## namemazda 626 0.752875
## namemazda glc 0.019175 *
## namemazda glc 4 0.913324
## namemazda glc custom 0.711545
## namemazda glc custom l 0.512674
## namemazda glc deluxe 0.720505
## namemazda rx-4 0.308958
## namemazda rx-7 gs 0.180548
## namemazda rx2 coupe 0.208460
## namemercedes-benz 240d 0.079923 .
## namemercedes-benz 280s 0.885247
## namemercedes benz 300d 0.278317
## namemercury capri 2000 0.861658
## namemercury capri v6 0.934648
## namemercury cougar brougham 0.637471
## namemercury grand marquis 0.943496
## namemercury lynx l 0.160468
## namemercury marquis 0.338069
## namemercury marquis brougham 0.169282
## namemercury monarch 0.596819
## namemercury monarch ghia 0.453489
## namemercury zephyr 0.790476
## namemercury zephyr 6 0.537995
## namenissan stanza xe 0.668323
## nameoldsmobile cutlass ciera (diesel) 0.000492 ***
## nameoldsmobile cutlass ls 0.015743 *
## nameoldsmobile cutlass salon brougham 0.148656
## nameoldsmobile cutlass supreme 0.269004
## nameoldsmobile delta 88 royale 0.386290
## nameoldsmobile omega 0.456054
## nameoldsmobile omega brougham 0.519087
## nameoldsmobile starfire sx 0.979098
## nameoldsmobile vista cruiser 0.403391
## nameopel 1900 0.899983
## nameopel manta 0.613446
## namepeugeot 304 0.067166 .
## namepeugeot 504 0.457171
## namepeugeot 504 (sw) 0.742359
## namepeugeot 505s turbo diesel 0.302418
## namepeugeot 604sl 0.337405
## nameplymouth 'cuda 340 0.999521
## nameplymouth arrow gs 0.891698
## nameplymouth champ 0.068044 .
## nameplymouth cricket 0.365191
## nameplymouth custom suburb 0.209569
## nameplymouth duster 0.306472
## nameplymouth fury 0.461822
## nameplymouth fury gran sedan 0.294497
## nameplymouth fury iii 0.112352
## nameplymouth grand fury 0.118138
## nameplymouth horizon 0.310336
## nameplymouth horizon 4 0.329010
## nameplymouth horizon miser 0.139755
## nameplymouth horizon tc3 0.212088
## nameplymouth reliant 0.884940
## nameplymouth sapporo 0.845310
## nameplymouth satellite 0.187186
## nameplymouth satellite custom 0.899143
## nameplymouth satellite custom (sw) 0.330392
## nameplymouth satellite sebring 0.618204
## nameplymouth valiant 0.689319
## nameplymouth valiant custom 0.996803
## nameplymouth volare 0.760626
## nameplymouth volare custom 0.715064
## nameplymouth volare premier v8 0.694696
## namepontiac astro 0.984828
## namepontiac catalina 0.049987 *
## namepontiac catalina brougham 0.129871
## namepontiac firebird 0.525762
## namepontiac grand prix 0.065314 .
## namepontiac grand prix lj 0.491020
## namepontiac j2000 se hatchback 0.493079
## namepontiac lemans v6 0.908285
## namepontiac phoenix 0.393024
## namepontiac phoenix lj 0.696086
## namepontiac safari (sw) 0.047108 *
## namepontiac sunbird coupe 0.978055
## namepontiac ventura sj 0.750192
## namerenault 12 (sw) 0.663573
## namerenault 12tl 0.823303
## namerenault 5 gtl 0.046983 *
## namesaab 99e 0.342500
## namesaab 99gle 0.331939
## namesaab 99le 0.889555
## namesubaru 0.970043
## namesubaru dl 0.880357
## nametoyota carina 0.468269
## nametoyota celica gt 0.899906
## nametoyota celica gt liftback 0.233256
## nametoyota corolla 0.933690
## nametoyota corolla 1200 0.468565
## nametoyota corolla 1600 (sw) 0.894419
## nametoyota corolla liftback 0.715735
## nametoyota corolla tercel 0.327968
## nametoyota corona 0.842379
## nametoyota corona hardtop 0.803893
## nametoyota corona liftback 0.923461
## nametoyota corona mark ii 0.976141
## nametoyota cressida 0.748894
## nametoyota mark ii 0.639756
## nametoyota starlet 0.447578
## nametoyota tercel 0.436079
## nametoyouta corona mark ii (sw) 0.750612
## nametriumph tr7 coupe 0.069741 .
## namevokswagen rabbit 0.383382
## namevolkswagen 1131 deluxe sedan 0.676597
## namevolkswagen 411 (sw) 0.784470
## namevolkswagen dasher 0.749866
## namevolkswagen jetta 0.731190
## namevolkswagen model 111 0.617833
## namevolkswagen rabbit 0.703474
## namevolkswagen rabbit custom 0.745228
## namevolkswagen rabbit custom diesel 4.24e-05 ***
## namevolkswagen rabbit l 0.338159
## namevolkswagen scirocco 0.770470
## namevolkswagen super beetle 0.929370
## namevolkswagen type 3 0.834581
## namevolvo 144ea 0.441829
## namevolvo 145e (sw) 0.357530
## namevolvo 244dl 0.607987
## namevolvo 245 0.425122
## namevolvo 264gl 0.135809
## namevolvo diesel 0.049758 *
## namevw dasher (diesel) 1.23e-05 ***
## namevw pickup 5.00e-05 ***
## namevw rabbit 0.091774 .
## namevw rabbit c (diesel) 2.49e-05 ***
## namevw rabbit custom NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.272 on 85 degrees of freedom
## Multiple R-squared: 0.9816, Adjusted R-squared: 0.9153
## F-statistic: 14.8 on 306 and 85 DF, p-value: < 2.2e-16
plot(fit)
## Warning: not plotting observations with leverage one:
## 2, 3, 4, 5, 10, 11, 12, 13, 15, 20, 23, 24, 26, 27, 28, 29, 31, 34, 36, 39, 42, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 67, 68, 69, 70, 71, 73, 75, 76, 77, 79, 80, 81, 82, 83, 84, 85, 89, 90, 93, 94, 95, 96, 98, 102, 104, 105, 110, 111, 113, 114, 115, 116, 120, 121, 124, 128, 134, 136, 137, 140, 147, 150, 151, 153, 156, 157, 160, 162, 163, 164, 165, 169, 175, 178, 181, 183, 185, 187, 195, 198, 199, 200, 201, 203, 206, 207, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 224, 226, 227, 228, 230, 231, 232, 233, 234, 235, 237, 240, 241, 242, 243, 244, 245, 246, 249, 250, 251, 253, 254, 255, 257, 258, 260, 262, 263, 264, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 286, 287, 290, 291, 292, 293, 294, 295, 296, 297, 300, 301, 303, 304, 306, 309, 311, 313, 316, 317, 319, 321, 324, 325, 326, 327, 328, 330, 331, 332, 333, 337, 340, 341, 342, 344, 345, 346, 347, 348, 349, 350, 351, 353, 356, 357, 358, 360, 361, 362, 363, 364, 365, 366, 367, 369, 371, 372, 373, 374, 375, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392
## Warning: not plotting observations with leverage one:
## 2, 3, 4, 5, 10, 11, 12, 13, 15, 20, 23, 24, 26, 27, 28, 29, 31, 34, 36, 39, 42, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 67, 68, 69, 70, 71, 73, 75, 76, 77, 79, 80, 81, 82, 83, 84, 85, 89, 90, 93, 94, 95, 96, 98, 102, 104, 105, 110, 111, 113, 114, 115, 116, 120, 121, 124, 128, 134, 136, 137, 140, 147, 150, 151, 153, 156, 157, 160, 162, 163, 164, 165, 169, 175, 178, 181, 183, 185, 187, 195, 198, 199, 200, 201, 203, 206, 207, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 224, 226, 227, 228, 230, 231, 232, 233, 234, 235, 237, 240, 241, 242, 243, 244, 245, 246, 249, 250, 251, 253, 254, 255, 257, 258, 260, 262, 263, 264, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 286, 287, 290, 291, 292, 293, 294, 295, 296, 297, 300, 301, 303, 304, 306, 309, 311, 313, 316, 317, 319, 321, 324, 325, 326, 327, 328, 330, 331, 332, 333, 337, 340, 341, 342, 344, 345, 346, 347, 348, 349, 350, 351, 353, 356, 357, 358, 360, 361, 362, 363, 364, 365, 366, 367, 369, 371, 372, 373, 374, 375, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
# Use update to add some interaction terms:
summary(update(fit, . ~ . + horsepower:weight))
