Data
cat("\014")
library(ISLR)
library(boot)
head(Auto) #data used
## mpg cylinders displacement horsepower weight acceleration year origin
## 1 18 8 307 130 3504 12.0 70 1
## 2 15 8 350 165 3693 11.5 70 1
## 3 18 8 318 150 3436 11.0 70 1
## 4 16 8 304 150 3433 12.0 70 1
## 5 17 8 302 140 3449 10.5 70 1
## 6 15 8 429 198 4341 10.0 70 1
## name
## 1 chevrolet chevelle malibu
## 2 buick skylark 320
## 3 plymouth satellite
## 4 amc rebel sst
## 5 ford torino
## 6 ford galaxie 500
?Auto #information about data
## starting httpd help server ... done
Leave one out cross validation (LOOCV) and 10 fold cross validation
glm.fit=glm(mpg~horsepower,data=Auto) #linear model
cv.glm(Auto,glm.fit) #left one observation and fits the data
## $call
## cv.glm(data = Auto, glmfit = glm.fit)
##
## $K
## [1] 392
##
## $delta
## [1] 24.23151 24.23114
##
## $seed
## [1] 403 10 -26898344 -1857319493 -1105222823
## [6] -1698836248 992997654 -2015718767 1663622979 787528274
## [11] -1552626460 -1435379929 -200649859 118761076 1340086362
## [16] -1667506011 -1042431297 1542265158 -467783728 -1080120845
## [21] -315865839 -2138513088 2129547550 605611497 1554900763
## [26] 2118586666 1476037196 126178831 2070133061 -1743215876
## [31] 200038738 1773498061 -644069753 1005015406 538225480
## [36] -193401013 -1544505687 -2130736136 -1534282970 -684657599
## [41] 1736381907 -1768941694 -1099605068 -921914569 2057982509
## [46] -283225276 627849322 -736042283 1420139631 -59861642
## [51] -1482285408 -210330781 -684298239 1905957744 648925966
## [56] 418819449 -1671263989 2076604986 1427648828 436444799
## [61] -1633155627 -526156820 1928363330 -685243747 -448549097
## [66] -1181430146 1755639352 -1297491685 -2075492743 781335240
## [71] 762473206 -2002525391 -466406557 1761872178 -477595004
## [76] -1561995577 1402150301 329709844 -1616177222 -31211003
## [81] -79096865 -207361434 721479152 451388179 727125169
## [86] 993365856 1664814334 -961180535 -1256150085 1629488522
## [91] -1922235284 -1954636305 -751397339 1627304668 741566642
## [96] 489237421 -1464635545 241908878 -345589400 1111812459
## [101] -404034807 -737002088 1560554694 228177441 -2092198221
## [106] -712983518 957531668 73775767 316961933 -2128938588
## [111] 752739210 1760972789 1643593295 1387022678 -875367424
## [116] -1922728637 740290785 -512193968 -1782008146 311624281
## [121] 1122511467 -2106482726 1922883740 -933719393 -286899979
## [126] 950946188 657712226 -1678040003 -1141815625 -481204898
## [131] -2024395624 1519351803 -686867047 551501352 114738902
## [136] -400813231 4929027 2129033618 -39942364 729475559
## [141] 1825064509 -1561956172 -1022957798 393399397 1825621247
## [146] 1731831174 -1615832304 1264000947 -46029743 660916224
## [151] 1388271838 89592617 1622085339 734764522 2120770956
## [156] 1567341263 -315423099 -1194449604 107079698 106743565
## [161] -1497357241 722142766 -1360072824 -1194349941 -2057356183
## [166] -865951688 -2138216218 2052558977 977741843 -840679486
## [171] -516175756 -537223561 489684845 -705658876 -86279382
## [176] 451076245 -849387729 2087577142 1031619168 1881981091
## [181] -968174655 -1948639312 1808689870 -896837575 -1182179765
## [186] 625697786 1937084156 747946815 -1786999787 1763469100
## [191] -919647230 1689808605 -478462505 -1526490946 1316866808
## [196] 229134555 -1986702535 -1806133624 -2003901898 1839184497
## [201] -1031749469 1073121778 954624324 -844316153 -46247971
## [206] 1160911060 -1648891910 -1261658299 1734986655 240812326
## [211] 1240920496 1810934355 29627761 930739360 1031492670
## [216] 359144265 -164804101 -2010763830 1928618796 -518780113
## [221] -1654992411 -1006183268 -2006779662 1668264301 -687341913
## [226] -1904332594 -988258776 -1016912341 -1874023351 -361964596
## [231] 127874272 -684950846 966279208 2076976044 1141838524
## [236] 212327922 -1398723024 -225884252 1612948920 -373225638
## [241] -584857456 539157372 1687771924 -2100068030 -1388780800
## [246] -7985220 2131632976 -646451934 1688409672 961783820
## [251] -322434980 2026262994 -31641088 459536724 -899906328
## [256] 1417854202 187391696 1253319980 -1106130700 -1975333486
## [261] -474640032 1038929932 1961981664 -2029180318 86042280
## [266] -2011134388 876569468 467461426 486340208 -824931516
## [271] 1780777944 135516026 518097456 1833233340 1650578004
## [276] 219841602 252412064 -1751237956 1889041872 -998946974
## [281] -426489112 167367884 -208728580 -287589902 -1810950528
## [286] 416028148 -24333688 -1710842054 20250448 326761580
## [291] 435778964 -719141806 2066094560 979397836 1867917472
## [296] -838891134 -1949247256 1304992492 844547388 -306199438
## [301] -1250816912 -389704668 181096504 300573466 -275749680
## [306] -140831940 69148564 -1130489982 1550806464 577499708
## [311] -1859356272 912806434 -534639352 410870412 1724450588
## [316] -784308078 -1230575232 -1293833708 613278504 -872063430
## [321] -599141936 1610790252 -1372492876 -1809708014 -762504736
## [326] -666903604 -1871312672 -1564344286 1845103912 1740123660
## [331] -2081588420 -1650621454 1766612720 830415428 -1517621672
## [336] 783450938 738058736 131690172 -1963447020 244659906
## [341] -2492320 -1462888580 759610320 1594092834 1085900456
## [346] -511075444 -1626968900 637945650 11352640 1370747060
## [351] 1912199752 -279261766 -438316528 1078884076 276694356
## [356] -1500826350 2093689248 -235587892 -1597923744 -1137882174
## [361] -115217624 680373164 1076592444 188775794 -775950544
## [366] -101501660 -40643784 1498828506 84482960 -2100000004
## [371] -595143788 347922498 -1358622464 -1333142468 -1773808304
## [376] -421211998 -2129820344 709827340 -738829604 88154450
## [381] -714332032 240069716 -1670573080 -106435334 341946192
## [386] 1777956652 -471868044 -1729577070 -2143277984 -412924532
## [391] 600851296 -1338923550 1434588072 -2050467636 -816016388
## [396] 1493152178 330153456 -259874876 880609624 884297082
## [401] 318437296 -920724036 -424127404 -1671559230 -1377802208
## [406] 1758478524 -827849136 -974276638 1133598824 1446107212
## [411] 1205298428 -412788750 -176620288 1620366708 -1925693432
## [416] -1284222022 -1204628016 -8368148 -1929910892 -1394810414
## [421] 395794784 24697676 -1911967456 -900987006 1044479720
## [426] -676615956 -1810692036 -2098643086 -1873916304 5946404
## [431] 1338560312 -2069447526 -1960394032 -2084712260 1736900244
## [436] 1245998722 -211910464 1033217852 -1484427120 1009384994
## [441] -105190392 1935682828 -432456548 -1151421934 1958351744
## [446] 54339092 603258408 -1220625094 635432400 -1399965588
## [451] -308591308 -1643918702 877657952 -621998260 1200871392
## [456] -865989726 1688866108 