## Friedman (1991) introduced several benchmark data sets create by sim ulation. One of these simulations used the following nonlinear equation to create data:
y =10sin(πx1x2) +20(x3 −0.5)2 +10x4 +5x5 +N(0,σ2)
where the x values are random variables uniformly distributed between [0, 1] (there are also 5 other non-informative variables also created in the simula tion). The package mlbench contains a function called mlbench.friedman1 that simulates these data:
## $x
## X1 X2 X3 X4 X5 X6
## 1 0.30776611 0.36959607 0.5112374204 0.031766335 0.0994260872 0.074048296
## 2 0.25767250 0.95632284 0.2777106559 0.579705492 0.2299340756 0.111866358
## 3 0.55232243 0.91357666 0.3606569283 0.154204836 0.4436262054 0.623944005
## 4 0.05638315 0.82333634 0.4375278510 0.125270503 0.5157049047 0.671081800
## 5 0.46854928 0.31948216 0.8030667314 0.147985811 0.9248942458 0.365894210
## 6 0.48377074 0.87770033 0.5206097285 0.913342628 0.0444568363 0.183181388
## 7 0.81240262 0.80035100 0.6961520705 0.257430407 0.1491565800 0.026719702
## 8 0.37032054 0.61135664 0.8478368984 0.542465295 0.8481738840 0.490452523
## 9 0.54655860 0.07242114 0.8457092519 0.649022463 0.1529559076 0.595927963
## 10 0.17026205 0.42158771 0.3918757404 0.149194370 0.8249667988 0.956143547
## 11 0.62499648 0.34446560 0.1535137568 0.848940450 0.8631921196 0.358389122
## 12 0.88216552 0.75173569 0.6394257932 0.293505082 0.6543586599 0.179455735
## 13 0.28035384 0.21875132 0.2871710216 0.552142001 0.0220086016 0.992507246
## 14 0.39848790 0.29213397 0.9283378811 0.873134855 0.9979430493 0.030701740
## 15 0.76255108 0.35595337 0.1556361194 0.646984442 0.1476474060 0.723105238
## 16 0.66902171 0.63196192 0.9638416641 0.397183392 0.0825577057 0.044423301
## 17 0.20461216 0.89253107 0.0012604799 0.029533450 0.7976932214 0.282239746
## 18 0.35752485 0.74403278 0.7075262053 0.356859171 0.3440654075 0.057903861
## 19 0.35947511 0.45722242 0.6301876018 0.698544672 0.7286060092 0.657859472
## 20 0.69029053 0.03609544 0.7730780446 0.299448328 0.3410495843 0.900996441
## 21 0.53581115 0.56851452 0.8926068812 0.804871990 0.8608303124 0.481952173
## 22 0.71080385 0.43901589 0.5112040832 0.774279111 0.4072234400 0.718140758
## 23 0.53834870 0.60048445 0.7490010730 0.211135178 0.5685604715 0.670357311
## 24 0.74897223 0.95138276 0.9263797966 0.377163417 0.9015503402 0.369554271
## 25 0.42010145 0.26943131 0.0917535194 0.311373628 0.9352645874 0.987303669
## 26 0.17142021 0.65883839 0.4966554858 0.897573769 0.8472000654 0.357945790
## 27 0.77030161 0.07647121 0.1975012596 0.416461456 0.4140229521 0.278885732
## 28 0.88195359 0.07128521 0.9941329013 0.835883982 0.3474344276 0.295218332
## 29 0.54909671 0.37033152 0.0368210422 0.321439728 0.4568983915 0.725533662
## 30 0.27772376 0.29710220 0.2175630701 0.137396708 0.9037745774 0.523708142
## 31 0.48830599 0.55107827 0.8909361428 0.617712915 0.3602777214 0.898709600
## 32 0.92850507 0.36989059 0.1189364642 0.675416509 0.5791492232 0.554534343
## 33 0.34869198 0.84568953 0.3690389942 0.272432104 0.6281828401 0.180944595
## 34 0.95415771 0.62079070 0.1623764301 0.186206969 0.7134869962 0.987677412
## 35 0.69527414 0.39914002 0.1666915186 0.330326371 0.0220602453 0.084494587
## 36 0.88945354 0.29966153 0.9725047122 0.121819999 0.4969065846 0.280153437
## 37 0.18040725 0.38111984 0.8103997440 0.235530552 0.4405028000 0.386777909