##
## Call:
## lm(formula = mpg ~ cylinders + displacement + horsepower + weight +
## acceleration + year + origin + name + horsepower:weight,
## data = Auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.842 0.000 0.000 0.000 5.842
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) 1.216e+01 1.258e+01 0.966
## cylinders -7.575e-01 5.845e-01 -1.296
## displacement -1.222e-02 1.544e-02 -0.791
## horsepower -1.649e-01 4.570e-02 -3.608
## weight -8.303e-03 1.675e-03 -4.956
## acceleration -4.750e-01 1.621e-01 -2.931
## year 6.758e-01 1.066e-01 6.338
## origin -4.836e-01 4.044e+00 -0.120
## nameamc ambassador dpl 3.266e+00 3.066e+00 1.065
## nameamc ambassador sst 3.850e+00 3.093e+00 1.245
## nameamc concord 5.893e-01 3.101e+00 0.190
## nameamc concord d/l -6.110e-01 3.249e+00 -0.188
## nameamc concord dl 6 6.912e-01 3.340e+00 0.207
## nameamc gremlin 8.350e-01 2.820e+00 0.296
## nameamc hornet 1.503e+00 2.767e+00 0.543
## nameamc hornet sportabout (sw) 1.414e+00 3.376e+00 0.419
## nameamc matador 1.538e+00 2.540e+00 0.605
## nameamc matador (sw) 2.653e+00 2.737e+00 0.969
## nameamc pacer 1.381e+00 3.349e+00 0.412
## nameamc pacer d/l -2.779e-02 3.359e+00 -0.008
## nameamc rebel sst 3.970e+00 3.119e+00 1.273
## nameamc spirit dl 3.017e-01 3.840e+00 0.079
## nameaudi 100 ls 2.500e+00 3.291e+00 0.760
## nameaudi 100ls -1.520e+00 2.860e+00 -0.531
## nameaudi 4000 4.579e+00 3.069e+00 1.492
## nameaudi 5000 -2.502e+00 3.295e+00 -0.759
## nameaudi 5000s (diesel) 1.305e+01 3.327e+00 3.922
## nameaudi fox 4.189e+00 3.158e+00 1.326
## namebmw 2002 4.460e+00 3.316e+00 1.345
## namebmw 320i -3.502e+00 3.237e+00 -1.082
## namebuick century 2.936e+00 2.912e+00 1.008
## namebuick century 350 1.081e+00 3.088e+00 0.350
## namebuick century limited 1.355e+00 3.451e+00 0.392
## namebuick century luxus (sw) 2.504e+00 3.229e+00 0.775
## namebuick century special 1.463e+00 3.289e+00 0.445
## namebuick electra 225 custom -1.027e+00 3.831e+00 -0.268
## namebuick estate wagon (sw) 3.611e+00 2.752e+00 1.312
## namebuick lesabre custom 2.867e+00 3.179e+00 0.902
## namebuick opel isuzu deluxe 1.501e+00 3.873e+00 0.388
## namebuick regal sport coupe (turbo) -1.165e+00 3.472e+00 -0.336
## namebuick skyhawk 2.375e+00 3.282e+00 0.724
## namebuick skylark 9.796e-01 3.114e+00 0.315
## namebuick skylark 320 3.938e+00 3.068e+00 1.284
## namebuick skylark limited 2.664e+00 3.727e+00 0.715
## namecadillac eldorado 8.929e+00 3.272e+00 2.729
## namecadillac seville 2.280e+00 3.207e+00 0.711
## namecapri ii 3.060e-01 3.754e+00 0.082
## namechevroelt chevelle malibu 2.405e+00 3.328e+00 0.723
## namechevrolet bel air 3.195e+00 3.150e+00 1.014
## namechevrolet camaro 1.114e+00 3.746e+00 0.297
## namechevrolet caprice classic 1.755e+00 2.557e+00 0.686
## namechevrolet cavalier 1.068e+00 3.842e+00 0.278
## namechevrolet cavalier 2-door 5.345e+00 3.865e+00 1.383
## namechevrolet cavalier wagon -2.467e-01 3.845e+00 -0.064
## namechevrolet chevelle concours (sw) 2.077e+00 3.182e+00 0.653
## namechevrolet chevelle malibu 4.087e+00 2.884e+00 1.417
## namechevrolet chevelle malibu classic 2.732e+00 2.814e+00 0.971
## namechevrolet chevette 1.007e+00 3.427e+00 0.294
## namechevrolet citation 1.115e+00 3.097e+00 0.360
## namechevrolet concours 1.786e-01 3.264e+00 0.055
## namechevrolet impala 2.444e+00 2.545e+00 0.960
## namechevrolet malibu 1.013e+00 2.755e+00 0.368
## namechevrolet malibu classic (sw) 2.084e+00 3.186e+00 0.654
## namechevrolet monte carlo 3.600e+00 3.362e+00 1.071
## namechevrolet monte carlo landau 1.231e+00 2.674e+00 0.460
## namechevrolet monte carlo s 3.292e+00 3.115e+00 1.057
## namechevrolet monza 2+2 3.221e+00 3.251e+00 0.991
## namechevrolet nova 1.443e+00 2.802e+00 0.515
## namechevrolet nova custom 9.935e-01 3.324e+00 0.299
## namechevrolet vega -2.054e-01 3.260e+00 -0.063
## namechevrolet vega (sw) 6.456e-01 3.739e+00 0.173
## namechevrolet vega 2300 5.472e+00 3.758e+00 1.456
## namechevrolet woody -1.439e+00 3.844e+00 -0.374
## namechevy c10 -1.269e+00 3.112e+00 -0.408
## namechevy c20 2.843e-01 3.752e+00 0.076
## namechevy s-10 4.286e+00 3.797e+00 1.129
## namechrysler cordoba 1.046e+00 3.170e+00 0.330
## namechrysler lebaron medallion -2.686e+00 3.816e+00 -0.704
## namechrysler lebaron salon -3.298e+00 3.404e+00 -0.969
## namechrysler lebaron town @ country (sw) 2.543e+00 3.123e+00 0.814
## namechrysler new yorker brougham 4.014e-01 3.518e+00 0.114
## namechrysler newport royal 2.094e+00 3.184e+00 0.658
## namedatsun 1200 8.835e+00 6.106e+00 1.447
## namedatsun 200-sx -1.856e+00 6.151e+00 -0.302
## namedatsun 200sx 6.115e+00 6.163e+00 0.992
## namedatsun 210 7.243e+00 5.873e+00 1.233
## namedatsun 210 mpg 6.525e+00 6.052e+00 1.078
## namedatsun 280-zx 9.634e+00 6.548e+00 1.471
## namedatsun 310 6.232e+00 5.949e+00 1.048
## namedatsun 310 gx 5.674e+00 5.939e+00 0.955
## namedatsun 510 9.075e-01 6.129e+00 0.148
## namedatsun 510 (sw) 6.195e+00 6.264e+00 0.989
## namedatsun 510 hatchback 9.752e+00 6.116e+00 1.594
## namedatsun 610 -5.370e-02 6.262e+00 -0.009
## namedatsun 710 3.867e+00 6.005e+00 0.644
## namedatsun 810 2.984e-01 6.524e+00 0.046
## namedatsun 810 maxima 8.912e-01 6.557e+00 0.136
## namedatsun b-210 4.251e+00 6.031e+00 0.705
## namedatsun b210 5.018e+00 6.125e+00 0.819
## namedatsun b210 gx 1.149e+01 6.076e+00 1.891
## namedatsun f-10 hatchback 4.740e+00 6.002e+00 0.790
## namedatsun pl510 4.024e+00 5.977e+00 0.673
## namedodge aries se 3.927e-02 3.819e+00 0.010
## namedodge aries wagon (sw) -2.103e+00 3.798e+00 -0.554
## namedodge aspen 6.723e-01 2.929e+00 0.230
## namedodge aspen 6 1.132e+00 3.281e+00 0.345
## namedodge aspen se 4.039e+00 3.315e+00 1.219
## namedodge challenger se 3.527e+00 3.139e+00 1.124
## namedodge charger 2.2 4.877e+00 3.938e+00 1.239
## namedodge colt 8.325e-01 3.391e+00 0.245
## namedodge colt (sw) 2.861e+00 3.894e+00 0.735
## namedodge colt hardtop 6.174e-01 3.852e+00 0.160
## namedodge colt hatchback custom 4.319e+00 3.984e+00 1.084
## namedodge colt m/m 5.202e+00 3.890e+00 1.337
## namedodge coronet brougham 2.048e+00 3.113e+00 0.658
## namedodge coronet custom 2.027e+00 3.070e+00 0.660
## namedodge coronet custom (sw) 2.162e+00 3.196e+00 0.676
## namedodge d100 -1.331e+00 3.076e+00 -0.433
## namedodge d200 5.028e-01 3.792e+00 0.133
## namedodge dart custom 5.714e-01 3.108e+00 0.184
## namedodge diplomat 3.227e+00 3.107e+00 1.038
## namedodge magnum xe 2.388e+00 3.111e+00 0.768
## namedodge monaco (sw) 1.679e+00 3.467e+00 0.484
## namedodge monaco brougham 1.157e+00 3.106e+00 0.372
## namedodge omni 1.525e+00 3.914e+00 0.390
## namedodge rampage -1.441e-01 4.012e+00 -0.036
## namedodge st. regis 2.512e+00 3.133e+00 0.802
## namefiat 124 sport coupe 2.095e+00 3.193e+00 0.656
## namefiat 124 tc -2.088e-01 3.133e+00 -0.067
## namefiat 124b 4.863e+00 3.171e+00 1.534
## namefiat 128 -6.056e-01 2.752e+00 -0.220
## namefiat 131 2.830e+00 3.152e+00 0.898
## namefiat strada custom 6.694e+00 3.044e+00 2.199
## namefiat x1.9 3.383e+00 3.105e+00 1.090
## nameford country 1.527e+00 3.327e+00 0.459
## nameford country squire (sw) 1.830e+00 2.740e+00 0.668
## nameford escort 2h 1.484e+00 3.852e+00 0.385
## nameford escort 4w 1.985e+00 3.980e+00 0.499
## nameford f108 -8.535e-01 3.124e+00 -0.273
## nameford f250 -2.986e-02 3.805e+00 -0.008
## nameford fairmont 1.664e+00 3.724e+00 0.447
## nameford fairmont (auto) -1.712e+00 3.386e+00 -0.506
## nameford fairmont (man) -2.545e-01 3.759e+00 -0.068
## nameford fairmont 4 -2.048e+00 3.727e+00 -0.550
## nameford fairmont futura -2.743e+00 3.791e+00 -0.723
## nameford fiesta 3.585e+00 4.038e+00 0.888
## nameford futura -5.137e-01 3.204e+00 -0.160
## nameford galaxie 500 3.805e+00 2.555e+00 1.489
## nameford gran torino 2.314e+00 2.567e+00 0.901
## nameford gran torino (sw) 3.586e+00 2.873e+00 1.248
## nameford granada 2.240e+00 3.312e+00 0.676
## nameford granada ghia 3.293e+00 3.470e+00 0.949
## nameford granada gl -2.568e+00 3.380e+00 -0.760
## nameford granada l -2.142e+00 3.402e+00 -0.630
## nameford ltd 2.005e+00 2.773e+00 0.723
## nameford ltd landau 5.440e-01 3.151e+00 0.173
## nameford maverick 1.486e+00 2.866e+00 0.519
## nameford mustang 1.729e+00 3.512e+00 0.492
## nameford mustang gl -7.359e-01 3.811e+00 -0.193
## nameford mustang ii -3.604e+00 3.218e+00 -1.120
## nameford mustang ii 2+2 1.220e+00 3.741e+00 0.326
## nameford pinto -8.712e-01 3.118e+00 -0.279
## nameford pinto (sw) -8.519e-01 3.781e+00 -0.225
## nameford pinto runabout -2.403e+00 3.776e+00 -0.637
## nameford ranger 2.965e-01 3.801e+00 0.078
## nameford thunderbird 2.791e+00 3.118e+00 0.895
## nameford torino 4.073e+00 3.172e+00 1.284
## nameford torino 500 3.951e+00 3.489e+00 1.132
## namehi 1200d 1.103e+00 4.067e+00 0.271
## namehonda accord 4.371e+00 5.823e+00 0.751
## namehonda accord cvcc 4.084e+00 6.103e+00 0.669
## namehonda accord lx 9.940e-01 6.029e+00 0.165
## namehonda civic 3.086e+00 5.753e+00 0.536
## namehonda civic (auto) -7.272e-01 5.920e+00 -0.123
## namehonda civic 1300 1.361e+00 5.886e+00 0.231
## namehonda civic 1500 gl 1.169e+01 5.871e+00 1.992
## namehonda civic cvcc 4.283e+00 5.794e+00 0.739
## namehonda prelude 3.139e+00 5.977e+00 0.525
## namemaxda glc deluxe 2.993e+00 5.918e+00 0.506
## namemaxda rx3 -8.105e+00 5.977e+00 -1.356
## namemazda 626 4.965e+00 6.001e+00 0.827
## namemazda glc 1.685e+01 6.014e+00 2.802
## namemazda glc 4 2.382e+00 5.941e+00 0.401
## namemazda glc custom -7.157e-01 5.990e+00 -0.119
## namemazda glc custom l 5.868e+00 6.019e+00 0.975
## namemazda glc deluxe 3.269e+00 6.040e+00 0.541
## namemazda rx-4 -3.505e+00 6.159e+00 -0.569
## namemazda rx-7 gs -5.653e+00 5.963e+00 -0.948
## namemazda rx2 coupe -5.038e+00 6.083e+00 -0.828
## namemercedes-benz 240d 8.742e+00 3.496e+00 2.500
## namemercedes-benz 280s 6.101e-01 3.768e+00 0.162
## namemercedes benz 300d 6.909e+00 3.610e+00 1.914
## namemercury capri 2000 -9.431e-01 3.849e+00 -0.245
## namemercury capri v6 6.925e-02 3.489e+00 0.020
## namemercury cougar brougham 1.617e+00 3.176e+00 0.509
## namemercury grand marquis 5.838e-01 3.163e+00 0.185
## namemercury lynx l 4.252e+00 3.948e+00 1.077
## namemercury marquis -7.615e-01 3.381e+00 -0.225
## namemercury marquis brougham 8.871e-02 3.520e+00 0.025
## namemercury monarch 1.381e-01 3.529e+00 0.039
## namemercury monarch ghia 3.233e+00 3.124e+00 1.035
## namemercury zephyr -1.899e-01 3.365e+00 -0.056
## namemercury zephyr 6 -1.530e+00 3.362e+00 -0.455
## namenissan stanza xe 5.670e+00 6.036e+00 0.939
## nameoldsmobile cutlass ciera (diesel) 1.495e+01 3.529e+00 4.235
## nameoldsmobile cutlass ls 1.126e+01 3.523e+00 3.196
## nameoldsmobile cutlass salon brougham 5.696e+00 2.945e+00 1.934
## nameoldsmobile cutlass supreme 4.524e+00 3.283e+00 1.378
## nameoldsmobile delta 88 royale 1.669e+00 3.165e+00 0.527
## nameoldsmobile omega -2.214e+00 3.049e+00 -0.726
## nameoldsmobile omega brougham 2.780e+00 3.486e+00 0.798
## nameoldsmobile starfire sx 1.110e-01 3.690e+00 0.030
## nameoldsmobile vista cruiser 8.055e-02 3.260e+00 0.025
## nameopel 1900 1.713e+00 2.758e+00 0.621
## nameopel manta -4.976e-01 2.742e+00 -0.181
## namepeugeot 304 6.710e+00 3.288e+00 2.041
## namepeugeot 504 4.068e+00 2.904e+00 1.401
## namepeugeot 504 (sw) 3.036e+00 3.496e+00 0.868
## namepeugeot 505s turbo diesel 5.700e+00 3.423e+00 1.665
## namepeugeot 604sl -2.585e+00 3.673e+00 -0.704
## nameplymouth 'cuda 340 9.794e-01 3.142e+00 0.312
## nameplymouth arrow gs -7.350e-01 3.806e+00 -0.193
## nameplymouth champ 5.503e+00 4.050e+00 1.359
## nameplymouth cricket 2.212e+00 3.889e+00 0.569
## nameplymouth custom suburb 1.866e+00 3.249e+00 0.574
## nameplymouth duster 3.971e+00 2.858e+00 1.389
## nameplymouth fury 3.854e+00 3.362e+00 1.146
## nameplymouth fury gran sedan 2.881e+00 3.138e+00 0.918
## nameplymouth fury iii 3.232e+00 2.552e+00 1.267
## nameplymouth grand fury 4.042e+00 3.206e+00 1.261
## nameplymouth horizon 3.018e+00 3.999e+00 0.755
## nameplymouth horizon 4 2.555e+00 3.985e+00 0.641
## nameplymouth horizon miser 4.577e+00 4.027e+00 1.136
## nameplymouth horizon tc3 3.858e+00 3.935e+00 0.981
## nameplymouth reliant -9.083e-01 3.549e+00 -0.256
## nameplymouth sapporo -3.955e-01 3.696e+00 -0.107
## nameplymouth satellite 5.672e+00 3.125e+00 1.815
## nameplymouth satellite custom 1.607e+00 3.349e+00 0.480
## nameplymouth satellite custom (sw) 3.005e+00 3.111e+00 0.966
## nameplymouth satellite sebring 2.727e+00 3.317e+00 0.822
## nameplymouth valiant 2.371e+00 2.923e+00 0.811
## nameplymouth valiant custom 1.194e+00 3.329e+00 0.359
## nameplymouth volare 2.049e+00 3.295e+00 0.622
## nameplymouth volare custom 2.278e+00 3.308e+00 0.688
## nameplymouth volare premier v8 -1.348e+00 3.076e+00 -0.438
## namepontiac astro 4.933e-03 3.693e+00 0.001
## namepontiac catalina 3.206e+00 2.672e+00 1.200
## namepontiac catalina brougham 3.662e+00 3.171e+00 1.155
## namepontiac firebird 3.936e+00 3.390e+00 1.161
## namepontiac grand prix 2.319e+00 3.459e+00 0.670
## namepontiac grand prix lj 1.128e+00 3.112e+00 0.363
## namepontiac j2000 se hatchback 2.147e+00 3.878e+00 0.554
## namepontiac lemans v6 1.254e+00 3.280e+00 0.382
## namepontiac phoenix 3.200e+00 3.440e+00 0.930
## namepontiac phoenix lj 2.278e+00 3.286e+00 0.693
## namepontiac safari (sw) 3.514e+00 3.530e+00 0.995
## namepontiac sunbird coupe 3.324e-01 3.713e+00 0.090
## namepontiac ventura sj 2.216e+00 3.276e+00 0.676
## namerenault 12 (sw) 2.072e+00 3.212e+00 0.645
## namerenault 12tl 2.227e-01 3.099e+00 0.072
## namerenault 5 gtl 5.843e+00 3.125e+00 1.870
## namesaab 99e 4.963e+00 3.369e+00 1.473
## namesaab 99gle -1.753e+00 3.360e+00 -0.522
## namesaab 99le 2.347e+00 2.950e+00 0.796
## namesubaru 2.325e+00 5.900e+00 0.394
## namesubaru dl 2.871e+00 5.835e+00 0.492
## nametoyota