Chapter 5 - Bootstrap
Bruce Kim
October 12, 2016
Chapter 6
- In this exercise, we will predict the number of applications received using the other variables in the College data set.
- Split the data set into a training set and a test set.
data <- College
set.seed(15495)
iTrain <- createDataPartition(y = College$Apps, p = 0.75, list = FALSE)
Train <- data[iTrain, ]
Test <- data[-iTrain, ]- Graph
The application to private university is low compared to public university. But, this might come from the fact that the number of private university in the sample is low compared to public.
qplot(x = Private, y = log(Apps+1), data = Train, geom = "boxplot",
main = "Application per Private status")
But, given the table, private college in the sample is significantly high than non-private ones, counting 421.
table(Train$Private)##
## No Yes
## 163 422- Fit a linear model using least squares on the training set, and report the test error obtained.
set.seed(13587)
ctrl <- trainControl(method = "repeatedcv", number = 10)
fit.lin <- train(Apps ~. , data = Train, trControl = ctrl, method = "lmStepAIC" )## Start: AIC=7323.86
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 179266 547505047 7322.0
## - Personal 1 298768 547624549 7322.2
## - Terminal 1 388306 547714087 7322.2
## - P.Undergrad 1 1473678 548799459 7323.3
## - perc.alumni 1 1900094 549225875 7323.7
## - PhD 1 1934977 549260758 7323.7
## <none> 547325781 7323.9
## - S.F.Ratio 1 3077936 550403718 7324.8
## - Outstate 1 5230917 552556699 7326.9
## - Top25perc 1 7182685 554508466 7328.7
## - Enroll 1 7531883 554857664 7329.1
## - F.Undergrad 1 8180795 555506576 7329.7
## - PrivateYes 1 9854403 557180184 7331.2
## - Grad.Rate 1 10396357 557722138 7331.8
## - Room.Board 1 11889094 559214875 7333.2
## - Expend 1 24494444 571820226 7344.9
## - Top10perc 1 52454155 599779937 7370.0
## - Accept 1 484103728 1031429509 7655.2
##
## Step: AIC=7322.04
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Personal +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Terminal 1 348181 547853228 7320.4
## - Personal 1 395139 547900186 7320.4
## - P.Undergrad 1 1522177 549027224 7321.5
## - perc.alumni 1 2002113 549507160 7322.0
## - PhD 1 2007124 549512171 7322.0
## <none> 547505047 7322.0
## - S.F.Ratio 1 3069514 550574561 7323.0
## - Outstate 1 5356621 552861668 7325.2
## - Top25perc 1 7185420 554690467 7326.9
## - Enroll 1 7591842 555096889 7327.3
## - F.Undergrad 1 8162473 555667521 7327.8
## - PrivateYes 1 9767857 557272904 7329.3
## - Grad.Rate 1 10472613 557977661 7330.0
## - Room.Board 1 12229472 559734519 7331.7
## - Expend 1 24663954 572169002 7343.2
## - Top10perc 1 52819935 600324982 7368.5
## - Accept 1 486013729 1033518776 7654.2
##
## Step: AIC=7320.37
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Personal +
## PhD + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 378212 548231440 7318.7
## - P.Undergrad 1 1530796 549384025 7319.8
## <none> 547853228 7320.4
## - perc.alumni 1 2154172 550007401 7320.4
## - S.F.Ratio 1 3170297 551023525 7321.4
## - Outstate 1 5730243 553583471 7323.8
## - Top25perc 1 7538864 555392092 7325.6
## - Enroll 1 7545437 555398666 7325.6
## - PhD 1 7570127 555423355 7325.6
## - F.Undergrad 1 7961255 555814483 7326.0
## - PrivateYes 1 9481218 557334447 7327.4
## - Grad.Rate 1 10582853 558436082 7328.4
## - Room.Board 1 11912066 559765295 7329.7
## - Expend 1 24425839 572279067 7341.3
## - Top10perc 1 54045176 601898405 7367.9
## - Accept 1 487429980 1035283209 7653.1
##
## Step: AIC=7318.73
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - P.Undergrad 1 1754029 549985469 7318.4
## <none> 548231440 7318.7
## - perc.alumni 1 2445129 550676570 7319.1
## - S.F.Ratio 1 3066579 551298020 7319.7
## - Outstate 1 5908184 554139624 7322.4
## - Enroll 1 7443471 555674911 7323.8
## - Top25perc 1 7499711 555731151 7323.9
## - PhD 1 7589604 555821044 7324.0
## - F.Undergrad 1 8481410 556712850 7324.8
## - PrivateYes 1 9649188 557880629 7325.9
## - Grad.Rate 1 10337468 558568908 7326.6
## - Room.Board 1 11751496 559982936 7327.9
## - Expend 1 24785342 573016782 7340.0
## - Top10perc 1 54082735 602314176 7366.2
## - Accept 1 493920080 1042151520 7654.6
##
## Step: AIC=7318.41
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + Outstate + Room.Board + PhD + S.F.Ratio + perc.alumni +
## Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 549985469 7318.4
## - perc.alumni 1 2552045 552537514 7318.8
## - S.F.Ratio 1 2944150 552929619 7319.2
## - Outstate 1 5997082 555982551 7322.1
## - PhD 1 6893802 556879271 7323.0
## - Top25perc 1 7434518 557419987 7323.5
## - Enroll 1 7678943 557664412 7323.7
## - Grad.Rate 1 9380862 559366331 7325.3
## - PrivateYes 1 9992465 559977934 7325.9
## - F.Undergrad 1 11627915 561613383 7327.4
## - Room.Board 1 12256255 562241724 7328.0
## - Expend 1 25860385 575845854 7340.6
## - Top10perc 1 52733116 602718585 7364.6
## - Accept 1 494693684 1044679153 7653.9
## Start: AIC=7362.46
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 3817 574726923 7360.5
## - Terminal 1 103151 574826257 7360.6
## - Books 1 236234 574959340 7360.7
## - perc.alumni 1 1347064 576070169 7361.7
## - P.Undergrad 1 1734428 576457534 7362.0
## <none> 574723106 7362.5
## - PhD 1 2309734 577032840 7362.6
## - S.F.Ratio 1 2731198 577454304 7363.0
## - Enroll 1 5349364 580072470 7365.3
## - Outstate 1 6288022 581011128 7366.2
## - Grad.Rate 1 6734972 581458078 7366.6
## - F.Undergrad 1 7253798 581976904 7367.1
## - Top25perc 1 9719831 584442937 7369.3
## - PrivateYes 1 13207871 587930977 7372.4
## - Room.Board 1 14818941 589542047 7373.9
## - Expend 1 26520901 601244006 7384.2
## - Top10perc 1 62701336 637424442 7415.0
## - Accept 1 496058019 1070781125 7688.4
##
## Step: AIC=7360.46
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Terminal 1 103075 574829998 7358.6
## - Books 1 232493 574959416 7358.7
## - perc.alumni 1 1355173 576082096 7359.7
## - P.Undergrad 1 1752425 576479348 7360.1
## <none> 574726923 7360.5
## - PhD 1 2313869 577040792 7360.6
## - S.F.Ratio 1 2782525 577509448 7361.0
## - Enroll 1 5358082 580085005 7363.4
## - Outstate 1 6295889 581022812 7364.2
## - Grad.Rate 1 6808399 581535322 7364.7
## - F.Undergrad 1 7268390 581995313 7365.1
## - Top25perc 1 9718724 584445647 7367.3
## - PrivateYes 1 13205954 587932877 7370.4
## - Room.Board 1 14917835 589644758 7372.0
## - Expend 1 26546371 601273295 7382.3
## - Top10perc 1 62708467 637435391 7413.0
## - Accept 1 499912537 1074639460 7688.3
##
## Step: AIC=7358.56
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 218339 575048338 7356.8