## 38 0.62939085 0.70113494 0.9533276304 0.932846630 0.5577421037 0.667581453
## 39 0.98956414 0.94686529 0.3999105268 0.782541414 0.1756188539 0.532471244
## 40 0.13028887 0.77282832 0.8522473196 0.451765149 0.5635869007 0.230961328
## 41 0.33066053 0.21955016 0.0645228573 0.110800071 0.6096523490 0.632278959
## 42 0.86512055 0.71611036 0.3025287671 0.888677896 0.6390128997 0.538720104
## 43 0.77758444 0.66421796 0.4904728676 0.813587458 0.7929890070 0.714349858
## 44 0.82730345 0.70625020 0.6462612394 0.196786764 0.3464461036 0.777633956
## 45 0.60332436 0.27962799 0.5106343264 0.600222423 0.3335031627 0.175094450
## 46 0.49123182 0.71225050 0.7972592346 0.039957963 0.9874712862 0.783995329
## 47 0.78035851 0.66094211 0.5650089453 0.473761984 0.7164507983 0.957895490
## 48 0.88422703 0.04101269 0.3535239859 0.776964946 0.4110368493 0.881403523
## 49 0.20771390 0.06114149 0.6590999437 0.579832911 0.5702433558 0.943892431
## 50 0.30708590 0.27976169 0.2392745761 0.321991737 0.1049496075 0.169567442
## 51 0.33052985 0.30196772 0.2652107875 0.993388399 0.8672685213 0.149763888
## 52 0.19867907 0.95661083 0.5182688513 0.496269367 0.4778781414 0.151125897
## 53 0.23569430 0.38981872 0.7379108686 0.681448376 0.2785666285 0.644125225
## 54 0.27488666 0.37178879 0.7796109060 0.737922634 0.4630207387 0.667740967
## 55 0.59132105 0.84314249 0.1146943965 0.907612953 0.0410848528 0.669545366
## 56 0.25339065 0.84723500 0.6123733493 0.441479176 0.8743469159 0.210182590
## 57 0.12348723 0.31933115 0.9109361754 0.748124177 0.7433382492 0.189972935
## 58 0.22990589 0.13250605 0.6340214594 0.754517887 0.0726328203 0.477299556
## 59 0.59757529 0.61710912 0.2746640330 0.445359526 0.4259650176 0.776646862
## 60 0.21140856 0.79130451 0.3528353381 0.366376052 0.5157740989 0.773280044
## 61 0.46370118 0.33804871 0.6708293566 0.079096999 0.7387045722 0.525627148
## 62 0.64710119 0.90544760 0.9067114191 0.205195134 0.2680203572 0.979644698
## 63 0.96057309 0.19755671 0.7302358318 0.885000820 0.4872992872 0.989232731
## 64 0.67639817 0.79408518 0.9197669888 0.916921713 0.9623953735 0.526594938
## 65 0.44514802 0.75460289 0.3824332571 0.617564355 0.8418851502 0.096804257
## 66 0.35777378 0.91139485 0.8541405378 0.366041041 0.2681082212 0.568567172
## 67 0.45573146 0.32268770 0.0547340901 0.675886585 0.2607396969 0.140151879
## 68 0.44541398 0.08616947 0.2539860290 0.410419659 0.9133851803 0.590034010
## 69 0.24509259 0.91120045 0.3671289976 0.669335288 0.5991072529 0.931667195
## 70 0.69435071 0.95517383 0.3605704079 0.910149408 0.0636683633 0.199648173
## 71 0.41223704 0.67114294 0.2805165309 0.414875424 0.7173663327 0.408749218
## 72 0.32772587 0.74498220 0.3886925101 0.152951632 0.7421439788 0.369433298
## 73 0.57256477 0.44001698 0.3481344425 0.377473720 0.2627069724 0.746998376
## 74 0.96699908 0.11503942 0.2789230670 0.465790255 0.5300226500 0.112991960
## 75 0.66177902 0.67564278 0.8010881350 0.244270759 0.8043558830 0.122959867
## 76 0.62469772 0.73155952 0.9950138407 0.118219357 0.7278188856 0.719678602
## 77 0.85665304 0.48398490 0.7532419621 0.008282355 0.8653947313 0.860271707
## 78 0.77477889 0.17104804 0.6033429285 0.650868898 0.0463959803 0.240911902
## 79 0.83402710 0.67584853 0.5939481801 0.056565584 0.0080812450 0.664294360
## 80 0.09151028 0.26298995 0.5822902881 0.130109230 0.9393897916 0.318897862
## 81 0.45952549 