carina -1.845e+00 6.310e+00 -0.292
## nametoyota celica gt 4.412e+00 6.174e+00 0.715
## nametoyota celica gt liftback -4.175e+00 6.190e+00 -0.674
## nametoyota corolla 2.958e+00 5.737e+00 0.516
## nametoyota corolla 1200 5.936e+00 5.978e+00 0.993
## nametoyota corolla 1600 (sw) 3.822e+00 6.195e+00 0.617
## nametoyota corolla liftback 1.078e-01 6.142e+00 0.018
## nametoyota corolla tercel 7.617e+00 6.028e+00 1.263
## nametoyota corona 1.607e+00 5.825e+00 0.276
## nametoyota corona hardtop 1.839e+00 6.242e+00 0.295
## nametoyota corona liftback 4.095e+00 6.209e+00 0.660
## nametoyota corona mark ii 3.357e+00 6.294e+00 0.533
## nametoyota cressida 1.524e+00 6.513e+00 0.234
## nametoyota mark ii 6.397e-01 6.471e+00 0.099
## nametoyota starlet 5.506e+00 5.905e+00 0.932
## nametoyota tercel 6.458e+00 5.974e+00 1.081
## nametoyouta corona mark ii (sw) 1.546e+00 6.272e+00 0.246
## nametriumph tr7 coupe 7.406e+00 3.125e+00 2.370
## namevokswagen rabbit -3.365e+00 3.052e+00 -1.103
## namevolkswagen 1131 deluxe sedan 7.066e-01 3.388e+00 0.209
## namevolkswagen 411 (sw) 5.232e-01 3.291e+00 0.159
## namevolkswagen dasher -4.883e-01 2.537e+00 -0.192
## namevolkswagen jetta 1.661e+00 3.054e+00 0.544
## namevolkswagen model 111 1.535e+00 3.259e+00 0.471
## namevolkswagen rabbit -9.320e-01 2.659e+00 -0.351
## namevolkswagen rabbit custom -5.531e-01 3.050e+00 -0.181
## namevolkswagen rabbit custom diesel 1.391e+01 3.230e+00 4.306
## namevolkswagen rabbit l 3.421e+00 3.066e+00 1.116
## namevolkswagen scirocco 1.048e+00 3.041e+00 0.345
## namevolkswagen super beetle -3.521e-01 3.311e+00 -0.106
## namevolkswagen type 3 1.002e+00 3.448e+00 0.290
## namevolvo 144ea -9.488e-01 3.425e+00 -0.277
## namevolvo 145e (sw) -1.516e+00 3.452e+00 -0.439
## namevolvo 244dl -6.691e-02 3.326e+00 -0.020
## namevolvo 245 -1.082e+00 3.398e+00 -0.319
## namevolvo 264gl -3.812e+00 3.463e+00 -1.101
## namevolvo diesel 9.013e+00 3.493e+00 2.581
## namevw dasher (diesel) 1.609e+01 3.310e+00 4.862
## namevw pickup 1.487e+01 3.390e+00 4.386
## namevw rabbit 5.057e+00 2.636e+00 1.918
## namevw rabbit c (diesel) 1.448e+01 3.218e+00 4.498
## namevw rabbit custom NA NA NA
## horsepower:weight 4.225e-05 1.259e-05 3.355
## Pr(>|t|)
## (Intercept) 0.336678
## cylinders 0.198530
## displacement 0.431022
## horsepower 0.000523 ***
## weight 3.68e-06 ***
## acceleration 0.004349 **
## year 1.11e-08 ***
## origin 0.905098
## nameamc ambassador dpl 0.289804
## nameamc ambassador sst 0.216699
## nameamc concord 0.849727
## nameamc concord d/l 0.851302
## nameamc concord dl 6 0.836548
## nameamc gremlin 0.767847
## nameamc hornet 0.588420
## nameamc hornet sportabout (sw) 0.676319
## nameamc matador 0.546599
## nameamc matador (sw) 0.335288
## nameamc pacer 0.681065
## nameamc pacer d/l 0.993418
## nameamc rebel sst 0.206680
## nameamc spirit dl 0.937575
## nameaudi 100 ls 0.449637
## nameaudi 100ls 0.596484
## nameaudi 4000 0.139512
## nameaudi 5000 0.449787
## nameaudi 5000s (diesel) 0.000178 ***
## nameaudi fox 0.188317
## namebmw 2002 0.182271
## namebmw 320i 0.282441
## namebuick century 0.316172
## namebuick century 350 0.727051
## namebuick century limited 0.695685
## namebuick century luxus (sw) 0.440301
## namebuick century special 0.657533
## namebuick electra 225 custom 0.789297
## namebuick estate wagon (sw) 0.193051
## namebuick lesabre custom 0.369849
## namebuick opel isuzu deluxe 0.699296
## namebuick regal sport coupe (turbo) 0.737982
## namebuick skyhawk 0.471303
## namebuick skylark 0.753835
## namebuick skylark 320 0.202804
## namebuick skylark limited 0.476742
## namecadillac eldorado 0.007737 **
## namecadillac seville 0.479072
## namecapri ii 0.935235
## namechevroelt chevelle malibu 0.471947
## namechevrolet bel air 0.313366
## namechevrolet camaro 0.766878
## namechevrolet caprice classic 0.494427
## namechevrolet cavalier 0.781761
## namechevrolet cavalier 2-door 0.170318
## namechevrolet cavalier wagon 0.948989
## namechevrolet chevelle concours (sw) 0.515748
## namechevrolet chevelle malibu 0.160104
## namechevrolet chevelle malibu classic 0.334446
## namechevrolet chevette 0.769531
## namechevrolet citation 0.719784
## namechevrolet concours 0.956502
## namechevrolet impala 0.339794
## namechevrolet malibu 0.713923
## namechevrolet malibu classic (sw) 0.514889
## namechevrolet monte carlo 0.287313
## namechevrolet monte carlo landau 0.646515
## namechevrolet monte carlo s 0.293610
## namechevrolet monza 2+2 0.324632
## namechevrolet nova 0.608045
## namechevrolet nova custom 0.765758
## namechevrolet vega 0.949924
## namechevrolet vega (sw) 0.863327
## namechevrolet vega 2300 0.149164
## namechevrolet woody 0.709061
## namechevy c10 0.684566
## namechevy c20 0.939784
## namechevy s-10 0.262226
## namechrysler cordoba 0.742301
## namechrysler lebaron medallion 0.483464
## namechrysler lebaron salon 0.335350
## namechrysler lebaron town @ country (sw) 0.417768
## namechrysler new yorker brougham 0.909430
## namechrysler newport royal 0.512530
## namedatsun 1200 0.151647
## namedatsun 200-sx 0.763602
## namedatsun 200sx 0.323966
## namedatsun 210 0.220900
## namedatsun 210 mpg 0.284061
## namedatsun 280-zx 0.144925
## namedatsun 310 0.297831
## namedatsun 310 gx 0.342092
## namedatsun 510 0.882643
## namedatsun 510 (sw) 0.325571
## namedatsun 510 hatchback 0.114603
## namedatsun 610 0.993179
## namedatsun 710 0.521429
## namedatsun 810 0.963623
## namedatsun 810 maxima 0.892205
## namedatsun b-210 0.482865
## namedatsun b210 0.414958
## namedatsun b210 gx 0.062126 .
## namedatsun f-10 hatchback 0.431954
## namedatsun pl510 0.502681
## namedodge aries se 0.991820
## namedodge aries wagon (sw) 0.581168
## namedodge aspen 0.819016
## namedodge aspen 6 0.731054
## namedodge aspen se 0.226434
## namedodge challenger se 0.264319
## namedodge charger 2.2 0.218968
## namedodge colt 0.806699
## namedodge colt (sw) 0.464637
## namedodge colt hardtop 0.873042
## namedodge colt hatchback custom 0.281421
## namedodge colt m/m 0.184747
## namedodge coronet brougham 0.512395
## namedodge coronet custom 0.510924
## namedodge coronet custom (sw) 0.500617
## namedodge d100 0.666250
## namedodge d200 0.894848
## namedodge dart custom 0.854554
## namedodge diplomat 0.302062
## namedodge magnum xe 0.444909
## namedodge monaco (sw) 0.629503
## namedodge monaco brougham 0.710469
## namedodge omni 0.697721
## namedodge rampage 0.971439
## namedodge st. regis 0.424809
## namefiat 124 sport coupe 0.513506
## namefiat 124 tc 0.947026
## namefiat 124b 0.128896
## namefiat 128 0.826340
## namefiat 131 0.371879
## namefiat strada custom 0.030601 *
## namefiat x1.9 0.278947
## nameford country 0.647588
## nameford country squire (sw) 0.506138
## nameford escort 2h 0.701006
## nameford escort 4w 0.619213
## nameford f108 0.785374
## nameford f250 0.993758
## nameford fairmont 0.656118
## nameford fairmont (auto) 0.614397
## nameford fairmont (man) 0.946181
## nameford fairmont 4 0.584066
## nameford fairmont futura 0.471401
## nameford fiesta 0.377192
## nameford futura 0.872993
## nameford galaxie 500 0.140130
## nameford gran torino 0.369919
## nameford gran torino (sw) 0.215435
## nameford granada 0.500583
## nameford granada ghia 0.345433
## nameford granada gl 0.449585
## nameford granada l 0.530723
## nameford ltd 0.471721
## nameford ltd landau 0.863347
## nameford maverick 0.605400
## nameford mustang 0.623831
## nameford mustang gl 0.847356
## nameford mustang ii 0.265987
## nameford mustang ii 2+2 0.745084
## nameford pinto 0.780646
## nameford pinto (sw) 0.822280
## nameford pinto runabout 0.526147
## nameford ranger 0.938009
## nameford thunderbird 0.373131
## nameford torino 0.202666
## nameford torino 500 0.260743
## namehi 1200d 0.786899
## namehonda accord 0.454987
## namehonda accord cvcc 0.505275
## namehonda accord lx 0.869446
## namehonda civic 0.593032
## namehonda civic (auto) 0.902522
## namehonda civic 1300 0.817701
## namehonda civic 1500 gl 0.049673 *
## namehonda civic cvcc 0.461839
## namehonda prelude 0.600810
## namemaxda glc deluxe 0.614282
## namemaxda rx3 0.178701
## namemazda 626 0.410348
## namemazda glc 0.006310 **
## namemazda glc 4 0.689528
## namemazda glc custom 0.905176
## namemazda glc custom l 0.332429
## namemazda glc deluxe 0.589786
## namemazda rx-4 0.570784
## namemazda rx-7 gs 0.345863
## namemazda rx2 coupe 0.409932
## namemercedes-benz 240d 0.014355 *
## namemercedes-benz 280s 0.871755
## namemercedes benz 300d 0.059058 .
## namemercury capri 2000 0.807042
## namemercury capri v6 0.984211
## namemercury cougar brougham 0.611867
## namemercury grand marquis 0.853983
## namemercury lynx l 0.284530
## namemercury marquis 0.822368
## namemercury marquis brougham 0.979952
## namemercury monarch 0.968883
## namemercury monarch ghia 0.303601
## namemercury zephyr 0.955133
## namemercury zephyr 6 0.650216
## namenissan stanza xe 0.350198
## nameoldsmobile cutlass ciera (diesel) 5.82e-05 ***
## nameoldsmobile cutlass ls 0.001963 **
## nameoldsmobile cutlass salon brougham 0.056439 .
## nameoldsmobile cutlass supreme 0.171784
## nameoldsmobile delta 88 royale 0.599291
## nameoldsmobile omega 0.469627
## nameoldsmobile omega brougham 0.427317
## nameoldsmobile starfire sx 0.976062
## nameoldsmobile vista cruiser 0.980347
## nameopel 1900 0.536377
## nameopel manta 0.856415
## namepeugeot 304 0.044428 *
## namepeugeot 504 0.164937
## namepeugeot 504 (sw) 0.387720
## namepeugeot 505s turbo diesel 0.099630 .
## namepeugeot 604sl 0.483459
## nameplymouth 'cuda 340 0.756058
## nameplymouth arrow gs 0.847325
## nameplymouth champ 0.177875
## nameplymouth cricket 0.571087
## nameplymouth custom suburb 0.567295
## nameplymouth duster 0.168415
## nameplymouth fury 0.254873
## nameplymouth fury gran sedan 0.361299
## nameplymouth fury iii 0.208785
## nameplymouth grand fury 0.210886
## nameplymouth horizon 0.452539
## nameplymouth horizon 4 0.523114
## nameplymouth horizon miser 0.259008
## nameplymouth horizon tc3 0.329627
## nameplymouth reliant 0.798602
## nameplymouth sapporo 0.915055
## nameplymouth satellite 0.073110 .
## nameplymouth satellite custom 0.632700
## nameplymouth satellite custom (sw) 0.336930
## nameplymouth satellite sebring 0.413372
## nameplymouth valiant 0.419535
## nameplymouth valiant custom 0.720651
## nameplymouth volare 0.535793
## nameplymouth volare custom 0.493091
## nameplymouth volare premier v8 0.662311
## namepontiac astro 0.998937
## namepontiac catalina 0.233547
## namepontiac catalina brougham 0.251407
## namepontiac firebird 0.248881
## namepontiac grand prix 0.504425
## namepontiac grand prix lj 0.717787
## namepontiac j2000 se hatchback 0.581262
## namepontiac lemans v6 0.703307
## namepontiac phoenix 0.354960
## namepontiac phoenix lj 0.490052
## namepontiac safari (sw) 0.322382
## namepontiac sunbird coupe 0.928885
## namepontiac ventura sj 0.500634
## namerenault 12 (sw) 0.520771
## namerenault 12tl 0.942877
## namerenault 5 gtl 0.064980 .
## namesaab 99e 0.144451
## namesaab 99gle 0.603147
## namesaab 99le 0.428541
## namesubaru 0.694519
## namesubaru dl 0.623946
## nametoyota carina 0.770666
## nametoyota celica gt 0.476813
## nametoyota celica gt liftback 0.501855
## nametoyota corolla 0.607535
## nametoyota corolla 1200 0.323576
## nametoyota corolla 1600 (sw) 0.538880
## nametoyota corolla liftback 0.986041
## nametoyota corolla tercel 0.209906
## nametoyota corona 0.783331
## nametoyota corona hardtop 0.768975
## nametoyota corona liftback 0.511364
## nametoyota corona mark ii 0.595193
## nametoyota cressida 0.815608
## nametoyota mark ii 0.921489
## nametoyota starlet 0.353755
## nametoyota tercel 0.282790
## nametoyouta corona mark ii (sw) 0.805937
## nametriumph tr7 coupe 0.020079 *
## namevokswagen rabbit 0.273385
## namevolkswagen 1131 deluxe sedan 0.835316
## namevolkswagen 411 (sw) 0.874067
## namevolkswagen dasher 0.847848
## namevolkswagen jetta 0.587921
## namevolkswagen model 111 0.638805
## namevolkswagen rabbit 0.726840
## namevolkswagen rabbit custom 0.856528
## namevolkswagen rabbit custom diesel 4.49e-05 ***
## namevolkswagen rabbit l 0.267754
## namevolkswagen scirocco 0.731268
## namevolkswagen super beetle 0.915566
## namevolkswagen type 3 0.772169
## namevolvo 144ea 0.782449
## namevolvo 145e (sw) 0.661732
## namevolvo 244dl 0.983997
## namevolvo 245 0.750882
## namevolvo 264gl 0.274103
## namevolvo diesel 0.011602 *
## namevw dasher (diesel) 5.35e-06 ***
## namevw pickup 3.33e-05 ***
## namevw rabbit 0.058472 .
## namevw rabbit c (diesel) 2.18e-05 ***
## namevw rabbit custom NA
## horsepower:weight 0.001193 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.146 on 84 degrees of freedom
## Multiple R-squared: 0.9838, Adjusted R-squared: 0.9244
## F-statistic: 16.57 on 307 and 84 DF, p-value: < 2.2e-16
# Lets see if this is indeed a better model:
anova(fit, update(fit, . ~ . + horsepower:weight))
## Analysis of Variance Table
##
## Model 1: mpg ~ cylinders + displacement + horsepower + weight + acceleration +
## year + origin + name
## Model 2: mpg ~ cylinders + displacement + horsepower + weight + acceleration +
## year + origin + name + horsepower:weight
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 85 438.73
## 2 84 386.89 1 51.845 11.257 0.001193 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Use update to add some nonlinear terms: Note that other terms i.e. displacement, weight, and accelation should also have a
# significant non-linear term:
summary(update(fit, . ~ . + I(horsepower^2)))
##
## Call:
## lm(formula = mpg ~ cylinders + displacement + horsepower + weight +
## acceleration + year + origin + name + I(horsepower^2), data = Auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.778 0.000 0.000 0.000 5.778