## - perc.alumni 1 1468769 576298768 7357.9
## - P.Undergrad 1 1743006 576573004 7358.2
## <none> 574829998 7358.6
## - S.F.Ratio 1 2821113 577651111 7359.1
## - Enroll 1 5297207 580127205 7361.4
## - Outstate 1 6481989 581311987 7362.5
## - PhD 1 6948297 581778295 7362.9
## - Grad.Rate 1 7013194 581843192 7362.9
## - F.Undergrad 1 7182873 582012871 7363.1
## - Top25perc 1 10012757 584842755 7365.7
## - PrivateYes 1 13102878 587932877 7368.4
## - Room.Board 1 14850772 589680770 7370.0
## - Expend 1 26453149 601283148 7380.3
## - Top10perc 1 63613806 638443805 7411.9
## - Accept 1 499882003 1074712002 7686.3
##
## Step: AIC=7356.76
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - perc.alumni 1 1513313 576561650 7356.1
## - P.Undergrad 1 1833438 576881775 7356.4
## <none> 575048338 7356.8
## - S.F.Ratio 1 2792727 577841064 7357.3
## - Enroll 1 5285735 580334073 7359.6
## - Outstate 1 6642418 581690755 7360.8
## - PhD 1 6949912 581998249 7361.1
## - Grad.Rate 1 6968633 582016970 7361.1
## - F.Undergrad 1 7223598 582271936 7361.3
## - Top25perc 1 9977917 585026255 7363.8
## - PrivateYes 1 13064603 588112940 7366.6
## - Room.Board 1 15293307 590341644 7368.6
## - Expend 1 26796468 601844806 7378.8
## - Top10perc 1 64129471 639177809 7410.5
## - Accept 1 499672300 1074720637 7684.3
##
## Step: AIC=7356.14
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - P.Undergrad 1 1963984 578525635 7355.9
## <none> 576561650 7356.1
## - S.F.Ratio 1 3190158 579751808 7357.0
## - Grad.Rate 1 5788485 582350136 7359.4
## - Enroll 1 6284929 582846579 7359.9
## - F.Undergrad 1 7382478 583944129 7360.8
## - PhD 1 7443634 584005284 7360.9
## - Outstate 1 9220074 585781724 7362.5
## - Top25perc 1 10665471 587227122 7363.8
## - PrivateYes 1 13610130 590171781 7366.4
## - Room.Board 1 16966909 593528560 7369.4
## - Expend 1 26660086 603221736 7378.0
## - Top10perc 1 64235137 640796787 7409.8
## - Accept 1 545338693 1121900343 7705.0
##
## Step: AIC=7355.93
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + Outstate + Room.Board + PhD + S.F.Ratio + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 578525635 7355.9
## - S.F.Ratio 1 2951857 581477492 7356.6
## - Grad.Rate 1 4829160 583354795 7358.3
## - Enroll 1 6191397 584717031 7359.5
## - PhD 1 6707840 585233475 7360.0
## - F.Undergrad 1 9353102 587878737 7362.4
## - Outstate 1 9389734 587915369 7362.4
## - Top25perc 1 10567831 589093465 7363.5
## - PrivateYes 1 14409087 592934722 7366.9
## - Room.Board 1 18291283 596816917 7370.3
## - Expend 1 27413402 605939036 7378.3
## - Top10perc 1 62598600 641124235 7408.1
## - Accept 1 544099403 1122625037 7703.3
## Start: AIC=7348.82
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 8996 560051940 7346.8
## - Books 1 234297 560277242 7347.0
## - Terminal 1 497976 560540920 7347.3
## - perc.alumni 1 1315799 561358744 7348.1
## <none> 560042945 7348.8
## - P.Undergrad 1 2438819 562481763 7349.1
## - PhD 1 2963338 563006283 7349.6
## - S.F.Ratio 1 3326648 563369593 7349.9
## - Enroll 1 5456341 565499285 7351.9
## - Outstate 1 5567326 565610270 7352.0
## - F.Undergrad 1 7310198 567353142 7353.7
## - Top25perc 1 7526573 567569517 7353.9
## - Grad.Rate 1 8523356 568566301 7354.8
## - Room.Board 1 12677821 572720765 7358.6
## - PrivateYes 1 15117758 575160702 7360.9
## - Expend 1 27734340 587777285 7372.3
## - Top10perc 1 58775682 618818626 7399.4
## - Accept 1 519744633 1079787577 7692.8
##
## Step: AIC=7346.83
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 226413 560278353 7345.0
## - Terminal 1 498628 560550568 7345.3
## - perc.alumni 1 1309161 561361101 7346.1
## <none> 560051940 7346.8
## - P.Undergrad 1 2457606 562509547 7347.1
## - PhD 1 2967988 563019928 7347.6
## - S.F.Ratio 1 3384079 563436019 7348.0
## - Enroll 1 5465101 565517042 7349.9
## - Outstate 1 5568357 565620297 7350.0
## - F.Undergrad 1 7311279 567363219 7351.7
## - Top25perc 1 7521736 567573676 7351.9
## - Grad.Rate 1 8587402 568639342 7352.9
## - Room.Board 1 12832000 572883940 7356.8
## - PrivateYes 1 15110337 575162277 7358.9
## - Expend 1 27786298 587838238 7370.3
## - Top10perc 1 58766916 618818856 7397.4
## - Accept 1 523505618 1083557558 7692.6
##
## Step: AIC=7345.04
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Terminal 1 459128 560737481 7343.5
## - perc.alumni 1 1386875 561665229 7344.3
## <none> 560278353 7345.0
## - P.Undergrad 1 2572772 562851125 7345.5
## - PhD 1 3043906 563322260 7345.9
## - S.F.Ratio 1 3439722 563718075 7346.3
## - Enroll 1 5437551 565715905 7348.1
## - Outstate 1 5816346 566094699 7348.5
## - F.Undergrad 1 7307529 567585882 7349.9
## - Top25perc 1 7485225 567763578 7350.0
## - Grad.Rate 1 8604856 568883209 7351.1
## - Room.Board 1 13251030 573529384 7355.4
## - PrivateYes 1 14968852 575247205 7356.9
## - Expend 1 28280068 588558422 7369.0
## - Top10perc 1 59234006 619512360 7396.0
## - Accept 1 523306135 1083584488 7690.7
##
## Step: AIC=7343.48
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - perc.alumni 1 1540268 562277749 7342.9
## <none> 560737481 7343.5
## - P.Undergrad 1 2566271 563303752 7343.9
## - S.F.Ratio 1 3528795 564266276 7344.8
## - Enroll 1 5324648 566062129 7346.5
## - Outstate 1 6152976 566890457 7347.2
## - F.Undergrad 1 7099315 567836796 7348.1
## - Top25perc 1 7897779 568635261 7348.8
## - Grad.Rate 1 8822017 569559498 7349.7
## - PhD 1 10816042 571553523 7351.5
## - Room.Board 1 12856696 573594177 7353.4
## - PrivateYes 1 14582881 575320362 7355.0
## - Expend 1 27963258 588700739 7367.1
## - Top10perc 1 60615147 621352628 7395.6
## - Accept 1 523177980 1083915461 7688.8
##
## Step: AIC=7342.92
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 562277749 7342.9
## - P.Undergrad 1 2587409 564865159 7343.3
## - S.F.Ratio 1 4011330 566289080 7344.7
## - Enroll 1 6404889 568682638 7346.9
## - F.Undergrad 1 7363496 569641246 7347.8
## - Grad.Rate 1 7501127 569778877 7347.9
## - Outstate 1 8280960 570558710 7348.6
## - Top25perc 1 8467145 570744894 7348.8
## - PhD 1 11540609 573818358 7351.6
## - Room.Board 1 14551472 576829221 7354.4
## - PrivateYes 1 15489881 577767630 7355.2
## - Expend 1 27968557 590246306 7366.5
## - Top10perc 1 60651318 622929068 7394.9
## - Accept 1 570691352 1132969101 7710.1
## Start: AIC=7313.3
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 713 536448143 7311.3
## - Personal 1 5073 536452504 7311.3
## - F.Undergrad 1 231500 536678931 7311.5
## - Terminal 1 309793 536757223 7311.6
## - Enroll 1 696267 537143698 7312.0
## - perc.alumni 1 855115 537302546 7312.1
## - PhD 1 2031211 538478641 7313.3
## <none> 536447431 7313.3
## - P.Undergrad 1 2074519 538521950 7313.3
## - S.F.Ratio 1 2605234 539052665 7313.9
## - Outstate 1 8184369 544631799 7319.3
## - Grad.Rate 1 9320010 545767441 7320.4
## - Top25perc 1 14615115 551062546 7325.4
## - PrivateYes 1 15612154 552059585 7326.4
## - Room.Board 1 17182738 553630168 7327.9
## - Expend 1 26719076 563166506 7336.9
## - Top10perc 1 69179486 605626917 7375.1
## - Accept 1 492814551 1029261981 7654.1
##
## Step: AIC=7311.3
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Personal +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 4598 536452742 7309.3