0.34148083 0.2386592855 0.960689858 0.2416624320 0.781142135
## 82 0.59939816 0.21024554 0.4542843816 0.259571558 0.8997069411 0.659678282
## 83 0.91972191 0.01631959 0.9955166257 0.009066601 0.5113481141 0.234904852
## 84 0.98282408 0.37676288 0.0827459826 0.992870629 0.6969351373 0.245747464
## 85 0.03780258 0.56230740 0.0519060055 0.652903802 0.9570553503 0.694650320
## 86 0.57793740 0.67998461 0.4937972128 0.724484820 0.0541673789 0.243674024
## 87 0.73331417 0.74538877 0.0539935965 0.714281988 0.1295977051 0.561437565
## 88 0.24874240 0.95007272 0.9504485731 0.825024178 0.7682044986 0.796577516
## 89 0.30073652 0.16309071 0.6331912614 0.148244921 0.8613149433 0.621433270
## 90 0.73346670 0.32475690 0.2699370806 0.675003473 0.7278726187 0.470291764
## 91 0.90695438 0.13271604 0.9968129364 0.846872858 0.9042041593 0.624193681
## 92 0.20981677 0.63729744 0.3588041114 0.992584993 0.7415114422 0.999853646
## 93 0.35813799 0.33092961 0.3717620778 0.304093186 0.1615115390 0.760427968
## 94 0.44829914 0.64907957 0.3302263985 0.145394889 0.4824496026 0.120353439
## 95 0.90642643 0.30288836 0.1043955134 0.519036944 0.4100493968 0.321884584
## 96 0.38943930 0.07123327 0.5799014289 0.832152318 0.4659072638 0.772022799
## 97 0.51745975 0.66239047 0.3330894660 0.918171508 0.4434991970 0.955274683
## 98 0.12523909 0.75960356 0.0037775792 0.348103863 0.0265242036 0.398758557
## 99 0.03014575 0.55336017 0.9945961095 0.332689337 0.6539522654 0.194347731
## 100 0.77180549 0.53927210 0.3692348611 0.838867004 0.3905836442 0.983098178
## 101 0.32741508 0.84959232 0.2202325612 0.446239590 0.0262239345 0.146438859
## 102 0.38947869 0.65322596 0.7431595023 0.694593564 0.2910003348 0.807343557
## 103 0.04105275 0.95088576 0.3059573120 0.902810826 0.0004488295 0.702470279
## 104 0.36139663 0.61722305 0.4022088493 0.029474204 0.6454668748 0.799476550
## 105 0.57097808 0.49284063 0.3935714429 0.471807718 0.8269246418 0.530801191
## 106 0.68488024 0.97600657 0.4407564539 0.408890214 0.7549124290 0.460155032
## 107 0.97111675 0.49034522 0.7728050761 0.336940273 0.5148178525 0.152719084
## 108 0.70195881 0.65517230 0.2095690435 0.663275549 0.6195992520 0.998106720
## 109 0.01154550 0.59880179 0.7481226882 0.873135848 0.3979892961 0.557312655
## 110 0.53553213 0.94756902 0.5853551526 0.086759413 0.4305372024 0.492183291
## 111 0.83657146 0.36801151 0.3244471955 0.334643598 0.6347250536 0.412586614
## 112 0.80686674 0.87818701 0.3750474500 0.933748877 0.4797932676 0.257401745
## 113 0.08093264 0.45487507 0.0269371939 0.918592991 0.5593633349 0.164202531
## 114 0.23890930 0.49646702 0.4833348761 0.686753216 0.5097432989 0.871655252
## 115 0.96598986 0.46061562 0.9700804388 0.383543578 0.8265101276 0.631293145
## 116 0.03767233 0.61790820 0.0003950703 0.008982167 0.5600976583 0.963963124
## 117 0.91640643 0.60414349 0.1057025485 0.719938769 0.0132807584 0.943785176
## 118 0.72622658 0.78587960 0.4399432044 0.480926614 0.4755937520 0.955002926
## 119 0.20077621 0.55526847 0.3122987410 0.003722787 0.0364418153 0.897926668
## 120 0.84020075 0.76897834 0.9713328420 0.572111683 0.2448342000 0.421930267
## 121 0.39666235 0.40428567 0.5852688691 0.080655038 0.9546872040 0.998057382
## 122 0.39270226 0.51071981 0.7339286285 0.379890728 0.2696251650 0.775501184
## 123 0.47255689 0.52353644 0.6635271511 0.999523677 0.0472132596 0.752772056
## 