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value
## (Intercept) 13.4912421 12.4770550 1.081
## cylinders -0.3144738 0.5993266 -0.525
## displacement -0.0374579 0.0183214 -2.044
## horsepower -0.2621504 0.0659609 -3.974
## weight -0.0002323 0.0015652 -0.148
## acceleration -0.6841611 0.1695856 -4.034
## year 0.6208250 0.1049124 5.918
## origin -0.7823831 4.0061328 -0.195
## nameamc ambassador dpl 2.6987097 3.0379886 0.888
## nameamc ambassador sst 2.9788543 3.0578823 0.974
## nameamc concord -0.7650492 3.0649689 -0.250
## nameamc concord d/l -0.7791586 3.2077220 -0.243
## nameamc concord dl 6 -0.8545857 3.2847983 -0.260
## nameamc gremlin 0.6368018 2.7792261 0.229
## nameamc hornet 0.9013961 2.7177902 0.332
## nameamc hornet sportabout (sw) 1.5435551 3.3381452 0.462
## nameamc matador 0.1842309 2.4936578 0.074
## nameamc matador (sw) 1.6619322 2.7332467 0.608
## nameamc pacer -0.4048234 3.2901978 -0.123
## nameamc pacer d/l -0.4608372 3.3030459 -0.140
## nameamc rebel sst 3.5070654 3.0732614 1.141
## nameamc spirit dl -1.9881353 3.8677342 -0.514
## nameaudi 100 ls 1.2786778 3.2238731 0.397
## nameaudi 100ls -3.0450648 2.7887722 -1.092
## nameaudi 4000 4.3461495 3.0325266 1.433
## nameaudi 5000 -3.7853253 3.2253961 -1.174
## nameaudi 5000s (diesel) 9.0736760 3.3400504 2.717
## nameaudi fox 3.9414134 3.1169087 1.265
## namebmw 2002 4.5674378 3.2757441 1.394
## namebmw 320i -4.2226894 3.1705142 -1.332
## namebuick century 1.4011846 2.8804685 0.486
## namebuick century 350 1.0585550 3.0523468 0.347
## namebuick century limited 0.8103443 3.4144782 0.237
## namebuick century luxus (sw) 1.7513193 3.2187291 0.544
## namebuick century special 0.0330588 3.2425309 0.010
## namebuick electra 225 custom -0.5686210 3.6599994 -0.155
## namebuick estate wagon (sw) 2.4857058 2.6944015 0.923
## namebuick lesabre custom 2.3158908 3.1596156 0.733
## namebuick opel isuzu deluxe 1.2224702 3.8345418 0.319
## namebuick regal sport coupe (turbo) -2.1274837 3.4519333 -0.616
## namebuick skyhawk 2.0930220 3.2365910 0.647
## namebuick skylark -0.0659723 3.0800374 -0.021
## namebuick skylark 320 3.9832516 3.0341116 1.313
## namebuick skylark limited 2.0390088 3.6886037 0.553
## namecadillac eldorado 9.5627855 3.2578680 2.935
## namecadillac seville 1.9920100 3.1781118 0.627
## namecapri ii -0.4618423 3.7177701 -0.124
## namechevroelt chevelle malibu -0.0254338 3.2887223 -0.008
## namechevrolet bel air 2.6341602 3.1236119 0.843
## namechevrolet camaro -0.2690131 3.7212534 -0.072
## namechevrolet caprice classic 1.4282013 2.5279990 0.565
## namechevrolet cavalier 0.5329066 3.8093007 0.140
## namechevrolet cavalier 2-door 5.3894662 3.8210889 1.410
## namechevrolet cavalier wagon -1.1431240 3.8207726 -0.299
## namechevrolet chevelle concours (sw) 0.2767795 3.1599923 0.088
## namechevrolet chevelle malibu 2.9101426 2.8163485 1.033
## namechevrolet chevelle malibu classic 0.5164508 2.8139734 0.184
## namechevrolet chevette 0.1336166 3.4262989 0.039
## namechevrolet citation 0.4427099 3.0637082 0.145
## namechevrolet concours -0.8673676 3.2107766 -0.270
## namechevrolet impala 2.0722869 2.5305589 0.819
## namechevrolet malibu 0.2382224 2.7178609 0.088
## namechevrolet malibu classic (sw) 0.9432691 3.1523165 0.299
## namechevrolet monte carlo 4.4688101 3.3629486 1.329
## namechevrolet monte carlo landau 1.3053964 2.6442644 0.494
## namechevrolet monte carlo s 3.1084862 3.0791748 1.010
## namechevrolet monza 2+2 1.8991995 3.1943025 0.595
## namechevrolet nova 0.2088998 2.7401158 0.076
## namechevrolet nova custom 0.2650691 3.2626505 0.081
## namechevrolet vega -0.6760630 3.2282120 -0.209
## namechevrolet vega (sw) -0.1282314 3.7068428 -0.035
## namechevrolet vega 2300 5.7571784 3.7190718 1.548
## namechevrolet woody -2.0805987 3.8231003 -0.544
## namechevy c10 -1.4444219 3.0766631 -0.469
## namechevy c20 -1.4364927 3.8531319 -0.373
## namechevy s-10 2.9534452 3.7868721 0.780
## namechrysler cordoba 1.8692515 3.0930655 0.604
## namechrysler lebaron medallion -2.8581110 3.7744368 -0.757
## namechrysler lebaron salon -6.5956410 3.3950140 -1.943
## namechrysler lebaron town @ country (sw) 3.3192169 3.1038937 1.069
## namechrysler new yorker brougham 0.8272003 3.3938517 0.244
## namechrysler newport royal 2.7011575 3.1100527 0.869
## namedatsun 1200 10.5830259 6.0859481 1.739
## namedatsun 200-sx -1.5328724 6.0867086 -0.252
## namedatsun 200sx 5.8839801 6.0762025 0.968
## namedatsun 210 7.4124797 5.8099610 1.276
## namedatsun 210 mpg 7.2971676 6.0012786 1.216
## namedatsun 280-zx 8.7766436 6.4303345 1.365
## namedatsun 310 6.1131881 5.8791149 1.040
## namedatsun 310 gx 6.0229587 5.8793883 1.024
## namedatsun 510 1.6059040 6.0827133 0.264
## namedatsun 510 (sw) 6.3463018 6.1922945 1.025
## namedatsun 510 hatchback 9.8693681 6.0437895 1.633
## namedatsun 610 0.0340258 6.1866237 0.005
## namedatsun 710 3.7834277 5.9306325 0.638
## namedatsun 810 -1.3501601 6.3894396 -0.211
## namedatsun 810 maxima -0.1730593 6.4400879 -0.027
## namedatsun b-210 4.5167638 5.9686511 0.757
## namedatsun b210 5.4452619 6.0655581 0.898
## namedatsun b210 gx 11.7883555 6.0135789 1.960
## namedatsun f-10 hatchback 5.2486532 5.9466151 0.883
## namedatsun pl510 4.0757286 5.9043551 0.690
## namedodge aries se -0.5682269 3.7855318 -0.150
## namedodge aries wagon (sw) -2.4975717 3.7564186 -0.665
## namedodge aspen -1.0982134 2.8957547 -0.379
## namedodge aspen 6 0.1542007 3.2381426 0.048
## namedodge aspen se 1.3475469 3.2953515 0.409
## namedodge challenger se 4.0920372 3.1240468 1.310
## namedodge charger 2.2 4.3432835 3.9019448 1.113
## namedodge colt 0.0692770 3.3711306 0.021
## namedodge colt (sw) 1.9785659 3.8726491 0.511
## namedodge colt hardtop 0.3193319 3.8149754 0.084
## namedodge colt hatchback custom 4.8644522 3.9270902 1.239
## namedodge colt m/m 5.3526078 3.8435223 1.393
## namedodge coronet brougham 1.1665366 3.1012986 0.376
## namedodge coronet custom 1.5909917 3.0337462 0.524
## namedodge coronet custom (sw) 0.8122908 3.2164860 0.253
## namedodge d100 -1.2503521 3.0432147 -0.411
## namedodge d200 -1.8097127 3.9745553 -0.455
## namedodge dart custom 0.4769412 3.0675554 0.155
## namedodge diplomat 3.1266037 3.0710915 1.018
## namedodge magnum xe 1.6488272 3.0831309 0.535
## namedodge monaco (sw) 1.5553188 3.4142667 0.456
## namedodge monaco brougham 0.4189212 3.0836582 0.136
## namedodge omni 0.4175843 3.9036970 0.107
## namedodge rampage -0.6319645 3.9742808 -0.159
## namedodge st. regis 2.5195953 3.0977286 0.813
## namefiat 124 sport coupe 1.7249141 3.1454760 0.548
## namefiat 124 tc -1.1430603 3.0826446 -0.371
## namefiat 124b 4.1082264 3.1308137 1.312
## namefiat 128 -1.4623593 2.7384678 -0.534
## namefiat 131 1.7778849 3.0960830 0.574
## namefiat strada custom 5.7081088 3.0178763 1.891
## namefiat x1.9 2.6220103 3.0783957 0.852
## nameford country 1.9362042 3.2620246 0.594
## nameford country squire (sw) 2.2393884 2.7029688 0.828
## nameford escort 2h 0.1028438 3.8633544 0.027
## nameford escort 4w 1.4462988 3.9525800 0.366
## nameford f108 -1.7626125 3.0848564 -0.571
## nameford f250 -1.2823453 3.8654079 -0.332
## nameford fairmont 0.2586938 3.7037613 0.070
## nameford fairmont (auto) -3.7330905 3.3613311 -1.111
## nameford fairmont (man) -1.6817362 3.7380128 -0.450
## nameford fairmont 4 -3.7631642 3.7153227 -1.013
## nameford fairmont futura -4.0924869 3.7700978 -1.086
## nameford fiesta 3.8744646 3.9779568 0.974
## nameford futura -0.2961777 3.1725068 -0.093
## nameford galaxie 500 3.8740969 2.5243800 1.535
## nameford gran torino 1.3803536 2.5538275 0.541
## nameford gran torino (sw) 1.8168642 2.9140950 0.623
## nameford granada 0.8256505 3.2480642 0.254
## nameford granada ghia -0.0133316 3.3974596 -0.004
## nameford granada gl -4.3257371 3.3529700 -1.290
## nameford granada l -1.3098677 3.3898837 -0.386
## nameford ltd 1.4057064 2.7609353 0.509
## nameford ltd landau -0.2019410 3.1081896 -0.065
## nameford maverick -0.0797784 2.8099795 -0.028
## nameford mustang -0.2050623 3.4321510 -0.060
## nameford mustang gl -2.3491935 3.7993860 -0.618
## nameford mustang ii -3.4056246 3.1857646 -1.069
## nameford mustang ii 2+2 -0.2629656 3.7200882 -0.071
## nameford pinto -2.2985153 3.1122503 -0.739
## nameford pinto (sw) -1.6332786 3.7485618 -0.436
## nameford pinto runabout -2.3304565 3.7339728 -0.624
## nameford ranger -0.9665395 3.7897668 -0.255
## nameford thunderbird 2.8262275 3.0827409 0.917
## nameford torino 3.1802053 3.1163690 1.020
## nameford torino 500 1.5169634 3.4103216 0.445
## namehi 1200d 0.3625240 4.0584381 0.089
## namehonda accord 4.1427132 5.7464610 0.721
## namehonda accord cvcc 4.6252687 6.0479348 0.765
## namehonda accord lx 0.7254444 5.9521495 0.122
## namehonda civic 3.2029690 5.6885852 0.563
## namehonda civic (auto) -0.3260908 5.8618619 -0.056
## namehonda civic 1300 2.1444439 5.8336879 0.368
## namehonda civic 1500 gl 12.1889386 5.8160338 2.096
## namehonda civic cvcc 4.7616874 5.7375259 0.830
## namehonda prelude 2.9217292 5.8992253 0.495
## namemaxda glc deluxe 2.8027986 5.8468409 0.479
## namemaxda rx3 -8.2570727 5.8987640 -1.400
## namemazda 626 3.8819592 5.8924986 0.659
## namemazda glc 16.5605690 5.9401022 2.788
## namemazda glc 4 2.7554231 5.8819028 0.468
## namemazda glc custom 0.1257715 5.9437158 0.021
## namemazda glc custom l 6.5490446 5.9679458 1.097
## namemazda glc deluxe 2.5464127 5.9673508 0.427
## namemazda rx-4 -4.7837634 6.0434328 -0.792
## namemazda rx-7 gs -6.4639722 5.8653994 -1.102
## namemazda rx2 coupe -5.8330791 5.9809851 -0.975
## namemercedes-benz 240d 4.6652441 3.4246244 1.362
## namemercedes-benz 280s -2.5364320 3.7486709 -0.677
## namemercedes benz 300d 2.7221631 3.4890661 0.780
## namemercury capri 2000 -1.4214282 3.8115460 -0.373
## namemercury capri v6 -0.5774685 3.4495857 -0.167
## namemercury cougar brougham -0.3531267 3.1856864 -0.111
## namemercury grand marquis 0.8273130 3.1321397 0.264
## namemercury lynx l 3.9506085 3.9105693 1.010
## namemercury marquis -0.3803577 3.2826925 -0.116
## namemercury marquis brougham 1.1424153 3.3474519 0.341
## namemercury monarch -3.2560243 3.4538491 -0.943
## namemercury monarch ghia 2.9832690 3.0846459 0.967
## namemercury zephyr -2.4929542 3.3475955 -0.745
## namemercury zephyr 6 -3.1061213 3.3289782 -0.933
## namenissan stanza xe 6.8047410 6.0108092 1.132
## nameoldsmobile cutlass ciera (diesel) 14.7386046 3.4806083 4.234
## nameoldsmobile cutlass ls 11.5264743 3.4890086 3.304
## nameoldsmobile cutlass salon brougham 4.2797073 2.8920554 1.480
## nameoldsmobile cutlass supreme 1.5404185 3.3024200 0.466
## nameoldsmobile delta 88 royale 1.3168078 3.1388249 0.420
## nameoldsmobile omega -2.5644180 3.0150465 -0.851
## nameoldsmobile omega brougham 2.1044674 3.4465906 0.611
## nameoldsmobile starfire sx -1.3915355 3.6657104 -0.380
## nameoldsmobile vista cruiser -0.3442072 3.2396086 -0.106
## nameopel 1900 1.9878655 2.7354641 0.727
## nameopel manta -1.3043643 2.6973235 -0.484
## namepeugeot 304 6.3436743 3.2514506 1.951
## namepeugeot 504 1.6033833 2.8278074 0.567
## namepeugeot 504 (sw) 0.7238651 3.4182129 0.212
## namepeugeot 505s turbo diesel 2.8263121 3.3427847 0.845
## namepeugeot 604sl -4.2813572 3.6197013 -1.183
## nameplymouth 'cuda 340 0.2242362 3.0952034 0.072
## nameplymouth arrow gs -0.4812877 3.7637529 -0.128
## nameplymouth champ 5.5384022 3.9965340 1.386
## nameplymouth cricket 2.6673030 3.8317356 0.696
## nameplymouth custom suburb 1.6739527 3.2137551 0.521
## nameplymouth duster 2.4459263 2.8209979 0.867
## nameplymouth fury 0.3823927 3.3606842 0.114
## nameplymouth fury gran sedan 2.0661712 3.1233663 0.662
## nameplymouth fury iii 2.3696587 2.5589577 0.926
## nameplymouth grand fury 2.8851512 3.2180908 0.897
## nameplymouth horizon 1.4876501 4.0118718 0.371
## nameplymouth horizon 4 0.8454475 4.0150123 0.211
## nameplymouth horizon miser 3.3668835 4.0313212 0.835
## nameplymouth horizon tc3 2.9391091 3.9210237 0.750
## nameplymouth reliant -1.5308019 3.5186112 -0.435
## nameplymouth sapporo -0.3369919 3.6563651 -0.092
## nameplymouth satellite 5.3480111 3.0785598 1.737
## nameplymouth satellite custom -0.6374563 3.3083879 -0.193
## nameplymouth satellite custom (sw) 2.3077479 3.0865888 0.748
## nameplymouth satellite sebring 0.2246499 3.2947079 0.068
## nameplymouth valiant 1.2040298 2.8715826 0.419
## nameplymouth valiant custom -0.7911182 3.2800255 -0.241
## nameplymouth volare 0.2124784 3.2543064 0.065
## nameplymouth volare custom -0.2781564 3.2865711 -0.085
## nameplymouth volare premier v8 -1.7547058 3.0446591 -0.576
## namepontiac astro -1.0803376 3.6666727 -0.295
## namepontiac catalina 3.4431492 2.6164524 1.316
## namepontiac catalina brougham 4.2314124 3.1169893 1.358
## namepontiac firebird 2.4551648 3.3170243 0.740
## namepontiac grand prix -0.3771782 3.7005765 -0.102
## namepontiac grand prix lj 2.0227487 3.0603462 0.661
## namepontiac j2000 se hatchback 0.8414393 3.8682593 0.218
## namepontiac lemans v6 0.8140282 3.2364159 0.252
## namepontiac phoenix 2.6784156 3.4048557 0.787
## namepontiac phoenix lj 0.9952129 3.2398481 0.307
## namepontiac safari (sw) 3.7305267 3.4520017 1.081
## namepontiac sunbird coupe -0.8337322 3.6813289 -0.226
## namepontiac ventura sj 0.6456624 3.2264393 0.200