## - F.Undergrad 1 231200 536679344 7309.5
## - Terminal 1 311277 536759420 7309.6
## - Enroll 1 696304 537144447 7310.0
## - perc.alumni 1 854592 537302736 7310.1
## - PhD 1 2033288 538481432 7311.3
## <none> 536448143 7311.3
## - P.Undergrad 1 2073809 538521953 7311.3
## - S.F.Ratio 1 2605580 539053724 7311.9
## - Outstate 1 8233172 544681315 7317.3
## - Grad.Rate 1 9319841 545767984 7318.4
## - Top25perc 1 14628421 551076565 7323.5
## - PrivateYes 1 15651123 552099266 7324.4
## - Room.Board 1 17368320 553816463 7326.1
## - Expend 1 26746604 563194747 7334.9
## - Top10perc 1 69229772 605677915 7373.1
## - Accept 1 492912150 1029360293 7652.1
##
## Step: AIC=7309.31
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - F.Undergrad 1 237920 536690662 7307.5
## - Terminal 1 308151 536760893 7307.6
## - Enroll 1 693081 537145823 7308.0
## - perc.alumni 1 895693 537348435 7308.2
## <none> 536452742 7309.3
## - PhD 1 2043871 538496612 7309.3
## - P.Undergrad 1 2141489 538594230 7309.4
## - S.F.Ratio 1 2607294 539060036 7309.9
## - Outstate 1 8310684 544763426 7315.4
## - Grad.Rate 1 9326177 545778919 7316.4
## - Top25perc 1 14630686 551083428 7321.5
## - PrivateYes 1 15649956 552102698 7322.4
## - Room.Board 1 17392851 553845593 7324.1
## - Expend 1 26894646 563347388 7333.0
## - Top10perc 1 69236254 605688996 7371.2
## - Accept 1 499588060 1036040802 7653.5
##
## Step: AIC=7307.54
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## P.Undergrad + Outstate + Room.Board + PhD + Terminal + S.F.Ratio +
## perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Terminal 1 286690 536977351 7305.8
## - Enroll 1 502997 537193659 7306.0
## - perc.alumni 1 923235 537613897 7306.4
## - PhD 1 2032295 538722957 7307.5
## <none> 536690662 7307.5
## - P.Undergrad 1 2698700 539389362 7308.2
## - S.F.Ratio 1 2700215 539390877 7308.2
## - Outstate 1 8845859 545536520 7314.1
## - Grad.Rate 1 9230387 545921049 7314.5
## - Top25perc 1 14691226 551381888 7319.7
## - PrivateYes 1 16203292 552893954 7321.2
## - Room.Board 1 17503058 554193719 7322.4
## - Expend 1 26847562 563538223 7331.2
## - Top10perc 1 70209972 606900634 7370.2
## - Accept 1 500422365 1037113027 7652.1
##
## Step: AIC=7305.82
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## P.Undergrad + Outstate + Room.Board + PhD + S.F.Ratio + perc.alumni +
## Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Enroll 1 508394 537485746 7304.3
## - perc.alumni 1 1007873 537985224 7304.8
## <none> 536977351 7305.8
## - P.Undergrad 1 2668520 539645872 7306.4
## - S.F.Ratio 1 2789079 539766430 7306.5
## - PhD 1 7757872 544735223 7311.4
## - Outstate 1 9153731 546131083 7312.7
## - Grad.Rate 1 9492289 546469640 7313.0
## - Top25perc 1 15097185 552074536 7318.4
## - PrivateYes 1 15924158 552901509 7319.2
## - Room.Board 1 17223045 554200396 7320.4
## - Expend 1 26816708 563794060 7329.5
## - Top10perc 1 70833530 607810881 7369.0
## - Accept 1 500218219 1037195570 7650.1
##
## Step: AIC=7304.32
## .outcome ~ PrivateYes + Accept + Top10perc + Top25perc + P.Undergrad +
## Outstate + Room.Board + PhD + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - perc.alumni 1 1324004 538809749 7303.6
## <none> 537485746 7304.3
## - P.Undergrad 1 2329220 539814965 7304.6
## - S.F.Ratio 1 2629662 540115407 7304.9
## - PhD 1 7779569 545265314 7309.9
## - Outstate 1 8667873 546153619 7310.7
## - Grad.Rate 1 9936155 547421900 7312.0
## - Top25perc 1 14776216 552261962 7316.6
## - PrivateYes 1 15521101 553006846 7317.3
## - Room.Board 1 18510542 555996287 7320.1
## - Expend 1 26972246 564457991 7328.1
## - Top10perc 1 71199812 608685558 7367.8
## - Accept 1 2681094775 3218580521 8243.8
##
## Step: AIC=7303.61
## .outcome ~ PrivateYes + Accept + Top10perc + Top25perc + P.Undergrad +
## Outstate + Room.Board + PhD + S.F.Ratio + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 538809749 7303.6
## - P.Undergrad 1 2307290 541117039 7303.9
## - S.F.Ratio 1 2910225 541719974 7304.4
## - PhD 1 8183150 546992900 7309.5
## - Grad.Rate 1 8823936 547633685 7310.2
## - Outstate 1 11177051 549986800 7312.4
## - Top25perc 1 15288736 554098486 7316.3
## - PrivateYes 1 16233179 555042929 7317.2
## - Room.Board 1 21273002 560082752 7322.0
## - Expend 1 26800551 565610300 7327.1
## - Top10perc 1 70525333 609335082 7366.3
## - Accept 1 2769028788 3307838537 8256.1
## Start: AIC=7335.88
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 977 546452524 7333.9
## - Books 1 54924 546506472 7333.9
## - Terminal 1 453574 546905122 7334.3
## - S.F.Ratio 1 941816 547393364 7334.8
## - Enroll 1 1495241 547946788 7335.3
## <none> 546451548 7335.9
## - P.Undergrad 1 2234591 548686139 7336.0
## - PhD 1 2487449 548938997 7336.3
## - Outstate 1 2790785 549242333 7336.6
## - perc.alumni 1 2986016 549437564 7336.7
## - F.Undergrad 1 3945722 550397270 7337.7
## - Grad.Rate 1 7943907 554395454 7341.5
## - PrivateYes 1 9671616 556123164 7343.1
## - Top25perc 1 9941311 556392859 7343.4
## - Room.Board 1 12533133 558984681 7345.8
## - Expend 1 23102309 569553857 7355.7
## - Top10perc 1 64211538 610663086 7392.4
## - Accept 1 526036771 1072488319 7689.2
##
## Step: AIC=7333.88
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 58578 546511102 7331.9
## - Terminal 1 452630 546905154 7332.3
## - S.F.Ratio 1 945596 547398120 7332.8
## - Enroll 1 1494388 547946913 7333.3
## <none> 546452524 7333.9
## - P.Undergrad 1 2288235 548740759 7334.1
## - PhD 1 2489623 548942148 7334.3
## - Outstate 1 2811140 549263664 7334.6
## - perc.alumni 1 3067222 549519746 7334.8
## - F.Undergrad 1 3977727 550430251 7335.7
## - Grad.Rate 1 7953063 554405587 7339.5
## - PrivateYes 1 9677140 556129664 7341.1
## - Top25perc 1 9944548 556397072 7341.4
## - Room.Board 1 12617933 559070457 7343.9
## - Expend 1 23175133 569627658 7353.8
## - Top10perc 1 64210888 610663413 7390.4
## - Accept 1 530675031 1077127556 7689.5
##
## Step: AIC=7331.93
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Terminal 1 433383 546944485 7330.4
## - S.F.Ratio 1 951440 547462542 7330.8
## - Enroll 1 1487491 547998593 7331.4
## <none> 546511102 7331.9
## - P.Undergrad 1 2326746 548837849 7332.2
## - PhD 1 2533184 549044286 7332.4
## - Outstate 1 2853133 549364235 7332.7
## - perc.alumni 1 3150215 549661317 7333.0
## - F.Undergrad 1 3991047 550502149 7333.8
## - Grad.Rate 1 7937553 554448655 7337.5
## - PrivateYes 1 9635459 556146561 7339.1
## - Top25perc 1 9937464 556448566 7339.4
## - Room.Board 1 12825202 559336304 7342.2
## - Expend 1 23341278 569852380 7352.0
## - Top10perc 1 64582136 611093238 7388.8
## - Accept 1 530676238 1077187340 7687.5
##
## Step: AIC=7330.35
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - S.F.Ratio 1 982125 547926610 7329.3