124 0.58365691 0.99279921 0.7229845193 0.097467466 0.9617045652 0.141268633
## 125 0.35238717 0.42964742 0.1110149436 0.804216082 0.0411765689 0.249210565
## 126 0.02847401 0.99601125 0.2185792171 0.084229584 0.5685715808 0.585415466
## 127 0.99508793 0.78660025 0.6225663018 0.877182388 0.4893754795 0.434916571
## 128 0.95755846 0.51591063 0.9592804280 0.982542838 0.8156825237 0.114269629
## 129 0.55165118 0.50268797 0.8123157280 0.609853369 0.5262332316 0.761027492
## 130 0.10195396 0.91163748 0.0221628349 0.684833081 0.8368379199 0.892411956
## 131 0.23791515 0.26441590 0.6825390456 0.494595101 0.0718262950 0.146017209
## 132 0.86009766 0.17385687 0.8307875313 0.275989021 0.7455581927 0.381221835
## 133 0.73826129 0.40033126 0.8078064425 0.003721118 0.3374601963 0.169478398
## 134 0.49731226 0.53835738 0.8418451962 0.664426274 0.6204041298 0.999622951
## 135 0.57992109 0.24496437 0.1876676735 0.548279016 0.7179785939 0.172281613
## 136 0.01618339 0.37585096 0.0949448342 0.596033634 0.9496248781 0.548413014
## 137 0.47212988 0.58025355 0.4488151143 0.308346305 0.2719512167 0.588928068
## 138 0.04238973 0.20895531 0.6004804880 0.897289331 0.9718085302 0.927986601
## 139 0.46315442 0.80133001 0.8635722811 0.916157075 0.4724074309 0.640372698
## 140 0.62999477 0.63880242 0.8514558950 0.971690540 0.7976263147 0.487533634
## 141 0.67324929 0.73633076 0.6977811693 0.342376201 0.9088888676 0.253437832
## 142 0.08703467 0.43881241 0.6439721654 0.928428851 0.9906902050 0.131614503
## 143 0.14358380 0.57981238 0.6546971288 0.918632505 0.2213202249 0.449664838
## 144 0.90847850 0.25604401 0.8803548680 0.691446334 0.1924467573 0.789089967
## 145 0.12253259 0.46371823 0.8569371656 0.769923869 0.7099349364 0.949743764
## 146 0.72886279 0.16861486 0.8468295794 0.602196601 0.8457011958 0.361604516
## 147 0.95037718 0.61389453 0.3265210520 0.769321489 0.0437571695 0.306042858
## 148 0.04335591 0.95810262 0.5470013041 0.097983083 0.7283248159 0.367767893
## 149 0.01959930 0.47819473 0.7343759690 0.231752394 0.2991912132 0.302059255
## 150 0.19907246 0.75115933 0.8052955386 0.706835322 0.2576841901 0.058446434
## 151 0.50508626 0.02058322 0.2064400080 0.028821961 0.9804799608 0.910469695
## 152 0.92638876 0.17096903 0.8801616649 0.631142367 0.8653444445 0.149091309
## 153 0.13840169 0.63996650 0.3960763614 0.672157781 0.6641179975 0.534857797
## 154 0.16919458 0.16497848 0.9830069796 0.452885734 0.8688727603 0.342600671
## 155 0.60662738 0.35472278 0.5614219203 0.675898803 0.8434061243 0.704598499
## 156 0.81587669 0.18642647 0.9086144671 0.009393311 0.9666821721 0.536068066
## 157 0.84338121 0.89765616 0.7151337676 0.063480382 0.9132655612 0.932174849
## 158 0.78807719 0.23778386 0.2356364124 0.279233183 0.2836070871 0.943759067
## 159 0.01902087 0.98494348 0.0039051792 0.467886943 0.4578090804 0.809700371
## 160 0.69808750 0.02133074 0.4793805082 0.776457262 0.8689027121 0.565672869
## 161 0.81509312 0.10753897 0.8721331256 0.366924266 0.5165516310 0.690012311
## 162 0.56840006 0.24482683 0.2623272671 0.900720072 0.2658771435 0.413597689
## 163 0.48006288 0.72236241 0.6634045555 0.521405264 0.8686213219 0.402317170
## 164 0.16137012 0.03273494 0.8796447231 0.289609326 0.6901659735 0.011976228
## 165 0.08925623 0.54934999 0.9115052556 0.244583334 0.5945103467 0.233068860
## 166 0.16268237 0.68280868 0.3903184666 0.589133301 