## namerenault 12 (sw) 1.2126101 3.1733046 0.382
## namerenault 12tl -0.0128054 3.0581881 -0.004
## namerenault 5 gtl 6.0663126 3.0856369 1.966
## namesaab 99e 4.7537706 3.3208915 1.431
## namesaab 99gle -2.3313608 3.2995831 -0.707
## namesaab 99le 1.4963482 2.8769887 0.520
## namesubaru 2.4516873 5.8330061 0.420
## namesubaru dl 3.0210152 5.7709486 0.523
## nametoyota carina -1.3629963 6.2508623 -0.218
## nametoyota celica gt 4.2935574 6.0882306 0.705
## nametoyota celica gt liftback -4.0214237 6.1165082 -0.657
## nametoyota corolla 2.7164995 5.6605687 0.480
## nametoyota corolla 1200 6.9206597 5.9334103 1.166
## nametoyota corolla 1600 (sw) 4.5058444 6.1459325 0.733
## nametoyota corolla liftback -0.0569608 6.0640247 -0.009
## nametoyota corolla tercel 7.9604848 5.9671635 1.334
## nametoyota corona 1.4736580 5.7483672 0.256
## nametoyota corona hardtop 2.2407693 6.1801705 0.363
## nametoyota corona liftback 3.4136102 6.1028403 0.559
## nametoyota corona mark ii 3.1621747 6.2043932 0.510
## nametoyota cressida 0.7531143 6.3991274 0.118
## nametoyota mark ii -0.3804554 6.3474013 -0.060
## nametoyota starlet 6.2860610 5.8510860 1.074
## nametoyota tercel 6.2555023 5.9027204 1.060
## nametoyouta corona mark ii (sw) 1.0793329 6.1717868 0.175
## nametriumph tr7 coupe 6.8284017 3.0718138 2.223
## namevokswagen rabbit -3.2219993 3.0164858 -1.068
## namevolkswagen 1131 deluxe sedan 0.2721744 3.3599146 0.081
## namevolkswagen 411 (sw) -0.7783205 3.2266907 -0.241
## namevolkswagen dasher -1.3607549 2.5107671 -0.542
## namevolkswagen jetta 1.0837055 3.0162488 0.359
## namevolkswagen model 111 2.0708934 3.2246964 0.642
## namevolkswagen rabbit -1.0074413 2.6296396 -0.383
## namevolkswagen rabbit custom -0.0383951 3.0258127 -0.013
## namevolkswagen rabbit custom diesel 13.2316034 3.2111877 4.120
## namevolkswagen rabbit l 4.1666751 3.0448404 1.368
## namevolkswagen scirocco 0.8516694 3.0081165 0.283
## namevolkswagen super beetle -1.2215056 3.2958805 -0.371
## namevolkswagen type 3 -0.3823414 3.4242307 -0.112
## namevolvo 144ea -2.1718341 3.3489156 -0.649
## namevolvo 145e (sw) -3.2200709 3.3722705 -0.955
## namevolvo 244dl -2.3247849 3.2531350 -0.715
## namevolvo 245 -3.3511585 3.3232491 -1.008
## namevolvo 264gl -5.4439312 3.3903783 -1.606
## namevolvo diesel 5.1076103 3.4678256 1.473
## namevw dasher (diesel) 13.8764124 3.3387667 4.156
## namevw pickup 14.7837501 3.3537401 4.408
## namevw rabbit 4.7721355 2.6061055 1.831
## namevw rabbit c (diesel) 13.3500155 3.2149484 4.152
## namevw rabbit custom NA NA NA
## I(horsepower^2) 0.0008249 0.0002256 3.657
## Pr(>|t|)
## (Intercept) 0.282665
## cylinders 0.601166
## displacement 0.044037 *
## horsepower 0.000149 ***
## weight 0.882372
## acceleration 0.000120 ***
## year 6.87e-08 ***
## origin 0.845633
## nameamc ambassador dpl 0.376905
## nameamc ambassador sst 0.332776
## nameamc concord 0.803498
## nameamc concord d/l 0.808674
## nameamc concord dl 6 0.795374
## nameamc gremlin 0.819325
## nameamc hornet 0.740968
## nameamc hornet sportabout (sw) 0.644991
## nameamc matador 0.941282
## nameamc matador (sw) 0.544799
## nameamc pacer 0.902370
## nameamc pacer d/l 0.889374
## nameamc rebel sst 0.257049
## nameamc spirit dl 0.608580
## nameaudi 100 ls 0.692648
## nameaudi 100ls 0.277998
## nameaudi 4000 0.155519
## nameaudi 5000 0.243872
## nameaudi 5000s (diesel) 0.008007 **
## nameaudi fox 0.209538
## namebmw 2002 0.166898
## namebmw 320i 0.186508
## namebuick century 0.627920
## namebuick century 350 0.729609
## namebuick century limited 0.812982
## namebuick century luxus (sw) 0.587812
## namebuick century special 0.991890
## namebuick electra 225 custom 0.876909
## namebuick estate wagon (sw) 0.358887
## namebuick lesabre custom 0.465620
## namebuick opel isuzu deluxe 0.750666
## namebuick regal sport coupe (turbo) 0.539352
## namebuick skyhawk 0.519606
## namebuick skylark 0.982962
## namebuick skylark 320 0.192818
## namebuick skylark limited 0.581878
## namecadillac eldorado 0.004297 **
## namecadillac seville 0.532496
## namecapri ii 0.901433
## namechevroelt chevelle malibu 0.993848
## namechevrolet bel air 0.401452
## namechevrolet camaro 0.942542
## namechevrolet caprice classic 0.573611
## namechevrolet cavalier 0.889077
## namechevrolet cavalier 2-door 0.162098
## namechevrolet cavalier wagon 0.765537
## namechevrolet chevelle concours (sw) 0.930412
## namechevrolet chevelle malibu 0.304428
## namechevrolet chevelle malibu classic 0.854824
## namechevrolet chevette 0.968985
## namechevrolet citation 0.885451
## namechevrolet concours 0.787713
## namechevrolet impala 0.415158
## namechevrolet malibu 0.930363
## namechevrolet malibu classic (sw) 0.765503
## namechevrolet monte carlo 0.187500
## namechevrolet monte carlo landau 0.622827
## namechevrolet monte carlo s 0.315625
## namechevrolet monza 2+2 0.553737
## namechevrolet nova 0.939411
## namechevrolet nova custom 0.935442
## namechevrolet vega 0.834625
## namechevrolet vega (sw) 0.972486
## namechevrolet vega 2300 0.125378
## namechevrolet woody 0.587733
## namechevy c10 0.639945
## namechevy c20 0.710228
## namechevy s-10 0.437632
## namechrysler cordoba 0.547249
## namechrysler lebaron medallion 0.451032
## namechrysler lebaron salon 0.055397 .
## namechrysler lebaron town @ country (sw) 0.287965
## namechrysler new yorker brougham 0.808030
## namechrysler newport royal 0.387582
## namedatsun 1200 0.085711 .
## namedatsun 200-sx 0.801780
## namedatsun 200sx 0.335642
## namedatsun 210 0.205535
## namedatsun 210 mpg 0.227416
## namedatsun 280-zx 0.175935
## namedatsun 310 0.301410
## namedatsun 310 gx 0.308578
## namedatsun 510 0.792418
## namedatsun 510 (sw) 0.308367
## namedatsun 510 hatchback 0.106217
## namedatsun 610 0.995625
## namedatsun 710 0.525244
## namedatsun 810 0.833156
## namedatsun 810 maxima 0.978625
## namedatsun b-210 0.451318
## namedatsun b210 0.371893
## namedatsun b210 gx 0.053277 .
## namedatsun f-10 hatchback 0.379956
## namedatsun pl510 0.491914
## namedodge aries se 0.881042
## namedodge aries wagon (sw) 0.507948
## namedodge aspen 0.705460
## namedodge aspen 6 0.962132
## namedodge aspen se 0.683636
## namedodge challenger se 0.193817
## namedodge charger 2.2 0.268838
## namedodge colt 0.983653
## namedodge colt (sw) 0.610756
## namedodge colt hardtop 0.933490
## namedodge colt hatchback custom 0.218910
## namedodge colt m/m 0.167407
## namedodge coronet brougham 0.707758
## namedodge coronet custom 0.601360
## namedodge coronet custom (sw) 0.801241
## namedodge d100 0.682217
## namedodge d200 0.650051
## namedodge dart custom 0.876817
## namedodge diplomat 0.311565
## namedodge magnum xe 0.594208
## namedodge monaco (sw) 0.649900
## namedodge monaco brougham 0.892263
## namedodge omni 0.915067
## namedodge rampage 0.874040
## namedodge st. regis 0.418306
## namefiat 124 sport coupe 0.584886
## namefiat 124 tc 0.711716
## namefiat 124b 0.193030
## namefiat 128 0.594748
## namefiat 131 0.567342
## namefiat strada custom 0.062013 .
## namefiat x1.9 0.396777
## nameford country 0.554402
## nameford country squire (sw) 0.409740
## nameford escort 2h 0.978826
## nameford escort 4w 0.715350
## nameford f108 0.569271
## nameford f250 0.740905
## nameford fairmont 0.944482
## nameford fairmont (auto) 0.269910
## nameford fairmont (man) 0.653941
## nameford fairmont 4 0.314028
## nameford fairmont futura 0.280800
## nameford fiesta 0.332861
## nameford futura 0.925842
## nameford galaxie 500 0.128622
## nameford gran torino 0.590280
## nameford gran torino (sw) 0.534662
## nameford granada 0.799964
## nameford granada ghia 0.996878
## nameford granada gl 0.200549
## nameford granada l 0.700174
## nameford ltd 0.611988
## nameford ltd landau 0.948352
## nameford maverick 0.977418
## nameford mustang 0.952499
## nameford mustang gl 0.538045
## nameford mustang ii 0.288126
## nameford mustang ii 2+2 0.943814
## nameford pinto 0.462246
## nameford pinto (sw) 0.664166
## nameford pinto runabout 0.534239
## nameford ranger 0.799316
## nameford thunderbird 0.361877
## nameford torino 0.310429
## nameford torino 500 0.657597
## namehi 1200d 0.929035
## namehonda accord 0.472963
## namehonda accord cvcc 0.446553
## namehonda accord lx 0.903286
## namehonda civic 0.574899
## namehonda civic (auto) 0.955769
## namehonda civic 1300 0.714099
## namehonda civic 1500 gl 0.039115 *
## namehonda civic cvcc 0.408936
## namehonda prelude 0.621700
## namemaxda glc deluxe 0.632921
## namemaxda rx3 0.165257
## namemazda 626 0.511828
## namemazda glc 0.006559 **
## namemazda glc 4 0.640671
## namemazda glc custom 0.983168
## namemazda glc custom l 0.275615
## namemazda glc deluxe 0.670672
## namemazda rx-4 0.430845
## namemazda rx-7 gs 0.273587
## namemazda rx2 coupe 0.332226
## namemercedes-benz 240d 0.176756
## namemercedes-benz 280s 0.500505
## namemercedes benz 300d 0.437467
## namemercury capri 2000 0.710142
## namemercury capri v6 0.867456
## namemercury cougar brougham 0.912001
## namemercury grand marquis 0.792322
## namemercury lynx l 0.315282
## namemercury marquis 0.908034
## namemercury marquis brougham 0.733746
## namemercury monarch 0.348526
## namemercury monarch ghia 0.336253
## namemercury zephyr 0.458532
## namemercury zephyr 6 0.353466
## namenissan stanza xe 0.260820
## nameoldsmobile cutlass ciera (diesel) 5.83e-05 ***
## nameoldsmobile cutlass ls 0.001404 **
## nameoldsmobile cutlass salon brougham 0.142663
## nameoldsmobile cutlass supreme 0.642100
## nameoldsmobile delta 88 royale 0.675905
## nameoldsmobile omega 0.397443
## nameoldsmobile omega brougham 0.543117
## nameoldsmobile starfire sx 0.705194
## nameoldsmobile vista cruiser 0.915638
## nameopel 1900 0.469429
## nameopel manta 0.629944
## namepeugeot 304 0.054387 .
## namepeugeot 504 0.572222
## namepeugeot 504 (sw) 0.832802
## namepeugeot 505s turbo diesel 0.400236
## namepeugeot 604sl 0.240228
## nameplymouth 'cuda 340 0.942419
## nameplymouth arrow gs 0.898554
## nameplymouth champ 0.169476
## nameplymouth cricket 0.488283
## nameplymouth custom suburb 0.603827
## nameplymouth duster 0.388389
## nameplymouth fury 0.909680
## nameplymouth fury gran sedan 0.510089
## nameplymouth fury iii 0.357086
## nameplymouth grand fury 0.372526
## nameplymouth horizon 0.711711
## nameplymouth horizon 4 0.833732
## nameplymouth horizon miser 0.405985
## nameplymouth horizon tc3 0.455604
## nameplymouth reliant 0.664636
## nameplymouth sapporo 0.926786
## nameplymouth satellite 0.086021 .
## nameplymouth satellite custom 0.847676
## nameplymouth satellite custom (sw) 0.456748
## nameplymouth satellite sebring 0.945800
## nameplymouth valiant 0.676074
## nameplymouth valiant custom 0.809994
## nameplymouth volare 0.948097
## nameplymouth volare custom 0.932754
## nameplymouth volare premier v8 0.565938
## namepontiac astro 0.768998
## namepontiac catalina 0.191767
## namepontiac catalina brougham 0.178248
## namepontiac firebird 0.461260
## namepontiac grand prix 0.919060
## namepontiac grand prix lj 0.510450
## namepontiac j2000 se hatchback 0.828328
## namepontiac lemans v6 0.802025
## namepontiac phoenix 0.433703
## namepontiac phoenix lj 0.759467
## namepontiac safari (sw) 0.282930
## namepontiac sunbird coupe 0.821382
## namepontiac ventura sj 0.841873
## namerenault 12 (sw) 0.703331
## namerenault 12tl 0.996669
## namerenault 5 gtl 0.052604 .
## namesaab 99e 0.156005
## namesaab 99gle 0.481794
## namesaab 99le 0.604356
## namesubaru 0.675330
## namesubaru dl 0.602014
## nametoyota carina 0.827920
## nametoyota celica gt 0.482623
## nametoyota celica gt liftback 0.512676
## nametoyota corolla 0.632547
## nametoyota corolla 1200 0.246758
## nametoyota corolla 1600 (sw) 0.465513
## nametoyota corolla liftback 0.992528
## nametoyota corolla tercel 0.185794
## nametoyota corona 0.798299
## nametoyota corona hardtop 0.717834
## nametoyota corona liftback 0.577413
## nametoyota corona mark ii 0.611621
## nametoyota cressida 0.906594
## nametoyota mark ii 0.952347
## nametoyota starlet 0.285746
## nametoyota tercel 0.292289
## nametoyouta corona mark ii (sw) 0.861593
## nametriumph tr7 coupe 0.028907 *
## namevokswagen rabbit 0.288522
## namevolkswagen 1131 deluxe sedan 0.935630
## namevolkswagen 411 (sw) 0.809978
## namevolkswagen dasher 0.589275
## namevolkswagen jetta 0.720280
## namevolkswagen model 111 0.522494
## namevolkswagen rabbit 0.702606
## namevolkswagen rabbit custom 0.989906
## namevolkswagen rabbit custom diesel 8.82e-05 ***
## namevolkswagen rabbit l 0.174824
## namevolkswagen scirocco 0.777779
## namevolkswagen super beetle 0.711857
## namevolkswagen type 3 0.911361
## namevolvo 144ea 0.518419
## namevolvo 145e (sw) 0.342385
## namevolvo 244dl 0.476820
## namevolvo 245 0.316159
## namevolvo 264gl 0.112093
## namevolvo diesel 0.144527
## namevw dasher (diesel) 7.76e-05 ***
## namevw pickup 3.06e-05 ***
## namevw rabbit 0.070626 .
## namevw rabbit c (diesel) 7.86e-05 ***
## namevw rabbit custom NA
## I(horsepower^2) 0.000444 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.123 on 84 degrees of freedom
## Multiple R-squared: 0.9841, Adjusted R-squared: 0.926
## F-statistic: 16.95 on 307 and 84 DF, p-value: < 2.2e-16
Exercise 10
fit_1 <- lm(Sales ~ Price + Urban + US, data = Carseats)