## - Enroll 1 1431545 548376030 7329.7
## <none> 546944485 7330.4
## - P.Undergrad 1 2327327 549271812 7330.6
## - Outstate 1 3172333 550116818 7331.4
## - perc.alumni 1 3416108 550360593 7331.6
## - F.Undergrad 1 3812538 550757023 7332.0
## - Grad.Rate 1 8419665 555364150 7336.4
## - PrivateYes 1 9296942 556241427 7337.2
## - PhD 1 9941681 556886166 7337.8
## - Top25perc 1 10371646 557316131 7338.3
## - Room.Board 1 12437076 559381561 7340.2
## - Expend 1 23149584 570094069 7350.2
## - Top10perc 1 65616416 612560902 7388.1
## - Accept 1 530890493 1077834979 7685.8
##
## Step: AIC=7329.3
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Enroll 1 1450587 549377198 7328.7
## <none> 547926610 7329.3
## - P.Undergrad 1 2245838 550172448 7329.5
## - Outstate 1 3245116 551171726 7330.4
## - perc.alumni 1 3899740 551826350 7331.0
## - F.Undergrad 1 4097368 552023979 7331.2
## - Grad.Rate 1 8648582 556575193 7335.5
## - PhD 1 9585253 557511863 7336.4
## - Top25perc 1 10349460 558276070 7337.2
## - PrivateYes 1 10657453 558584064 7337.4
## - Room.Board 1 12081867 560008477 7338.8
## - Expend 1 22707220 570633830 7348.7
## - Top10perc 1 65163124 613089734 7386.5
## - Accept 1 530582944 1078509554 7684.2
##
## Step: AIC=7328.69
## .outcome ~ PrivateYes + Accept + Top10perc + Top25perc + F.Undergrad +
## P.Undergrad + Outstate + Room.Board + PhD + perc.alumni +
## Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 549377198 7328.7
## - P.Undergrad 1 2280234 551657431 7328.9
## - F.Undergrad 1 2818685 552195883 7329.4
## - Outstate 1 2981798 552358995 7329.5
## - perc.alumni 1 4621727 553998924 7331.1
## - Grad.Rate 1 8656575 558033773 7334.9
## - PhD 1 9603033 558980230 7335.8
## - Top25perc 1 9904712 559281909 7336.1
## - PrivateYes 1 10580044 559957242 7336.7
## - Room.Board 1 13180044 562557242 7339.2
## - Expend 1 22690087 572067284 7348.0
## - Top10perc 1 63896529 613273727 7384.7
## - Accept 1 744200826 1293578023 7778.0
## Start: AIC=7315.87
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 883 539072696 7313.9
## - Books 1 432041 539503854 7314.3
## - Terminal 1 443360 539515174 7314.3
## - P.Undergrad 1 1688001 540759814 7315.5
## <none> 539071813 7315.9
## - PhD 1 2146981 541218794 7316.0
## - perc.alumni 1 2207920 541279733 7316.0
## - S.F.Ratio 1 4249893 543321706 7318.0
## - Enroll 1 5028133 544099946 7318.8
## - Outstate 1 7008550 546080363 7320.7
## - F.Undergrad 1 7412458 546484272 7321.1
## - Top25perc 1 8504866 547576679 7322.1
## - Grad.Rate 1 9422680 548494493 7323.0
## - Room.Board 1 9466305 548538118 7323.0
## - PrivateYes 1 10198449 549270262 7323.7
## - Expend 1 39192783 578264596 7350.8
## - Top10perc 1 51089371 590161184 7361.5
## - Accept 1 516592896 1055664709 7667.4
##
## Step: AIC=7313.87
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Terminal 1 442690 539515386 7312.3
## - Books 1 447908 539520605 7312.3
## - P.Undergrad 1 1730426 540803122 7313.6
## <none> 539072696 7313.9
## - PhD 1 2146923 541219620 7314.0
## - perc.alumni 1 2264253 541336949 7314.1
## - S.F.Ratio 1 4281890 543354587 7316.0
## - Enroll 1 5027359 544100055 7316.8
## - Outstate 1 7033899 546106595 7318.7
## - F.Undergrad 1 7490130 546562826 7319.1
## - Top25perc 1 8504843 547577540 7320.1
## - Grad.Rate 1 9436648 548509344 7321.0
## - Room.Board 1 9506322 548579018 7321.1
## - PrivateYes 1 10221881 549294577 7321.8
## - Expend 1 39254603 578327299 7348.8
## - Top10perc 1 51090357 590163053 7359.5
## - Accept 1 521413517 1060486213 7667.8
##
## Step: AIC=7312.3
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 362356 539877742 7310.7
## - P.Undergrad 1 1737536 541252922 7312.0
## <none> 539515386 7312.3
## - perc.alumni 1 2497975 542013361 7312.7
## - S.F.Ratio 1 4435913 543951299 7314.6
## - Enroll 1 4959665 544475051 7315.1
## - F.Undergrad 1 7306634 546822020 7317.4
## - Outstate 1 7420851 546936237 7317.5
## - PhD 1 8695728 548211114 7318.7
## - Top25perc 1 8997129 548512515 7319.0
## - Room.Board 1 9147941 548663327 7319.1
## - Grad.Rate 1 9725452 549240838 7319.7
## - PrivateYes 1 9889656 549405042 7319.9
## - Expend 1 39128770 578644156 7347.1
## - Top10perc 1 52413282 591928668 7359.1
## - Accept 1 521622624 1061138010 7666.1
##
## Step: AIC=7310.66
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - P.Undergrad 1 1800479 541678222 7310.4
## <none> 539877742 7310.7
## - perc.alumni 1 2653139 542530881 7311.2
## - S.F.Ratio 1 4480116 544357858 7313.0
## - Enroll 1 4900049 544777792 7313.4
## - F.Undergrad 1 7427118 547304860 7315.8
## - Outstate 1 7599600 547477343 7316.0
## - PhD 1 8748295 548626037 7317.1
## - Top25perc 1 8899430 548777172 7317.3
## - Grad.Rate 1 9681210 549558953 7318.0
## - Room.Board 1 9723443 549601185 7318.0
## - PrivateYes 1 9881000 549758743 7318.2
## - Expend 1 39849477 579727219 7346.1
## - Top10perc 1 52706204 592583947 7357.7
## - Accept 1 521978711 1061856453 7664.5
##
## Step: AIC=7310.41
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + Outstate + Room.Board + PhD + S.F.Ratio + perc.alumni +
## Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 541678222 7310.4
## - perc.alumni 1 2805185 544483407 7311.1
## - S.F.Ratio 1 4331088 546009309 7312.6
## - Enroll 1 4952838 546631060 7313.2
## - Outstate 1 7637862 549316083 7315.8
## - PhD 1 8131819 549810040 7316.2
## - Grad.Rate 1 8585709 550263930 7316.7
## - Top25perc 1 8824606 550502828 7316.9
## - F.Undergrad 1 9521474 551199696 7317.6
## - PrivateYes 1 10339507 552017729 7318.4
## - Room.Board 1 10458800 552137022 7318.5
## - Expend 1 40843834 582522055 7346.6
## - Top10perc 1 51381513 593059734 7356.1
## - Accept 1 520324837 1062003059 7662.5
## Start: AIC=7301.25
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 54390 524348294 7299.3
## - Personal 1 127341 524421245 7299.4
## - Terminal 1 683374 524977278 7299.9
## - S.F.Ratio 1 1065360 525359264 7300.3
## - PhD 1 1344277 525638181 7300.6
## <none> 524293904 7301.2
## - P.Undergrad 1 2600524 526894427 7301.9
## - perc.alumni 1 2761915 527055819 7302.0
## - Outstate 1 3585424 527879328 7302.8
## - Top25perc 1 5547167 529841070 7304.8
## - Enroll 1 6476010 530769913 7305.7
## - Grad.Rate 1 6778816 531072720 7306.0
## - F.Undergrad 1 7795134 532089038 7307.0
## - PrivateYes 1 9305773 533599676 7308.5
## - Room.Board 1 12675541 536969444 7311.8
## - Expend 1 19151473 543445376 7318.1
## - Top10perc 1 46041680 570335584 7343.5
## - Accept 1 550702657 1074996560 7676.9
##
## Step: AIC=7299.3
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Personal +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 107078 524455372 7297.4