909674858 190317471 2100510249
## [461] -1837211458 1944795564 -682023171 -1069161913 898707760
## [466] 1408219726 1220715131 -1679900195 -1035204598 2077350184
## [471] 640837521 -1367479933 215713412 920761522 1997161479
## [476] 1370558545 -812892202 -813494604 -1197953339 -2047959025
## [481] -1326518136 -1306439258 -127088301 1818426037 -2079698926
## [486] -1252285984 675959881 -913374597 -107001012 2089418458
## [491] 833589967 1395258009 1045733038 933510076 -1653373907
## [496] 741788631 1130881568 1410589566 -738349749 1083838285
## [501] -1067293318 1110005688 -622981791 2104705299 11188532
## [506] 414217026 572449623 -1178180959 -1175481498 -2074235548
## [511] 1907972245 -1894950465 -807793320 -1157434506 1833734531
## [516] 749786053 -1614739230 1275669840 311917689 82775979
## [521] -1021610724 1779794506 1160807999 -354542967 -1345208674
## [526] 874027852 290077469 -1377351001 2067038672 381462894
## [531] -1779379173 -1775927939 747895658 1934654984 297054897
## [536] 1278901539 -1916907996 -463690542 -859871961 -69046415
## [541] -1577964106 302323028 2129171429 -1686483473 965825832
## [546] 315090310 1463927219 -1191830251 -825491598 -723366976
## [551] 956324905 -2043991909 1780790636 -1883034246 1197170351
## [556] 900892089 -685430834 -1551612132 216528525 1960687351
## [561] -690898432 -1506605986 -512587989 256386093 -1196854118
## [566] -793692072 -1065652287 -126091149 1951742356 2033236002
## [571] -1565708489 2136027649 1269787398 -1968883900 -2072327563
## [576] 1080273887 -53088456 2066020630 661480739 -1177069851
## [581] -1077858558 983614832 465974553 978767115 1565150716
## [586] -2051447254 1004629599 -849113623 -1365242114 1752993516
## [591] -439550403 -1900818937 2070340080 -1027939954 -1642584133
## [596] 880841117 720310090 -374901912 -1348278959 -969775549
## [601] 1614449476 -1415161870 1621079495 -1504011375 -9825514
## [606] -1741543564 -1205094907 -1823982001 -2120590776 -987853850
## [611] 2029528339 2081159797 -395327406 -283055456 1474918281
## [616] -650378309 416318476 434856346 1814208783 1711951705
## [621] 286999022 -438637444 -1604675347 836915095 305231968
## [626] 189776244
loocv=function(fit){
h=lm.influence(fit)$h
mean((residuals(fit)/(1-h^2)))
}
#loocv
loocv(glm.fit)
## [1] 0.0001626385
cv.error = rep(0,10)
degree = 1:10
for(d in degree){
glm.fit=glm(mpg~poly(horsepower,d),data=Auto)
cv.error[d]=loocv(glm.fit)
}
plot(degree,cv.error,type='b',xlab="Degree of fitted model",ylab="Cross validation Error",col="blue",ylim=c(0,24))
p=which.min(cv.error)
points(p,cv.error[p],pch=20,col="green")
#10 fold cross validation
cv.error10=rep(0,10)
for( d in degree){
glm.fit=glm(mpg~poly(horsepower,d),data=Auto)
cv.error10[d]=cv.glm(Auto,glm.fit,K=10)$delta[1]
}
lines(degree,cv.error10,type="b",col="red")
p1=which.min(cv.error10)
points(p1,cv.error10[p1],pch=20,col="yellow")
legend("topleft",legend=c("Loocv","10 fold CV"),col=c("blue","red"),pch=1)
plot(mpg~horsepower,data=Auto,xlab="Horsepower",ylab="Miles per gallon",main="Best fit line")
glm.fit1=glm(mpg~poly(horsepower,p),data=Auto)
glm.fit2=glm(mpg~poly(horsepower,p1),data=Auto)
points(Auto$horsepower,fitted(glm.fit1),col="blue",pch=20)
points(Auto$horsepower,fitted(glm.fit2),col="red",pch=20)
legend("topright",legend=c("LOOCV","10 fold"),col=c("blue","red"),pch=20)