summary(fit_1)
##
## Call:
## lm(formula = Sales ~ Price + Urban + US, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9206 -1.6220 -0.0564 1.5786 7.0581
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.043469 0.651012 20.036 < 2e-16 ***
## Price -0.054459 0.005242 -10.389 < 2e-16 ***
## UrbanYes -0.021916 0.271650 -0.081 0.936
## USYes 1.200573 0.259042 4.635 4.86e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.472 on 396 degrees of freedom
## Multiple R-squared: 0.2393, Adjusted R-squared: 0.2335
## F-statistic: 41.52 on 3 and 396 DF, p-value: < 2.2e-16
fit_2 <- update(fit, . ~ . - Urban)
confint(fit_2, level = 0.95)
## 2.5 % 97.5 %
## (Intercept) -2.521072e+01 25.585326295
## cylinders -2.144167e+00 0.307974681
## displacement -2.801806e-02 0.034100283
## horsepower -1.001407e-01 0.015456257
## weight -6.597404e-03 -0.001787893
## acceleration -8.225110e-01 -0.140386794
## year 4.134250e-01 0.859570558
## origin -7.112396e+00 9.760923634
## nameamc ambassador dpl -3.081785e+00 9.824501176
## nameamc ambassador sst -3.139209e+00 9.867737277
## nameamc concord -6.634193e+00 6.389192526
## nameamc concord d/l -8.492300e+00 5.119203547
## nameamc concord dl 6 -7.517358e+00 6.457985133
## nameamc gremlin -6.308484e+00 5.455272834
## nameamc hornet -5.502859e+00 6.040911506
## nameamc hornet sportabout (sw) -7.415954e+00 6.609731801
## nameamc matador -4.841939e+00 5.766405532
## nameamc matador (sw) -2.635436e+00 8.873294610
## nameamc pacer -6.985350e+00 7.009676134
## nameamc pacer d/l -8.675046e+00 5.311043346
## nameamc rebel sst -3.653805e+00 9.405687083
## nameamc spirit dl -7.366251e+00 8.792251369
## nameaudi 100 ls -5.921428e+00 7.793936489
## nameaudi 100ls -9.067884e+00 2.800988068
## nameaudi 4000 -2.445480e+00 10.455167332
## nameaudi 5000 -1.097031e+01 2.752149766
## nameaudi 5000s (diesel) 4.705410e+00 18.600443234
## nameaudi fox -3.419397e+00 9.818370072
## namebmw 2002 -4.736473e+00 8.902259276
## namebmw 320i -1.203738e+01 1.396027789
## namebuick century -3.898273e+00 8.324823749
## namebuick century 350 -4.300622e+00 8.626737400
## namebuick century limited -6.108928e+00 8.417940240
## namebuick century luxus (sw) -3.053375e+00 10.456523165
## namebuick century special -6.423896e+00 7.367222542
## namebuick electra 225 custom -1.356447e+00 12.488244600
## namebuick estate wagon (sw) -3.444321e+00 8.021043328
## namebuick lesabre custom -2.783147e+00 10.540907491
## namebuick opel isuzu deluxe -5.772272e+00 10.494078009
## namebuick regal sport coupe (turbo) -8.074107e+00 6.532589668
## namebuick skyhawk -5.689012e+00 8.045042688
## namebuick skylark -6.060688e+00 7.032538202
## namebuick skylark 320 -3.220933e+00 9.662027914
## namebuick skylark limited -5.317780e+00 10.371055813
## namecadillac eldorado 6.779078e-01 14.335702492
## namecadillac seville -1.870291e+00 11.282117623
## namecapri ii -7.688046e+00 8.115635188
## namechevroelt chevelle malibu -5.771806e+00 8.153579019
## namechevrolet bel air -3.100145e+00 10.153634134
## namechevrolet camaro -6.866618e+00 8.900558131
## namechevrolet caprice classic -3.893422e+00 6.865804684
## namechevrolet cavalier -6.365561e+00 9.789075341
## namechevrolet cavalier 2-door -2.061106e+00 14.183072046
## namechevrolet cavalier wagon -7.705490e+00 8.459592377
## namechevrolet chevelle concours (sw) -5.188990e+00 8.184963317
## namechevrolet chevelle malibu -3.480260e+00 8.497306938
## namechevrolet chevelle malibu classic -3.763584e+00 8.061327286
## namechevrolet chevette -4.328171e+00 9.921347513
## namechevrolet citation -5.680714e+00 7.350763122
## namechevrolet concours -7.794554e+00 5.870415611
## namechevrolet impala -1.376876e+00 9.180825543
## namechevrolet malibu -5.444528e+00 6.122389074
## namechevrolet malibu classic (sw) -5.131567e+00 8.265384910
## namechevrolet monte carlo -5.224618e+00 8.735739546
## namechevrolet monte carlo landau -4.266565e+00 6.987528811
## namechevrolet monte carlo s -3.733137e+00 9.367783262
## namechevrolet monza 2+2 -4.836733e+00 8.758376218
## namechevrolet nova -5.816638e+00 5.843371695
## namechevrolet nova custom -7.509304e+00 6.341698321
## namechevrolet vega -6.986098e+00 6.738479835
## namechevrolet vega (sw) -7.032604e+00 8.704173542
## namechevrolet vega 2300 -2.600958e+00 13.219223225
## namechevrolet woody -7.780263e+00 8.265065859
## namechevy c10 -8.232607e+00 4.858965931
## namechevy c20 -3.085957e+00 11.849843722
## namechevy s-10 -3.162665e+00 12.807227137
## namechrysler cordoba -3.380992e+00 9.697654329
## namechrysler lebaron medallion -1.082404e+01 5.240189288
## namechrysler lebaron salon -1.164846e+01 2.598671500
## namechrysler lebaron town @ country (sw) -4.481761e+00 8.650322406
## namechrysler new yorker brougham -1.458391e+00 12.023353100
## namechrysler newport royal -2.152870e+00 10.936753071
## namedatsun 1200 -5.370027e+00 20.274870868
## namedatsun 200-sx -1.800500e+01 7.540352585
## namedatsun 200sx -9.989239e+00 15.624276258
## namedatsun 210 -6.713040e+00 17.925246331
## namedatsun 210 mpg -7.634819e+00 17.775434890
## namedatsun 280-zx -7.684983e+00 19.477083834
## namedatsun 310 -7.837928e+00 17.125717684
## namedatsun 310 gx -8.415049e+00 16.501978508
## namedatsun 510 -1.519414e+01 10.256448015
## namedatsun 510 (sw) -9.975868e+00 16.100581329
## namedatsun 510 hatchback -6.163162e+00 19.268559879
## namedatsun 610 -1.639661e+01 9.632407602
## namedatsun 710 -1.120852e+01 13.871020696
## namedatsun 810 -1.676902e+01 10.338340875
## namedatsun 810 maxima -1.608340e+01 11.198763579
## namedatsun b-210 -1.026822e+01 15.012056131
## namedatsun b210 -9.517753e+00 16.180408420
## namedatsun b210 gx -3.129314e+00 22.338624545
## namedatsun f-10 hatchback -9.633384e+00 15.534311920
## namedatsun pl510 -1.145343e+01 13.416778538
## namedodge aries se -7.632117e+00 8.439747070
## namedodge aries wagon (sw) -1.024946e+01 5.735805772
## namedodge aspen -6.347337e+00 5.933570330
## namedodge aspen 6 -6.523407e+00 7.256265536
## namedodge aspen se -3.944112e+00 9.948420963
## namedodge challenger se -4.477932e+00 8.607300956
## namedodge charger 2.2 -2.974878e+00 13.594094416
## namedodge colt -5.644263e+00 8.609055128
## namedodge colt (sw) -4.461930e+00 11.895829765
## namedodge colt hardtop -6.566200e+00 9.610295327
## namedodge colt hatchback custom -2.716594e+00 13.973847481
## namedodge colt m/m -1.941928e+00 14.385220136
## namedodge coronet brougham -3.871843e+00 9.211167938
## namedodge coronet custom -4.849102e+00 8.062837656
## namedodge coronet custom (sw) -3.386832e+00 9.992471244
## namedodge d100 -8.144151e+00 4.798770156
## namedodge d200 -2.374072e+00 12.523863337
## namedodge dart custom -7.192013e+00 5.791759393
## namedodge diplomat -3.965302e+00 9.089060949
## namedodge magnum xe -4.199335e+00 8.897470737
## namedodge monaco (sw) -1.500851e+00 12.320748922
## namedodge monaco brougham -5.085928e+00 7.983599375
## namedodge omni -5.608579e+00 10.810489117
## namedodge rampage -8.118147e+00 8.760409452
## namedodge st. regis -4.706579e+00 8.456318786
## namefiat 124 sport coupe -5.830282e+00 7.517867709
## namefiat 124 tc -7.843932e+00 5.275107262
## namefiat 124b -2.427707e+00 10.896566376
## namefiat 128 -6.091229e+00 5.485589132
## namefiat 131 -5.015645e+00 8.159439567
## namefiat strada custom 1.003326e-01 12.911148312
## namefiat x1.9 -3.113599e+00 9.955353727
## nameford country -3.044694e+00 10.666322951
## nameford country squire (sw) -3.160462e+00 8.336508645
## nameford escort 2h -5.155085e+00 10.961500089
## nameford escort 4w -4.463770e+00 12.128070381
## nameford f108 -8.070334e+00 5.055786154
## nameford f250 -1.879365e+00 12.632349008
## nameford fairmont -6.149283e+00 9.526243360
## nameford fairmont (auto) -9.533072e+00 4.691359229
## nameford fairmont (man) -8.179328e+00 7.644661005
## nameford fairmont 4 -9.921560e+00 5.768903670
## nameford fairmont futura -1.063379e+01 5.324642728
## nameford fiesta -2.816041e+00 13.996398603
## nameford futura -8.601874e+00 4.768261485
## nameford galaxie 500 -9.193453e-01 9.804304622
## nameford gran torino -3.007353e+00 7.797650601
## nameford gran torino (sw) -1.723904e+00 10.335722121
## nameford granada -6.109489e+00 7.714598477
## nameford granada ghia -5.931327e+00 8.452417122
## nameford granada gl -1.028317e+01 3.924896634
## nameford granada l -1.032546e+01 3.934341321
## nameford ltd -2.876614e+00 8.739290260
## nameford ltd landau -6.851726e+00 6.377002480
## nameford maverick -5.773989e+00 6.181042823
## nameford mustang -7.390243e+00 7.216715879
## nameford mustang gl -8.629805e+00 7.413337860
## nameford mustang ii -1.198609e+01 1.393068671
## nameford mustang ii 2+2 -6.722851e+00 9.024509002
## nameford pinto -7.338556e+00 5.788315227
## nameford pinto (sw) -8.608711e+00 7.304645861
## nameford pinto runabout -1.006502e+01 5.825285933
## nameford ranger -7.081898e+00 8.899403193
## nameford thunderbird -3.335651e+00 9.776798162
## nameford torino -3.824668e+00 9.431688308
## nameford torino 500 -5.171912e+00 9.328086520
## namehi 1200d -1.649951e+00 14.194600366
## namehonda accord -1.021341e+01 14.110453643
## namehonda accord cvcc -1.071976e+01 14.847704309
## namehonda accord lx -1.373132e+01 11.511444331
## namehonda civic -1.098755e+01 13.094058929
## namehonda civic (auto) -1.474315e+01 10.097071585
## namehonda civic 1300 -1.189602e+01 12.857145773
## namehonda civic 1500 gl -2.166950e+00 22.473047434
## namehonda civic cvcc -8.992491e+00 15.357786002
## namehonda prelude -1.178255e+01 13.192260907
## namemaxda glc deluxe -1.099810e+01 13.834453687
## namemaxda rx3 -2.332811e+01 1.593154361
## namemazda 626 -1.050645e+01 14.475224163
## namemazda glc 2.533511e+00 27.761686682
## namemazda glc 4 -1.177474e+01 13.142920772
## namemazda glc custom -1.491154e+01 10.221578588
## namemazda glc custom l -8.450226e+00 16.799194399
## namemazda glc deluxe -1.040542e+01 14.990554037
## namemazda rx-4 -1.941555e+01 6.219116353
## namemazda rx-7 gs -2.086877e+01 3.988841855
## namemazda rx2 coupe -2.073196e+01 4.590163633
## namemercedes-benz 240d -7.835999e-01 13.646300552
## namemercedes-benz 280s -8.470087e+00 7.320462044
## namemercedes benz 300d -3.332137e+00 11.436784991
## namemercury capri 2000 -8.812814e+00 7.388521431
## namemercury capri v6 -7.642747e+00 7.035603007
## namemercury cougar brougham -5.094385e+00 8.274302566
## namemercury grand marquis -6.873785e+00 6.399232094
## namemercury lynx l -2.374045e+00 14.118783727
## namemercury marquis -3.434218e+00 9.890988048
## namemercury marquis brougham -2.061125e+00 11.554413990
## namemercury monarch -9.263086e+00 5.358353046
## namemercury monarch ghia -4.074028e+00 9.041684960
## namemercury zephyr -8.014176e+00 6.119528022
## namemercury zephyr 6 -9.261526e+00 4.867405606
## namenissan stanza xe -9.850484e+00 15.286050528
## nameoldsmobile cutlass ciera (diesel) 6.064185e+00 20.799764713
## nameoldsmobile cutlass ls 1.743041e+00 16.304098361
## nameoldsmobile cutlass salon brougham -1.642455e+00 10.663515001
## nameoldsmobile cutlass supreme -3.037417e+00 10.756435461
## nameoldsmobile delta 88 royale -3.718198e+00 9.513656942
## nameoldsmobile omega -8.831726e+00 3.999478766
## nameoldsmobile omega brougham -4.944909e+00 9.720448050
## nameoldsmobile starfire sx -7.867302e+00 7.662068114
## nameoldsmobile vista cruiser -3.838790e+00 9.452612744
## nameopel 1900 -5.379838e+00 6.108195120
## nameopel manta -7.202888e+00 4.275717433
## namepeugeot 304 -4.662480e-01 13.371696672
## namepeugeot 504 -3.749583e+00 8.261868839
## namepeugeot 504 (sw) -6.063030e+00 8.474441836
## namepeugeot 505s turbo diesel -3.392699e+00 10.797949969
## namepeugeot 604sl -1.143079e+01 3.961899440
## nameplymouth 'cuda 340 -6.583497e+00 6.587485075
## nameplymouth arrow gs -8.559496e+00 7.459245264
## nameplymouth champ -5.916485e-01 16.211330240
## nameplymouth cricket -4.407945e+00 11.853982242
## nameplymouth custom suburb -2.429884e+00 10.917208952
## nameplymouth duster -2.890989e+00 9.091314009
## nameplymouth fury -4.418109e+00 9.647388215
## nameplymouth fury gran sedan -3.095845e+00 10.092612557
## nameplymouth fury iii -1.028966e+00 9.628090681
## nameplymouth grand fury -1.380452e+00 12.019790654
## nameplymouth horizon -4.077935e+00 12.680100850
## nameplymouth horizon 4 -4.216829e+00 12.442917971
## nameplymouth horizon miser -2.104081e+00 14.709918929
## nameplymouth horizon tc3 -3.028929e+00 13.448756730
## nameplymouth reliant -8.010794e+00 6.920780046
## nameplymouth sapporo -8.542421e+00 7.011473598
## nameplymouth satellite -2.161798e+00 10.890787357
## nameplymouth satellite custom -6.563692e+00 7.460342792
## nameplymouth satellite custom (sw) -3.323449e+00 9.770115298
## nameplymouth satellite sebring -5.205111e+00 8.704715034
## nameplymouth valiant -4.877955e+00 7.343766535
## nameplymouth valiant custom -6.979486e+00 6.951332677
## nameplymouth volare -5.845819e+00 7.969537486
## nameplymouth volare custom -5.657543e+00 8.212765128
## nameplymouth volare premier v8 -7.755572e+00 5.191152900
## namepontiac astro -7.699309e+00 7.848449794
## namepontiac catalina 3.251251e-04 10.889749806
## namepontiac catalina brougham -1.526419e+00 11.702315704
## namepontiac firebird -4.796293e+00 