## - Terminal 1 657421 525005715 7298.0
## - S.F.Ratio 1 1077670 525425963 7298.4
## - PhD 1 1373268 525721562 7298.7
## <none> 524348294 7299.3
## - P.Undergrad 1 2622253 526970546 7299.9
## - perc.alumni 1 2807516 527155810 7300.1
## - Outstate 1 3627626 527975919 7300.9
## - Top25perc 1 5532577 529880871 7302.8
## - Enroll 1 6481953 530830246 7303.8
## - Grad.Rate 1 6781524 531129818 7304.1
## - F.Undergrad 1 7818430 532166724 7305.1
## - PrivateYes 1 9256241 533604535 7306.5
## - Room.Board 1 12875190 537223483 7310.1
## - Expend 1 19243540 543591834 7316.3
## - Top10perc 1 46208354 570556648 7341.7
## - Accept 1 550650909 1074999202 7674.9
##
## Step: AIC=7297.41
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Terminal 1 667928 525123300 7296.1
## - S.F.Ratio 1 1163376 525618747 7296.6
## - PhD 1 1377287 525832659 7296.8
## <none> 524455372 7297.4
## - P.Undergrad 1 2526618 526981990 7297.9
## - perc.alumni 1 2714642 527170014 7298.1
## - Outstate 1 3544743 528000115 7299.0
## - Top25perc 1 5539291 529994663 7300.9
## - Enroll 1 6501900 530957271 7301.9
## - Grad.Rate 1 6904565 531359937 7302.3
## - F.Undergrad 1 7714973 532170345 7303.1
## - PrivateYes 1 9244997 533700369 7304.6
## - Room.Board 1 13025658 537481030 7308.3
## - Expend 1 19161911 543617282 7314.3
## - Top10perc 1 46185635 570641007 7339.8
## - Accept 1 557484146 1081939517 7676.3
##
## Step: AIC=7296.08
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - S.F.Ratio 1 1297629 526420929 7295.4
## <none> 525123300 7296.1
## - P.Undergrad 1 2544075 527667375 7296.6
## - perc.alumni 1 2991161 528114461 7297.1
## - Outstate 1 3886909 529010209 7298.0
## - Top25perc 1 5854690 530977990 7299.9
## - Enroll 1 6301935 531425235 7300.4
## - PhD 1 6699038 531822338 7300.7
## - Grad.Rate 1 7237448 532360748 7301.3
## - F.Undergrad 1 7353991 532477291 7301.4
## - PrivateYes 1 8811477 533934777 7302.8
## - Room.Board 1 12524105 537647405 7306.5
## - Expend 1 18915775 544039075 7312.7
## - Top10perc 1 47152974 572276274 7339.3
## - Accept 1 557684660 1082807960 7674.7
##
## Step: AIC=7295.38
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 526420929 7295.4
## - P.Undergrad 1 2454422 528875352 7295.8
## - perc.alumni 1 3465985 529886915 7296.8
## - Outstate 1 4088622 530509551 7297.4
## - Top25perc 1 5814021 532234951 7299.2
## - PhD 1 6295532 532716461 7299.6
## - Enroll 1 6304427 532725357 7299.6
## - Grad.Rate 1 7451108 533872037 7300.8
## - F.Undergrad 1 7787946 534208875 7301.1
## - PrivateYes 1 10102573 536523502 7303.4
## - Room.Board 1 12180558 538601487 7305.4
## - Expend 1 17786384 544207313 7310.9
## - Top10perc 1 46700820 573121749 7338.1
## - Accept 1 556789742 1083210671 7672.9
## Start: AIC=7283.38
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 55372 494694899 7281.4
## - perc.alumni 1 171618 494811144 7281.6
## - Books 1 188688 494828214 7281.6
## - Terminal 1 276338 494915864 7281.7
## - PhD 1 1642647 496282174 7283.1
## <none> 494639526 7283.4
## - P.Undergrad 1 3282443 497921969 7284.9
## - S.F.Ratio 1 4919730 499559257 7286.6
## - Grad.Rate 1 5602446 500241972 7287.3
## - Top25perc 1 6409245 501048771 7288.2
## - Outstate 1 7118472 501757998 7288.9
## - F.Undergrad 1 9958891 504598417 7291.9
## - PrivateYes 1 10717531 505357057 7292.7
## - Room.Board 1 11838520 506478046 7293.8
## - Enroll 1 13673441 508312967 7295.7
## - Expend 1 30486964 525126490 7312.9
## - Top10perc 1 46784169 541423696 7329.0
## - Accept 1 577650487 1072290013 7689.1
##
## Step: AIC=7281.44
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - perc.alumni 1 151584 494846483 7279.6
## - Books 1 161954 494856852 7279.6
## - Terminal 1 276239 494971137 7279.7
## - PhD 1 1652883 496347782 7281.2
## <none> 494694899 7281.4
## - P.Undergrad 1 3227307 497922206 7282.9
## - S.F.Ratio 1 5079375 499774273 7284.8
## - Grad.Rate 1 5710896 500405794 7285.5
## - Top25perc 1 6397444 501092342 7286.2
## - Outstate 1 7063445 501758344 7286.9
## - F.Undergrad 1 9906580 504601479 7289.9
## - PrivateYes 1 10680526 505375424 7290.7
## - Room.Board 1 11987527 506682425 7292.1
## - Enroll 1 13683062 508377961 7293.8
## - Expend 1 30438596 525133494 7310.9
## - Top10perc 1 46737941 541432839 7327.0
## - Accept 1 582534866 1077229764 7689.6
##
## Step: AIC=7279.6
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + Terminal + S.F.Ratio + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 181760 495028243 7277.8
## - Terminal 1 313093 495159576 7277.9
## - PhD 1 1628272 496474754 7279.3
## <none> 494846483 7279.6
## - P.Undergrad 1 3275324 498121807 7281.1
## - S.F.Ratio 1 5270745 500117227 7283.2
## - Grad.Rate 1 5620660 500467142 7283.5
## - Top25perc 1 6566086 501412569 7284.5
## - Outstate 1 8038461 502884944 7286.1
## - F.Undergrad 1 10014969 504861451 7288.2
## - PrivateYes 1 10941956 505788438 7289.1
## - Room.Board 1 12612546 507459028 7290.9
## - Enroll 1 14537304 509383787 7292.9
## - Expend 1 30371578 525218060 7309.0
## - Top10perc 1 46721441 541567924 7325.1
## - Accept 1 625534174 1120380656 7708.2
##
## Step: AIC=7277.79
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## Terminal + S.F.Ratio + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Terminal 1 287155 495315398 7276.1
## - PhD 1 1687964 496716207 7277.6
## <none> 495028243 7277.8
## - P.Undergrad 1 3358640 498386883 7279.4
## - S.F.Ratio 1 5316457 500344700 7281.4
## - Grad.Rate 1 5597446 500625689 7281.7
## - Top25perc 1 6517428 501545670 7282.7
## - Outstate 1 8267556 503295799 7284.5
## - F.Undergrad 1 10087066 505115309 7286.4
## - PrivateYes 1 10823462 505851704 7287.2
## - Room.Board 1 12943683 507971926 7289.4
## - Enroll 1 14554696 509582939 7291.1
## - Expend 1 30650837 525679080 7307.5
## - Top10perc 1 46904219 541932461 7323.5
## - Accept 1 625627076 1120655318 7706.4
##
## Step: AIC=7276.1
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 495315398 7276.1
## - P.Undergrad 1 3384975 498700373 7277.7
## - S.F.Ratio 1 5464111 500779509 7279.9
## - Grad.Rate 1 5784997 501100395 7280.2
## - PhD 1 6127696 501443094 7280.6
## - Top25perc 1 6701279 502016676 7281.2
## - Outstate 1 8669665 503985063 7283.2
## - F.Undergrad 1 9914514 505229912 7284.5
## - PrivateYes 1 10581739 505897136 7285.2
## - Room.Board 1 12662458 507977856 7287.4
## - Enroll 1 14495364 509810762 7289.3
## - Expend 1 30536983 525852381 7305.6
## - Top10perc 1 47216164 542531562 7322.1
## - Accept 1 626932637 1122248035 7705.1
## Start: AIC=7286.5
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 13712 497589746 7284.5
## - Terminal 1 445971 498022004 7285.0
## - Books 1 954701 498530735 7285.5
## - S.F.Ratio 1 1236977 498813011 7285.8
## - perc.alumni 1 1328936 498904969 7285.9
## - PhD 1 1698584 499274617 7286.3
## <none> 497576034 7286.5
## - Outstate 1 2830390 500406424 7287.5
## - P.Undergrad 1 3738017 501314051 7288.4
## - F.Undergrad 1 3835242 501411276 7288.5
## - Enroll 1 3933689 501509722 7288.6
## - Top25perc 1 4995663 502571697 7289.8
## - Grad.Rate 1 7879175 505455208 7292.8
## - Room.Board 1 8433287 506009320 7293.4
## - PrivateYes 1 13336241 510912275 7298.4
## - Expend 1 15595481 513171514 7300.8
## - Top10perc 1 41501551 539077585 7326.7
## - Accept 1 512714052 1010290086 7657.7
##
## Step: AIC=7284.51
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Terminal 1 450097 498039843 7283.0
## - Books 1 942547 498532293 7283.5
## - S.F.Ratio 1 1281481 498871227 7283.9
## - perc.alumni 1 1315684 498905430 7283.9
## - PhD 1 1696282 499286028 7284.3
## <none> 497589746 7284.5
## - Outstate 1 2816683 500406428 7285.5
## - P.Undergrad 1 3744747 501334493 7286.5
## - F.Undergrad 1 3823964 501413710 7286.5
## - Enroll 1 3938556 501528302 7286.7
## - Top25perc 1 4998956 502588702 7287.8
## - Grad.Rate 1 7940586 505530332 7290.9
## - Room.Board 1 8509481 506099227 7291.4
## - PrivateYes 1 13322572 510912318 7296.4
## - Expend 1 15582569 513172315 7298.8
## - Top10perc 1 41511569 539101315 7324.7
## - Accept 1 516841630 1014431376 7657.9
##
## Step: AIC=7282.99
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 840757 498880600 7281.9
## - S.F.Ratio 1 1356650 499396493 7282.4
## - perc.alumni 1 1433491 499473334 7282.5
## <none> 498039843 7283.0
## - Outstate 1 3059864 501099707 7284.2
## - F.Undergrad 1 3652530 501692373 7284.8
## - P.Undergrad 1 3772499 501812342 7285.0
## - Enroll 1 3867935 501907778 7285.1
## - Top25perc 1 5252099 503291942 7286.5
## - PhD 1 7245670 505285513 7288.6
## - Grad.Rate 1 8131821 506171664 7289.5
## - Room.Board 1 8185512 506225355 7289.6
## - PrivateYes 1 12945660 510985503 7294.5
## - Expend 1 15371411 513411254 7297.0
## - Top10perc 1 42278947 540318790 7323.9
## - Accept 1 517516575 1015556418 7656.5
##
## Step: AIC=7281.88
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - S.F.Ratio 1 1423225 500303825 7281.4
## - perc.alumni 1 1537669 500418269 7281.5
## <none> 498880600 7281.9
## - Outstate 1 3285468 502166068 7283.3
## - F.Undergrad 1 3758294 502638894 7283.8
## - Enroll 1 3848230 502728830 7283.9
## - P.Undergrad 1 3933285 502813885 7284.0
## - Top25perc 1 5298408 504179008 7285.4
## - PhD 1 7225615 506106215 7287.5
## - Grad.Rate 1 8063746 506944346 7288.3
## - Room.Board 1 8784506 507665106 7289.1
## - PrivateYes 1 12777729 511658329 7293.2
## - Expend 1 15848586 514729186 7296.4
## - Top10perc 1 43197806 542078406 7323.6
## - Accept 1 516757587 1015638187 7654.5
##
## Step: AIC=7281.38
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - perc.alumni 1 1876181 502180006 7281.4
## <none> 500303825 7281.4
## - Outstate 1 3536394 503840219 7283.1
## - P.Undergrad 1 3781042 504084866 7283.3
## - Enroll 1 3960879 504264704 7283.5
## - F.Undergrad 1 4060587 504364412 7283.6
## - Top25perc 1 5148936 505452761 7284.8
## - PhD 1 6719922 507023747 7286.4
## - Grad.Rate 1 8269836 508573661 7288.0
## - Room.Board 1 8539473 508843297 7288.3
## - PrivateYes 1 14263899 514567724 7294.2
## - Expend 1 14464035 514767860 7294.4
## - Top10perc 1 42480029 542783854 7322.3
## - Accept 1 518031280 1018335105 7653.9
##
## Step: AIC=7281.35
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 502180006 7281.4
## - P.Undergrad 1 3932180 506112186 7283.5
## - F.Undergrad 1 4239969 506419975 7283.8
## - Enroll 1 4742479 506922485 7284.3
## - Outstate 1 5690133 507870139 7285.3
## - Top25perc 1 5832731 508012737 7285.4
## - Grad.Rate 1 6978087 509158092 7286.6
## - PhD 1 7168376 509348382 7286.8
## - Room.Board 1 10315475 512495481 7290.1
## - Expend 1 14067355 516247361 7293.9
## - PrivateYes 1 15307459 517487464 7295.2
## - Top10perc 1 42642517 544822523 7322.3
## - Accept 1 557417653 1059597659 7672.9
## Start: AIC=7310.44
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 310 533531048 7308.4
## - Books 1 176381 533707119 7308.6
## - P.Undergrad 1 178250 533708988 7308.6
## - S.F.Ratio 1 899385 534430123 7309.3
## - perc.alumni 1 1012545 534543283 7309.4
## - PhD 1 1026824 534557562 7309.4
## - Terminal 1 1149878 534680616 7309.6
## <none> 533530738 7310.4
## - Enroll 1 4120551 537651288 7312.5
## - Outstate 1 5142583 538673321 7313.5
## - F.Undergrad 1 5361635 538892373 7313.7
## - Grad.Rate 1 6389820 539920558 7314.7
## - Top25perc 1 9561228 543091966 7317.8
## - PrivateYes 1 11459624 544990362 7319.6
## - Room.Board 1 12745331 546276069 7320.9
## - Expend 1 23386145 556916883 7331.0
## - Top10perc 1 58345147 591875885 7363.0
## - Accept 1 506675798 1040206536 7659.6
##
## Step: AIC=7308.44
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 178145 533709193 7306.6
## - P.Undergrad 1 178782 533709830 7306.6
## - S.F.Ratio 1 909286 534440334 7307.3
## - perc.alumni 1 1022680 534553728 7307.4
## - PhD 1 1026712 534557760 7307.4
## - Terminal 1 1150672 534681720 7307.6
## <none> 533531048 7308.4
## - Enroll 1 4123487 537654535 7310.5
## - Outstate 1 5174747 538705795 7311.5
## - F.Undergrad 1 5383848 538914896 7311.7
## - Grad.Rate 1 6413072 539944120 7312.7
## - Top25perc 1 9561012 543092060 7315.8
## - PrivateYes 1 11461683 544992731 7317.6
## - Room.Board 1 12799466 546330514 7318.9
## - Expend 1 23436600 556967648 7329.0
## - Top10perc 1 58351803 591882850 7361.0
## - Accept 1 509838966 1043370014 7659.2
##
## Step: AIC=7306.61
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - P.Undergrad 1 174165 533883358 7304.8
## - S.F.Ratio 1 931333 534640527 7305.5
## - PhD 1 1048233 534757427 7305.6
## - perc.alumni 1 1068235 534777428 7305.7
## - Terminal 1 1101025 534810218 7305.7
## <none> 533709193 7306.6
## - Enroll 1 4111948 537821141 7308.6
## - Outstate 1 5346418 539055612 7309.9
## - F.Undergrad 1 5425005 539134198 7309.9
## - Grad.Rate 1 6376637 540085831 7310.9
## - Top25perc 1 9537158 543246351 7313.9
## - PrivateYes 1 11340319 545049512 7315.7
## - Room.Board 1 13258334 546967527 7317.5
## - Expend 1 23711262 557420456 7327.5
## - Top10perc 1 58656681 592365874 7359.5
## - Accept 1 509684952 1043394145 7657.2
##
## Step: AIC=7304.78
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + Outstate + Room.Board + PhD + Terminal + S.F.Ratio +
## perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - S.F.Ratio 1 933136 534816494 7303.7
## - PhD 1 986374 534869732 7303.8
## - Terminal 1 1103923 534987281 7303.9
## - perc.alumni 1 1174439 535057797 7303.9
## <none> 533883358 7304.8
## - Enroll 1 4280932 538164290 7307.0
## - Outstate 1 5382185 539265542 7308.1
## - Grad.Rate 1 6203360 540086718 7308.9
## - F.Undergrad 1 6327535 540210893 7309.0
## - Top25perc 1 9555582 543438940 7312.1
## - PrivateYes 1 11459121 545342479 7314.0
## - Room.Board 1 13771609 547654966 7316.2
## - Expend 1 23858286 557741644 7325.8
## - Top10perc 1 58497858 592381216 7357.5
## - Accept 1 509694128 1043577486 7655.3
##
## Step: AIC=7303.7
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + Outstate + Room.Board + PhD + Terminal + perc.alumni +
## Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - PhD 1 846082 535662576 7302.5