9.319525671
## namepontiac grand prix -4.148548e-01 13.216945054
## namepontiac grand prix lj -4.245968e+00 8.776142946
## namepontiac j2000 se hatchback -5.328750e+00 10.972800631
## namepontiac lemans v6 -6.483052e+00 7.283053474
## namepontiac phoenix -4.114430e+00 10.367614263
## namepontiac phoenix lj -5.532882e+00 8.249781191
## namepontiac safari (sw) 9.363397e-02 14.232172375
## namepontiac sunbird coupe -7.706423e+00 7.923291846
## namepontiac ventura sj -5.758675e+00 7.963115337
## namerenault 12 (sw) -5.268975e+00 8.233308995
## namerenault 12tl -7.226178e+00 5.762885375
## namerenault 5 gtl 9.069678e-02 13.206018498
## namesaab 99e -3.650224e+00 10.391902636
## namesaab 99gle -1.042413e+01 3.560741274
## namesaab 99le -5.663990e+00 6.517329411
## namesubaru -1.254750e+01 12.080938957
## namesubaru dl -1.129244e+01 13.148229252
## nametoyota carina -1.796766e+01 8.330965982
## nametoyota celica gt -1.198473e+01 13.608633282
## nametoyota celica gt liftback -2.058375e+01 5.084590650
## nametoyota corolla -1.147422e+01 12.479587810
## nametoyota corolla 1200 -7.956873e+00 17.151147347
## nametoyota corolla 1600 (sw) -1.204198e+01 13.770070279
## nametoyota corolla liftback -1.519351e+01 10.476227385
## nametoyota corolla tercel -6.395331e+00 18.924756223
## nametoyota corona -1.334929e+01 10.915113860
## nametoyota corona hardtop -1.458144e+01 11.334691083
## nametoyota corona liftback -1.226086e+01 13.509834326
## nametoyota corona mark ii -1.325476e+01 12.860772986
## nametoyota cressida -1.569225e+01 11.328023931
## nametoyota mark ii -1.657789e+01 10.241808625
## nametoyota starlet -7.653819e+00 17.186127380
## nametoyota tercel -7.603241e+00 17.472287386
## nametoyouta corona mark ii (sw) -1.508962e+01 10.918618345
## nametriumph tr7 coupe -4.968459e-01 12.543505979
## namevokswagen rabbit -9.242237e+00 3.588024661
## namevolkswagen 1131 deluxe sedan -5.616750e+00 8.612099062
## namevolkswagen 411 (sw) -7.813300e+00 5.918435048
## namevolkswagen dasher -6.193285e+00 4.476795091
## namevolkswagen jetta -5.306004e+00 7.531434077
## namevolkswagen model 111 -5.131819e+00 8.587022609
## namevolkswagen rabbit -6.670773e+00 4.520983737
## namevolkswagen rabbit custom -7.463379e+00 5.360731653
## namevolkswagen rabbit custom diesel 7.943695e+00 21.500326875
## namevolkswagen rabbit l -3.325831e+00 9.576541096
## namevolkswagen scirocco -5.458894e+00 7.343541736
## namevolkswagen super beetle -6.645816e+00 7.267936982
## namevolkswagen type 3 -6.491839e+00 8.020805436
## namevolvo 144ea -9.884725e+00 4.351811434
## namevolvo 145e (sw) -1.051493e+01 3.837155715
## namevolvo 244dl -8.706730e+00 5.125012984
## namevolvo 245 -9.914119e+00 4.217867312
## namevolvo 264gl -1.267928e+01 1.750515564
## namevolvo diesel 7.873274e-03 14.549406608
## namevw dasher (diesel) 9.309088e+00 23.242171238
## namevw pickup 8.194527e+00 22.454525802
## namevw rabbit -7.890473e-01 10.302806384
## namevw rabbit c (diesel) 8.404969e+00 21.924170725
## namevw rabbit custom NA NA
Exercise 10
fit_1 <- lm(Sales ~ Price + Urban + US, data = Carseats)
summary(fit_1)
##
## Call:
## lm(formula = Sales ~ Price + Urban + US, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9206 -1.6220 -0.0564 1.5786 7.0581
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.043469 0.651012 20.036 < 2e-16 ***
## Price -0.054459 0.005242 -10.389 < 2e-16 ***
## UrbanYes -0.021916 0.271650 -0.081 0.936
## USYes 1.200573 0.259042 4.635 4.86e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.472 on 396 degrees of freedom
## Multiple R-squared: 0.2393, Adjusted R-squared: 0.2335
## F-statistic: 41.52 on 3 and 396 DF, p-value: < 2.2e-16
fit_2 <- update(fit, . ~ . - Urban)
confint(fit_2, level = 0.95)
## 2.5 % 97.5 %
## (Intercept) -2.521072e+01 25.585326295
## cylinders -2.144167e+00 0.307974681
## displacement -2.801806e-02 0.034100283
## horsepower -1.001407e-01 0.015456257
## weight -6.597404e-03 -0.001787893
## acceleration -8.225110e-01 -0.140386794
## year 4.134250e-01 0.859570558
## origin -7.112396e+00 9.760923634
## nameamc ambassador dpl -3.081785e+00 9.824501176
## nameamc ambassador sst -3.139209e+00 9.867737277
## nameamc concord -6.634193e+00 6.389192526
## nameamc concord d/l -8.492300e+00 5.119203547
## nameamc concord dl 6 -7.517358e+00 6.457985133
## nameamc gremlin -6.308484e+00 5.455272834
## nameamc hornet -5.502859e+00 6.040911506
## nameamc hornet sportabout (sw) -7.415954e+00 6.609731801
## nameamc matador -4.841939e+00 5.766405532
## nameamc matador (sw) -2.635436e+00 8.873294610
## nameamc pacer -6.985350e+00 7.009676134
## nameamc pacer d/l -8.675046e+00 5.311043346
## nameamc rebel sst -3.653805e+00 9.405687083
## nameamc spirit dl -7.366251e+00 8.792251369
## nameaudi 100 ls -5.921428e+00 7.793936489
## nameaudi 100ls -9.067884e+00 2.800988068
## nameaudi 4000 -2.445480e+00 10.455167332
## nameaudi 5000 -1.097031e+01 2.752149766
## nameaudi 5000s (diesel) 4.705410e+00 18.600443234
## nameaudi fox -3.419397e+00 9.818370072
## namebmw 2002 -4.736473e+00 8.902259276
## namebmw 320i -1.203738e+01 1.396027789
## namebuick century -3.898273e+00 8.324823749
## namebuick century 350 -4.300622e+00 8.626737400
## namebuick century limited -6.108928e+00 8.417940240
## namebuick century luxus (sw) -3.053375e+00 10.456523165
## namebuick century special -6.423896e+00 7.367222542
## namebuick electra 225 custom -1.356447e+00 12.488244600
## namebuick estate wagon (sw) -3.444321e+00 8.021043328
## namebuick lesabre custom -2.783147e+00 10.540907491
## namebuick opel isuzu deluxe -5.772272e+00 10.494078009
## namebuick regal sport coupe (turbo) -8.074107e+00 6.532589668
## namebuick skyhawk -5.689012e+00 8.045042688
## namebuick skylark -6.060688e+00 7.032538202
## namebuick skylark 320 -3.220933e+00 9.662027914
## namebuick skylark limited -5.317780e+00 10.371055813
## namecadillac eldorado 6.779078e-01 14.335702492
## namecadillac seville -1.870291e+00 11.282117623
## namecapri ii -7.688046e+00 8.115635188
## namechevroelt chevelle malibu -5.771806e+00 8.153579019
## namechevrolet bel air -3.100145e+00 10.153634134
## namechevrolet camaro -6.866618e+00 8.900558131
## namechevrolet caprice classic -3.893422e+00 6.865804684
## namechevrolet cavalier -6.365561e+00 9.789075341
## namechevrolet cavalier 2-door -2.061106e+00 14.183072046
## namechevrolet cavalier wagon -7.705490e+00 8.459592377
## namechevrolet chevelle concours (sw) -5.188990e+00 8.184963317
## namechevrolet chevelle malibu -3.480260e+00 8.497306938
## namechevrolet chevelle malibu classic -3.763584e+00 8.061327286
## namechevrolet chevette -4.328171e+00 9.921347513
## namechevrolet citation -5.680714e+00 7.350763122
## namechevrolet concours -7.794554e+00 5.870415611
## namechevrolet impala -1.376876e+00 9.180825543
## namechevrolet malibu -5.444528e+00 6.122389074
## namechevrolet malibu classic (sw) -5.131567e+00 8.265384910
## namechevrolet monte carlo -5.224618e+00 8.735739546
## namechevrolet monte carlo landau -4.266565e+00 6.987528811
## namechevrolet monte carlo s -3.733137e+00 9.367783262
## namechevrolet monza 2+2 -4.836733e+00 8.758376218
## namechevrolet nova -5.816638e+00 5.843371695
## namechevrolet nova custom -7.509304e+00 6.341698321
## namechevrolet vega -6.986098e+00 6.738479835
## namechevrolet vega (sw) -7.032604e+00 8.704173542
## namechevrolet vega 2300 -2.600958e+00 13.219223225
## namechevrolet woody -7.780263e+00 8.265065859
## namechevy c10 -8.232607e+00 4.858965931
## namechevy c20 -3.085957e+00 11.849843722
## namechevy s-10 -3.162665e+00 12.807227137
## namechrysler cordoba -3.380992e+00 9.697654329
## namechrysler lebaron medallion -1.082404e+01 5.240189288
## namechrysler lebaron salon -1.164846e+01 2.598671500
## namechrysler lebaron town @ country (sw) -4.481761e+00 8.650322406
## namechrysler new yorker brougham -1.458391e+00 12.023353100
## namechrysler newport royal -2.152870e+00 10.936753071
## namedatsun 1200 -5.370027e+00 20.274870868
## namedatsun 200-sx -1.800500e+01 7.540352585
## namedatsun 200sx -9.989239e+00 15.624276258
## namedatsun 210 -6.713040e+00 17.925246331
## namedatsun 210 mpg -7.634819e+00 17.775434890
## namedatsun 280-zx -7.684983e+00 19.477083834
## namedatsun 310 -7.837928e+00 17.125717684
## namedatsun 310 gx -8.415049e+00 16.501978508
## namedatsun 510 -1.519414e+01 10.256448015
## namedatsun 510 (sw) -9.975868e+00 16.100581329
## namedatsun 510 hatchback -6.163162e+00 19.268559879
## namedatsun 610 -1.639661e+01 9.632407602
## namedatsun 710 -1.120852e+01 13.871020696
## namedatsun 810 -1.676902e+01 10.338340875
## namedatsun 810 maxima -1.608340e+01 11.198763579
## namedatsun b-210 -1.026822e+01 15.012056131
## namedatsun b210 -9.517753e+00 16.180408420
## namedatsun b210 gx -3.129314e+00 22.338624545
## namedatsun f-10 hatchback -9.633384e+00 15.534311920
## namedatsun pl510 -1.145343e+01 13.416778538
## namedodge aries se -7.632117e+00 8.439747070
## namedodge aries wagon (sw) -1.024946e+01 5.735805772
## namedodge aspen -6.347337e+00 5.933570330
## namedodge aspen 6 -6.523407e+00 7.256265536
## namedodge aspen se -3.944112e+00 9.948420963
## namedodge challenger se -4.477932e+00 8.607300956
## namedodge charger 2.2 -2.974878e+00 13.594094416
## namedodge colt -5.644263e+00 8.609055128
## namedodge colt (sw) -4.461930e+00 11.895829765
## namedodge colt hardtop -6.566200e+00 9.610295327
## namedodge colt hatchback custom -2.716594e+00 13.973847481
## namedodge colt m/m -1.941928e+00 14.385220136
## namedodge coronet brougham -3.871843e+00 9.211167938
## namedodge coronet custom -4.849102e+00 8.062837656
## namedodge coronet custom (sw) -3.386832e+00 9.992471244
## namedodge d100 -8.144151e+00 4.798770156
## namedodge d200 -2.374072e+00 12.523863337
## namedodge dart custom -7.192013e+00 5.791759393
## namedodge diplomat -3.965302e+00 9.089060949
## namedodge magnum xe -4.199335e+00 8.897470737
## namedodge monaco (sw) -1.500851e+00 12.320748922
## namedodge monaco brougham -5.085928e+00 7.983599375
## namedodge omni -5.608579e+00 10.810489117
## namedodge rampage -8.118147e+00 8.760409452
## namedodge st. regis -4.706579e+00 8.456318786
## namefiat 124 sport coupe -5.830282e+00 7.517867709
## namefiat 124 tc -7.843932e+00 5.275107262
## namefiat 124b -2.427707e+00 10.896566376
## namefiat 128 -6.091229e+00 5.485589132
## namefiat 131 -5.015645e+00 8.159439567
## namefiat strada custom 1.003326e-01 12.911148312
## namefiat x1.9 -3.113599e+00 9.955353727
## nameford country -3.044694e+00 10.666322951
## nameford country squire (sw) -3.160462e+00 8.336508645
## nameford escort 2h -5.155085e+00 10.961500089
## nameford escort 4w -4.463770e+00 12.128070381
## nameford f108 -8.070334e+00 5.055786154
## nameford f250 -1.879365e+00 12.632349008
## nameford fairmont -6.149283e+00 9.526243360
## nameford fairmont (auto) -9.533072e+00 4.691359229
## nameford fairmont (man) -8.179328e+00 7.644661005
## nameford fairmont 4 -9.921560e+00 5.768903670
## nameford fairmont futura -1.063379e+01 5.324642728
## nameford fiesta -2.816041e+00 13.996398603
## nameford futura -8.601874e+00 4.768261485
## nameford galaxie 500 -9.193453e-01 9.804304622
## nameford gran torino -3.007353e+00 7.797650601
## nameford gran torino (sw) -1.723904e+00 10.335722121
## nameford granada -6.109489e+00 7.714598477
## nameford granada ghia -5.931327e+00 8.452417122
## nameford granada gl -1.028317e+01 3.924896634
## nameford granada l -1.032546e+01 3.934341321
## nameford ltd -2.876614e+00 8.739290260
## nameford ltd landau -6.851726e+00 6.377002480
## nameford maverick -5.773989e+00 6.181042823
## nameford mustang -7.390243e+00 7.216715879
## nameford mustang gl -8.629805e+00 7.413337860
## nameford mustang ii -1.198609e+01 1.393068671
## nameford mustang ii 2+2 -6.722851e+00 9.024509002
## nameford pinto -7.338556e+00 5.788315227
## nameford pinto (sw) -8.608711e+00 7.304645861
## nameford pinto runabout -1.006502e+01 5.825285933
## nameford ranger -7.081898e+00 8.899403193
## nameford thunderbird -3.335651e+00 9.776798162
## nameford torino -3.824668e+00 9.431688308
## nameford torino 500 -5.171912e+00 9.328086520
## namehi 1200d -1.649951e+00 14.194600366
## namehonda accord -1.021341e+01 14.110453643
## namehonda accord cvcc -1.071976e+01 14.847704309
## namehonda accord lx -1.373132e+01 11.511444331
## namehonda civic -1.098755e+01 13.094058929
## namehonda civic (auto) -1.474315e+01 10.097071585
## namehonda civic 1300 -1.189602e+01 12.857145773
## namehonda civic 1500 gl -2.166950e+00 22.473047434
## namehonda civic cvcc -8.992491e+00 15.357786002
## namehonda prelude -1.178255e+01 13.192260907
## namemaxda glc deluxe -1.099810e+01 13.834453687
## namemaxda rx3 -2.332811e+01 1.593154361
## namemazda 626 -1.050645e+01 14.475224163
## namemazda glc 2.533511e+00 27.761686682
## namemazda glc 4 -1.177474e+01 13.142920772
## namemazda glc custom -1.491154e+01 10.221578588
## namemazda glc custom l -8.450226e+00 16.799194399
## namemazda glc deluxe -1.040542e+01 14.990554037
## namemazda rx-4 -1.941555e+01 6.219116353
## namemazda rx-7 gs -2.086877e+01 3.988841855
## namemazda rx2 coupe -2.073196e+01 4.590163633
## namemercedes-benz 240d -7.835999e-01 13.646300552
## namemercedes-benz 280s -8.470087e+00 7.320462044