## - Terminal 1 1180951 535997445 7302.9
## - perc.alumni 1 1316699 536133193 7303.0
## <none> 534816494 7303.7
## - Enroll 1 4275780 539092274 7305.9
## - Outstate 1 5642014 540458508 7307.2
## - Grad.Rate 1 6339911 541156405 7307.9
## - F.Undergrad 1 6717786 541534280 7308.3
## - Top25perc 1 9413301 544229795 7310.9
## - PrivateYes 1 12989961 547806455 7314.3
## - Room.Board 1 13546330 548362823 7314.9
## - Expend 1 23444396 558260890 7324.3
## - Top10perc 1 57858647 592675141 7355.7
## - Accept 1 508909539 1043726033 7653.4
##
## Step: AIC=7302.53
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + Outstate + Room.Board + Terminal + perc.alumni +
## Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - perc.alumni 1 1234029 536896604 7301.7
## <none> 535662576 7302.5
## - Enroll 1 4312826 539975402 7304.8
## - Outstate 1 5829862 541492438 7306.2
## - Grad.Rate 1 5984258 541646834 7306.4
## - Terminal 1 6661183 542323759 7307.0
## - F.Undergrad 1 6803193 542465769 7307.2
## - Top25perc 1 9645112 545307688 7309.9
## - PrivateYes 1 12293217 547955793 7312.5
## - Room.Board 1 13531017 549193593 7313.7
## - Expend 1 23582323 559244899 7323.2
## - Top10perc 1 57063698 592726274 7353.8
## - Accept 1 508612789 1044275365 7651.7
##
## Step: AIC=7301.74
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + Outstate + Room.Board + Terminal + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 536896604 7301.7
## - Enroll 1 4944559 541841163 7304.6
## - Grad.Rate 1 5037065 541933669 7304.7
## - F.Undergrad 1 6974817 543871421 7306.5
## - Terminal 1 7253765 544150370 7306.8
## - Outstate 1 7787229 544683833 7307.3
## - Top25perc 1 10306378 547202982 7309.7
## - PrivateYes 1 13259418 550156022 7312.6
## - Room.Board 1 15138373 552034977 7314.4
## - Expend 1 23301491 560198095 7322.1
## - Top10perc 1 56816677 593713282 7352.7
## - Accept 1 544759778 1081656382 7668.2
## Start: AIC=8131.69
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## Personal + PhD + Terminal + S.F.Ratio + perc.alumni + Expend +
## Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Personal 1 154 598776566 8129.7
## - Books 1 218993 598995405 8129.9
## - Terminal 1 492872 599269283 8130.2
## - perc.alumni 1 1632931 600409343 8131.3
## <none> 598776411 8131.7
## - PhD 1 2164686 600941097 8131.8
## - P.Undergrad 1 2264712 601041123 8131.9
## - S.F.Ratio 1 2524598 601301009 8132.2
## - Enroll 1 5371967 604148378 8134.9
## - Outstate 1 5627274 604403686 8135.2
## - F.Undergrad 1 6362526 605138937 8135.9
## - Grad.Rate 1 8753287 607529698 8138.2
## - Top25perc 1 9271176 608047587 8138.7
## - PrivateYes 1 13219866 611996277 8142.5
## - Room.Board 1 14051744 612828156 8143.3
## - Expend 1 27754954 626531365 8156.2
## - Top10perc 1 61963032 660739443 8187.3
## - Accept 1 577987055 1176763467 8524.9
##
## Step: AIC=8129.69
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + Books +
## PhD + Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Books 1 222101 598998667 8127.9
## - Terminal 1 493300 599269866 8128.2
## - perc.alumni 1 1656836 600433402 8129.3
## <none> 598776566 8129.7
## - PhD 1 2164627 600941193 8129.8
## - P.Undergrad 1 2302472 601079037 8129.9
## - S.F.Ratio 1 2551496 601328062 8130.2
## - Enroll 1 5375390 604151956 8132.9
## - Outstate 1 5650730 604427296 8133.2
## - F.Undergrad 1 6402985 605179551 8133.9
## - Grad.Rate 1 8790601 607567167 8136.2
## - Top25perc 1 9271021 608047587 8136.7
## - PrivateYes 1 13226572 612003138 8140.5
## - Room.Board 1 14127243 612903809 8141.3
## - Expend 1 27798530 626575096 8154.2
## - Top10perc 1 61964027 660740593 8185.3
## - Accept 1 583396531 1182173097 8525.6
##
## Step: AIC=8127.91
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## Terminal + S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - Terminal 1 450200 599448868 8126.3
## - perc.alumni 1 1740194 600738861 8127.6
## <none> 598998667 8127.9
## - PhD 1 2231564 601230231 8128.1
## - P.Undergrad 1 2373454 601372121 8128.2
## - S.F.Ratio 1 2573326 601571993 8128.4
## - Enroll 1 5360289 604358956 8131.1
## - Outstate 1 5829368 604828035 8131.6
## - F.Undergrad 1 6448155 605446823 8132.2
## - Grad.Rate 1 8775993 607774660 8134.4
## - Top25perc 1 9242352 608241020 8134.9
## - PrivateYes 1 13111988 612110655 8138.6
## - Room.Board 1 14542618 613541285 8139.9
## - Expend 1 28134254 627132921 8152.8
## - Top10perc 1 62399872 661398540 8183.9
## - Accept 1 583174760 1182173427 8523.6
##
## Step: AIC=8126.35
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + perc.alumni + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## - perc.alumni 1 1913071 601361939 8126.2
## <none> 599448868 8126.3
## - P.Undergrad 1 2374306 601823174 8126.7
## - S.F.Ratio 1 2672426 602121294 8126.9
## - Enroll 1 5264355 604713222 8129.5
## - Outstate 1 6192567 605641435 8130.4
## - F.Undergrad 1 6241780 605690648 8130.4
## - PhD 1 8736205 608185072 8132.8
## - Grad.Rate 1 9073572 608522440 8133.1
## - Top25perc 1 9645386 609094254 8133.7
## - PrivateYes 1 12750170 612199038 8136.7
## - Room.Board 1 14135123 613583990 8138.0
## - Expend 1 27903301 627352169 8151.0
## - Top10perc 1 63493685 662942553 8183.2
## - Accept 1 583337754 1182786622 8521.9
##
## Step: AIC=8126.21
## .outcome ~ PrivateYes + Accept + Enroll + Top10perc + Top25perc +
## F.Undergrad + P.Undergrad + Outstate + Room.Board + PhD +
## S.F.Ratio + Expend + Grad.Rate
##
## Df Sum of Sq RSS AIC
## <none> 601361939 8126.2
## - P.Undergrad 1 2514321 603876260 8126.7
## - S.F.Ratio 1 3150166 604512105 8127.3
## - Enroll 1 6306097 607668037 8130.3
## - F.Undergrad 1 6429257 607791196 8130.4
## - Grad.Rate 1 7599632 608961571 8131.6
## - Outstate 1 8789144 610151083 8132.7
## - PhD 1 9265075 610627014 8133.2
## - Top25perc 1 10407214 611769153 8134.2
## - PrivateYes 1 13518384 614880323 8137.2
## - Room.Board 1 16100014 617461953 8139.7
## - Expend 1 27856132 629218071 8150.7
## - Top10perc 1 63506083 664868022 8182.9
## - Accept 1 632886309 1234248248 8544.8s <- summary(fit.lin$finalModel)
kable(s$coefficients)| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | -884.3047105 | 410.6653519 | -2.153346 | 0.0317095 |
| PrivateYes | -541.9610039 | 151.2709602 | -3.582717 | 0.0003691 |
| Accept | 1.3427678 | 0.0547757 | 24.513930 | 0.0000000 |
| Enroll | -0.5122095 | 0.2093231 | -2.446980 | 0.0147062 |
| Top10perc | 49.8041827 | 6.4136915 | 7.765291 | 0.0000000 |
| Top25perc | -16.1375527 | 5.1335801 | -3.143528 | 0.0017559 |
| F.Undergrad | 0.0860211 | 0.0348156 | 2.470760 | 0.0137735 |
| P.Undergrad | 0.0513483 | 0.0332327 | 1.545114 | 0.1228728 |
| Outstate | -0.0597080 | 0.0206685 | -2.888839 | 0.0040134 |
| Room.Board | 0.2127280 | 0.0544078 | 3.909878 | 0.0001034 |
| PhD | -11.0125178 | 3.7128899 | -2.966023 | 0.0031429 |
| S.F.Ratio | 25.9643984 | 15.0127918 | 1.729485 | 0.0842628 |
| Expend | 0.0693197 | 0.0134786 | 5.142929 | 0.0000004 |
| Grad.Rate | 8.7354050 | 3.2518962 | 2.686250 | 0.0074362 |
All variable shows high significance. The test error is as follows.