## namemercedes benz 300d -3.332137e+00 11.436784991
## namemercury capri 2000 -8.812814e+00 7.388521431
## namemercury capri v6 -7.642747e+00 7.035603007
## namemercury cougar brougham -5.094385e+00 8.274302566
## namemercury grand marquis -6.873785e+00 6.399232094
## namemercury lynx l -2.374045e+00 14.118783727
## namemercury marquis -3.434218e+00 9.890988048
## namemercury marquis brougham -2.061125e+00 11.554413990
## namemercury monarch -9.263086e+00 5.358353046
## namemercury monarch ghia -4.074028e+00 9.041684960
## namemercury zephyr -8.014176e+00 6.119528022
## namemercury zephyr 6 -9.261526e+00 4.867405606
## namenissan stanza xe -9.850484e+00 15.286050528
## nameoldsmobile cutlass ciera (diesel) 6.064185e+00 20.799764713
## nameoldsmobile cutlass ls 1.743041e+00 16.304098361
## nameoldsmobile cutlass salon brougham -1.642455e+00 10.663515001
## nameoldsmobile cutlass supreme -3.037417e+00 10.756435461
## nameoldsmobile delta 88 royale -3.718198e+00 9.513656942
## nameoldsmobile omega -8.831726e+00 3.999478766
## nameoldsmobile omega brougham -4.944909e+00 9.720448050
## nameoldsmobile starfire sx -7.867302e+00 7.662068114
## nameoldsmobile vista cruiser -3.838790e+00 9.452612744
## nameopel 1900 -5.379838e+00 6.108195120
## nameopel manta -7.202888e+00 4.275717433
## namepeugeot 304 -4.662480e-01 13.371696672
## namepeugeot 504 -3.749583e+00 8.261868839
## namepeugeot 504 (sw) -6.063030e+00 8.474441836
## namepeugeot 505s turbo diesel -3.392699e+00 10.797949969
## namepeugeot 604sl -1.143079e+01 3.961899440
## nameplymouth 'cuda 340 -6.583497e+00 6.587485075
## nameplymouth arrow gs -8.559496e+00 7.459245264
## nameplymouth champ -5.916485e-01 16.211330240
## nameplymouth cricket -4.407945e+00 11.853982242
## nameplymouth custom suburb -2.429884e+00 10.917208952
## nameplymouth duster -2.890989e+00 9.091314009
## nameplymouth fury -4.418109e+00 9.647388215
## nameplymouth fury gran sedan -3.095845e+00 10.092612557
## nameplymouth fury iii -1.028966e+00 9.628090681
## nameplymouth grand fury -1.380452e+00 12.019790654
## nameplymouth horizon -4.077935e+00 12.680100850
## nameplymouth horizon 4 -4.216829e+00 12.442917971
## nameplymouth horizon miser -2.104081e+00 14.709918929
## nameplymouth horizon tc3 -3.028929e+00 13.448756730
## nameplymouth reliant -8.010794e+00 6.920780046
## nameplymouth sapporo -8.542421e+00 7.011473598
## nameplymouth satellite -2.161798e+00 10.890787357
## nameplymouth satellite custom -6.563692e+00 7.460342792
## nameplymouth satellite custom (sw) -3.323449e+00 9.770115298
## nameplymouth satellite sebring -5.205111e+00 8.704715034
## nameplymouth valiant -4.877955e+00 7.343766535
## nameplymouth valiant custom -6.979486e+00 6.951332677
## nameplymouth volare -5.845819e+00 7.969537486
## nameplymouth volare custom -5.657543e+00 8.212765128
## nameplymouth volare premier v8 -7.755572e+00 5.191152900
## namepontiac astro -7.699309e+00 7.848449794
## namepontiac catalina 3.251251e-04 10.889749806
## namepontiac catalina brougham -1.526419e+00 11.702315704
## namepontiac firebird -4.796293e+00 9.319525671
## namepontiac grand prix -4.148548e-01 13.216945054
## namepontiac grand prix lj -4.245968e+00 8.776142946
## namepontiac j2000 se hatchback -5.328750e+00 10.972800631
## namepontiac lemans v6 -6.483052e+00 7.283053474
## namepontiac phoenix -4.114430e+00 10.367614263
## namepontiac phoenix lj -5.532882e+00 8.249781191
## namepontiac safari (sw) 9.363397e-02 14.232172375
## namepontiac sunbird coupe -7.706423e+00 7.923291846
## namepontiac ventura sj -5.758675e+00 7.963115337
## namerenault 12 (sw) -5.268975e+00 8.233308995
## namerenault 12tl -7.226178e+00 5.762885375
## namerenault 5 gtl 9.069678e-02 13.206018498
## namesaab 99e -3.650224e+00 10.391902636
## namesaab 99gle -1.042413e+01 3.560741274
## namesaab 99le -5.663990e+00 6.517329411
## namesubaru -1.254750e+01 12.080938957
## namesubaru dl -1.129244e+01 13.148229252
## nametoyota carina -1.796766e+01 8.330965982
## nametoyota celica gt -1.198473e+01 13.608633282
## nametoyota celica gt liftback -2.058375e+01 5.084590650
## nametoyota corolla -1.147422e+01 12.479587810
## nametoyota corolla 1200 -7.956873e+00 17.151147347
## nametoyota corolla 1600 (sw) -1.204198e+01 13.770070279
## nametoyota corolla liftback -1.519351e+01 10.476227385
## nametoyota corolla tercel -6.395331e+00 18.924756223
## nametoyota corona -1.334929e+01 10.915113860
## nametoyota corona hardtop -1.458144e+01 11.334691083
## nametoyota corona liftback -1.226086e+01 13.509834326
## nametoyota corona mark ii -1.325476e+01 12.860772986
## nametoyota cressida -1.569225e+01 11.328023931
## nametoyota mark ii -1.657789e+01 10.241808625
## nametoyota starlet -7.653819e+00 17.186127380
## nametoyota tercel -7.603241e+00 17.472287386
## nametoyouta corona mark ii (sw) -1.508962e+01 10.918618345
## nametriumph tr7 coupe -4.968459e-01 12.543505979
## namevokswagen rabbit -9.242237e+00 3.588024661
## namevolkswagen 1131 deluxe sedan -5.616750e+00 8.612099062
## namevolkswagen 411 (sw) -7.813300e+00 5.918435048
## namevolkswagen dasher -6.193285e+00 4.476795091
## namevolkswagen jetta -5.306004e+00 7.531434077
## namevolkswagen model 111 -5.131819e+00 8.587022609
## namevolkswagen rabbit -6.670773e+00 4.520983737
## namevolkswagen rabbit custom -7.463379e+00 5.360731653
## namevolkswagen rabbit custom diesel 7.943695e+00 21.500326875
## namevolkswagen rabbit l -3.325831e+00 9.576541096
## namevolkswagen scirocco -5.458894e+00 7.343541736
## namevolkswagen super beetle -6.645816e+00 7.267936982
## namevolkswagen type 3 -6.491839e+00 8.020805436
## namevolvo 144ea -9.884725e+00 4.351811434
## namevolvo 145e (sw) -1.051493e+01 3.837155715
## namevolvo 244dl -8.706730e+00 5.125012984
## namevolvo 245 -9.914119e+00 4.217867312
## namevolvo 264gl -1.267928e+01 1.750515564
## namevolvo diesel 7.873274e-03 14.549406608
## namevw dasher (diesel) 9.309088e+00 23.242171238
## namevw pickup 8.194527e+00 22.454525802
## namevw rabbit -7.890473e-01 10.302806384
## namevw rabbit c (diesel) 8.404969e+00 21.924170725
## namevw rabbit custom NA NA
Exercise 11
set.seed(1)
n <- 100
x <- rnorm(n)
y <- 2 * x + rnorm(n)
# Part (a):
fit <- lm(y ~ x + 0)
summary(fit)
##
## Call:
## lm(formula = y ~ x + 0)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9154 -0.6472 -0.1771 0.5056 2.3109
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## x 1.9939 0.1065 18.73 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9586 on 99 degrees of freedom
## Multiple R-squared: 0.7798, Adjusted R-squared: 0.7776
## F-statistic: 350.7 on 1 and 99 DF, p-value: < 2.2e-16
# Part (b):
fit <- lm(x ~ y + 0)
summary(fit)
##
## Call:
## lm(formula = x ~ y + 0)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8699 -0.2368 0.1030 0.2858 0.8938
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## y 0.39111 0.02089 18.73 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4246 on 99 degrees of freedom
## Multiple R-squared: 0.7798, Adjusted R-squared: 0.7776
## F-statistic: 350.7 on 1 and 99 DF, p-value: < 2.2e-16
# Part (f): verify that these two regressions give the same t-statistic
fit_x_to_y <- lm(x ~ y)
summary(fit_x_to_y)
##
## Call:
## lm(formula = x ~ y)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.90848 -0.28101 0.06274 0.24570 0.85736
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.03880 0.04266 0.91 0.365
## y 0.38942 0.02099 18.56 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4249 on 98 degrees of freedom
## Multiple R-squared: 0.7784, Adjusted R-squared: 0.7762
## F-statistic: 344.3 on 1 and 98 DF, p-value: < 2.2e-16
fit_y_to_x <- lm(y ~ x)
summary(fit_y_to_x)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.8768 -0.6138 -0.1395 0.5394 2.3462
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.03769 0.09699 -0.389 0.698
## x 1.99894 0.10773 18.556 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9628 on 98 degrees of freedom
## Multiple R-squared: 0.7784, Adjusted R-squared: 0.7762
## F-statistic: 344.3 on 1 and 98 DF, p-value: < 2.2e-16
Exercise 12
set.seed(1)
# Different coefficient estimates in regressions y ~ x and x ~ y:
x <- rnorm(100)
y <- 2 * x + rnorm(100)
coef(lm(y ~ x))
## (Intercept) x
## -0.03769261 1.99893961
coef(lm(x ~ y))
## (Intercept) y
## 0.03880394 0.38942451
# The same coefficient estimates in regressions y ~ x and x ~ y:
x <- rnorm(100)
y <- x
coef(lm(y ~ x))
## (Intercept) x
## -1.110223e-17 1.000000e+00
coef(lm(x ~ y))
## (Intercept) y
## -1.110223e-17 1.000000e+00
Exercise 13
set.seed(1)
x <- rnorm(100)
eps <- rnorm(100, mean = 0, sd = sqrt(0.25))
y_pure <- -1 + 0.5 * x
y <- y_pure + eps
plot(x, y)
fit <- lm(y ~ x)
summary(fit)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.93842 -0.30688 -0.06975 0.26970 1.17309
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.01885 0.04849 -21.010 < 2e-16 ***
## x 0.49947 0.05386 9.273 4.58e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4814 on 98 degrees of freedom
## Multiple R-squared: 0.4674, Adjusted R-squared: 0.4619
## F-statistic: 85.99 on 1 and 98 DF, p-value: 4.583e-15
abline(fit)
abline(a = -1, b = 1/2, col = "green")
legend(-3, 1, c("estimated", "truth"), col = c("black", "green"), lty = c(1, 1))
# Try to fit a quadradic model:
qfit <- lm(y ~ x + I(x^2))
summary(qfit)
##
## Call:
## lm(formula = y ~ x + I(x^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.98252 -0.31270 -0.06441 0.29014 1.13500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.97164 0.05883 -16.517 < 2e-16 ***
## x 0.50858 0.05399 9.420 2.4e-15 ***
## I(x^2) -0.05946 0.04238 -1.403 0.164
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.479 on 97 degrees of freedom
## Multiple R-squared: 0.4779, Adjusted R-squared: 0.4672
## F-statistic: 44.4 on 2 and 97 DF, p-value: 2.038e-14
# Fit different amounts of noise:
confint(fit, level = 0.95)
## 2.5 % 97.5 %
## (Intercept) -1.1150804 -0.9226122
## x 0.3925794 0.6063602
eps_less <- rnorm(100, mean = 0, sd = sqrt(0.1))
y <- y_pure + eps_less
confint(lm(y ~ x), level = 0.95)
## 2.5 % 97.5 %
## (Intercept) -1.0570515 -0.9256389
## x 0.4337114 0.5796757
eps_more <- rnorm(100, mean = 0, sd = sqrt(0.5))
y <- y_pure + eps_more
confint(lm(y ~ x), level = 0.95)
## 2.5 % 97.5 %
## (Intercept) -1.0999424 -0.8185064
## x 0.3043238 0.6169242
Exercise 14
set.seed(1)
x1 <- runif(100)
x2 <- 0.5 * x1 + rnorm(100)/10
y <- 2 + 2 * x1 + 0.3 * x2 + rnorm(100)
# Look at the correlation between x_1 and x_2:
cor(x1, x2)
## [1] 0.8351212
plot(x1, x2)
# dev.off()
summary(lm(y ~ x1 + x2))
##
## Call:
## lm(formula = y ~ x1 + x2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8311 -0.7273 -0.0537 0.6338 2.3359
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.1305 0.2319 9.188 7.61e-15 ***
## x1 1.4396 0.7212 1.996 0.0487 *
## x2 1.0097 1.1337 0.891 0.3754
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.056 on 97 degrees of freedom
## Multiple R-squared: 0.2088, Adjusted R-squared: 0.1925
## F-statistic: 12.8 on 2 and 97 DF, p-value: 1.164e-05
summary(lm(y ~ x1))
##
## Call:
## lm(formula = y ~ x1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.89495 -0.66874 -0.07785 0.59221 2.45560
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.1124 0.2307 9.155 8.27e-15 ***
## x1 1.9759 0.3963 4.986 2.66e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.055 on 98 degrees of freedom
## Multiple R-squared: 0.2024, Adjusted R-squared: 0.1942
## F-statistic: 24.86 on 1 and 98 DF, p-value: 2.661e-06
summary(lm(y ~ x2))
##
## Call:
## lm(formula = y ~ x2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.62687 -0.75156 -0.03598 0.72383 2.44890
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.3899 0.1949 12.26 < 2e-16 ***
## x2 2.8996 0.6330 4.58 1.37e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.072 on 98 degrees of freedom
## Multiple R-squared: 0.1763, Adjusted R-squared: 0.1679
## F-statistic: 20.98 on 1 and 98 DF, p-value: 1.366e-05
x1 <- c(x1, 0.1)
x2 <- c(x2, 0.8)
y <- c(y, 6)
# Consider what each model thinks about the mismeasured point:
plot(lm(y ~ x1 + x2)) # 101 is a high-leverage point in this model
plot(lm(y ~ x1)) # 101 is a outlier and a high-leverage point in this model
plot(lm(y ~ x2)) # 101 is a high-leverage point in this model
Exercise 15
library(MASS)
set.seed(1)
# Loop over each predictor and look for a statistically signficant simple linear regression:
crim <- Boston[, 1]
model_f_value <- c()
model_p_value <- c()
univariate_beta_value <- c()
possible_predictors <- colnames(Boston)
for (pi in 1:length(possible_predictors)) {
if (possible_predictors[pi] == "crim") {
next
}
x <- Boston[, pi]
m <- lm(crim ~ x, data = Boston)
s <- summary(m)
model_f_value <- c(model_f_value, s$fstatistic[1])
model_p_value <- c(model_p_value, anova(m)$"Pr(>F)"[1])
univariate_beta_value <- c(univariate_beta_value, coefficients(m)["x"])
print(sprintf("%s %10.6f", possible_predictors[pi], coefficients(m)["x"]))
}
## [1] "zn -0.073935"
## [1] "indus 0.509776"
## [1] "chas -1.892777"
## [1] "nox 31.248531"
## [1] "rm -2.684051"
## [1] "age 0.107786"
## [1] "dis -1.550902"
## [1] "rad 0.617911"
## [1] "tax 0.029742"
## [1] "ptratio 1.151983"
## [1] "black -0.036280"
## [1] "lstat 0.548805"
## [1] "medv -0.363160"