pred.lin <- predict(fit.lin, Test, exact = T)
RMSE.lin <- mean((pred.lin - Test$Apps)^2)
RMSE.lin## [1] 1411877- Fit a ridge regression model on the training set, with λ chosen by cross-validation. Report the test error obtained.
s <- 10^seq(10,-2, length = 100)
grid <- expand.grid(lambda = s)
set.seed(13587)
fit.ridge <- train(Apps~., data = Train, trControl = ctrl, method = "ridge", tuneGrid = grid, preProcess = c("center", "scale"))## Loading required package: elasticnet## Loading required package: lars## Loaded lars 1.2par(mar = c(5.1,4.1,1,3))
plot.enet(fit.ridge$finalModel, xvar = "penalty",use.color = TRUE)
The selected lambda penalty is 0.01. the coefficient for the Test data is as follows.
pred.ridge.coef <- predict.enet(fit.ridge$finalModel, s = 0.01,Test, type = "coef",
mode = "penalty")
d<- data.frame(pred.ridge.coef$coefficients)
kable(d)| pred.ridge.coef.coefficients | |
|---|---|
| PrivateYes | -251.849767 |
| Accept | 2864.797799 |
| Enroll | -121.453033 |
| Top10perc | 795.950845 |
| Top25perc | -235.906467 |
| F.Undergrad | 376.701506 |
| P.Undergrad | 74.337610 |
| Outstate | -160.236317 |
| Room.Board | 243.270633 |
| Books | 21.363013 |
| Personal | -8.441542 |
| PhD | -118.600307 |
| Terminal | -62.879376 |
| S.F.Ratio | 86.722045 |
| perc.alumni | -107.842789 |
| Expend | 385.209199 |
| Grad.Rate | 179.466340 |
The RMSE for ridge is high compared to linear regression.
pred.ridge <- predict(fit.ridge, Test)
RMSE.ridge <- mean((pred.ridge - Test$Apps)^2)
RMSE.ridge## [1] 1650614- Fit a lasso model on the training set, with λ chosen by cross-validation. Report the test error obtained, along with the number of non-zero coefficient estimates.
set.seed(13587)
fit.lasso <- train(Apps ~., data = Train, trControl = ctrl, method = "lasso", tuneLength = 20, preProcess = c("center", "scale"))
plot.enet(fit.lasso$finalModel, xvar = "penalty", use.color = TRUE)
As you see in the graph, the varaible, Personal, and, Enroll goes to zero.
pred.lasso.coef <- predict.enet(fit.lasso$finalModel, s = fit.lasso$bestTune[[1]] ,data = Test,type = "coefficients", mode = "fraction")
d <- data.frame(pred.lasso.coef$coefficients)
kable(d)| pred.lasso.coef.coefficients | |
|---|---|
| PrivateYes | -231.15107 |
| Accept | 2938.87588 |
| Enroll | 0.00000 |
| Top10perc | 689.32594 |
| Top25perc | -137.54066 |
| F.Undergrad | 162.61747 |
| P.Undergrad | 63.33652 |
| Outstate | -130.84013 |
| Room.Board | 197.83351 |
| Books | 11.63300 |
| Personal | 0.00000 |
| PhD | -94.26298 |
| Terminal | -46.36495 |
| S.F.Ratio | 60.27958 |
| perc.alumni | -89.62794 |
| Expend | 345.34295 |
| Grad.Rate | 129.15292 |
RMSE for lasso is 1585615.
pred.lasso.var <- predict(fit.lasso, Test)
RMSE.lasso <- mean((pred.lasso.var - Test$Apps)^2)
RMSE.lasso## [1] 1585615- Fit a PCR model on the training set, with M chosen by cross-validation. Report the test error obtained, along with the value of M selected by cross-validation.
set.seed(13587)
pcr.fit <- train(Apps ~ ., data = Train, trControl = ctrl, preProcess = c("center", "scale"), method = "pcr")## Loading required package: pls##
## Attaching package: 'pls'## The following object is masked from 'package:caret':
##
## R2## The following object is masked from 'package:stats':
##
## loadingssummary(pcr.fit$finalModel)## Data: X dimension: 585 17
## Y dimension: 585 1
## Fit method: svdpc
## Number of components considered: 3
## TRAINING: % variance explained
## 1 comps 2 comps 3 comps
## X 32.72 58.07 64.81
## .outcome 2.16 76.62 77.80pred.pcr <- predict(pcr.fit, Test)
RMSE.pcr <- mean((pred.pcr - Test$Apps)^2)
RMSE.pcr## [1] 6918780- Fit a PLS model on the training set, with M chosen by cross validation. Report the test error obtained, along with the value of M selected by cross-validation.
set.seed(13587)
pls.fit <- train(Apps ~ ., data = Train, trControl = ctrl, preProcess = c("center", "scale"), thresh = 0.95, method = "pls")
summary(pls.fit$finalModel)## Data: X dimension: 585 17
## Y dimension: 585 1
## Fit method: oscorespls
## Number of components considered: 3
## TRAINING: % variance explained
## 1 comps 2 comps 3 comps
## X 25.54 43.41 63.58
## .outcome 81.19 86.72 89.28pred.pls <- predict(pls.fit, Test)
RMSE.pls <- mean((pred.pls - Test$Apps)^2)
RMSE.pls## [1] 3752658c <- c(RMSE.lin, RMSE.ridge, RMSE.lasso, RMSE.pcr, RMSE.pls)
d <- data.frame(c,row.names = c("Linear","Ridge", "Lasso", "pcr", "pls")); colnames(d) <- "RMSE"
kable(d)| RMSE | |
|---|---|
| Linear | 1411877 |
| Ridge | 1650614 |
| Lasso | 1585615 |
| pcr | 6918780 |
| pls | 3752658 |
For this model, Ridge regression is better.