0.9235723831 0.217937226
## 167 0.02672845 0.30024090 0.8651506912 0.380756364 0.1493828474 0.808993577
## 168 0.70962948 0.38877446 0.5146185814 0.705413333 0.8064511195 0.541325973
## 169 0.76101818 0.73244615 0.7411989463 0.116040773 0.3114460232 0.223447104
## 170 0.85747478 0.96249642 0.9602066136 0.598454862 0.9208744697 0.335785166
## 171 0.43726582 0.76059617 0.5697099713 0.846073140 0.6495810472 0.656496287
## 172 0.41713645 0.58167316 0.3110995081 0.350864020 0.1783565462 0.696957609
## 173 0.58564949 0.46287299 0.7433016279 0.316167029 0.4413796300 0.297452353
## 174 0.82496758 0.35630962 0.4504729696 0.780196068 0.7546392297 0.396184891
## 175 0.79313923 0.38392182 0.4738918107 0.254789922 0.2576926639 0.500004759
## 176 0.32615257 0.20578103 0.4744165663 0.840200149 0.9989377656 0.979932919
## 177 0.95793194 0.13878037 0.7407055742 0.751392944 0.5224501409 0.793372326
## 178 0.65301961 0.38908214 0.1071925669 0.308782266 0.9981128222 0.753225460
## 179 0.45867582 0.26604622 0.6421807767 0.458046929 0.4026084305 0.606081025
## 180 0.60602188 0.70329628 0.4221840035 0.414898014 0.5843024231 0.291302044
## 181 0.28872194 0.40787817 0.8005092293 0.325016026 0.8918118891 0.349007594
## 182 0.71783084 0.26556419 0.6167882476 0.135616546 0.8534271207 0.364771754
## 183 0.92339744 0.40097786 0.2493683256 0.910110965 0.4292331270 0.372681924
## 184 0.67493949 0.19731313 0.6812233408 0.150384865 0.2787725986 0.128495624
## 185 0.18593999 0.82993169 0.3477386320 0.837922945 0.8918579654 0.953522193
## 186 0.34806716 0.52798773 0.8914637144 0.544273399 0.9873077427 0.115461037
## 187 0.12351953 0.39513019 0.6572394262 0.115952749 0.1395892045 0.001983741
## 188 0.10811622 0.57396657 0.9386654657 0.044229344 0.5403982888 0.317312683
## 189 0.29795320 0.97097207 0.1341775106 0.282693473 0.3105859275 0.733074472
## 190 0.83819990 0.65014983 0.9724600734 0.881263746 0.8520803752 0.027663035
## 191 0.99277109 0.33360116 0.3507485189 0.836947951 0.0435301224 0.013777922
## 192 0.43713441 0.33144743 0.2370002337 0.057761824 0.3721722844 0.304183315
## 193 0.20256457 0.94243488 0.6156287836 0.048721011 0.5159765771 0.392545077
## 194 0.96387150 0.38111249 0.7471337013 0.316636332 0.7677630151 0.866850457
## 195 0.66038711 0.56432392 0.9635183825 0.131432124 0.2873498579 0.178233114
## 196 0.29811683 0.51151569 0.9326846676 0.035612436 0.8166487757 0.496499726
## 197 0.11926219 0.13886056 0.7921867422 0.120834680 0.0052734755 0.379694718
## 198 0.59975160 0.23978941 0.3117346237 0.567882622 0.0223096041 0.190654986
## 199 0.12019055 0.71800910 0.0934134405 0.127340811 0.2429706121 0.994402615
## 200 0.78843202 0.29722378 0.2072938555 0.758052353 0.8313589729 0.028777078
## X7 X8 X9 X10
## 1 0.973458072 0.693972470 0.376184175 0.57044188
## 2 0.771742517 0.202279339 0.229491826 0.47866167
## 3 0.494979990 0.522201575 0.969307939 0.30722717
## 4 0.392606059 0.813396338 0.131597392 0.88554257
## 5 0.105305870 0.916158199 0.609028496 0.54182441
## 6 0.356070566 0.946388445 0.284045842 0.42213317
## 7 0.780769942 0.813432247 0.263594302 0.11916849
## 8 0.637963134 0.549542098 0.950865732 0.67138137
## 9 0.789269735 0.069797633 0.820791990 0.79867491
## 10 0.807865057 0.062319819 0.452669792 0.15219687
## 11 0.066967647 0.977735519 0.583413674 0.60302169
## 12 0.463041426 0.570571361 0.345205690 0.25304986
## 13 0.721013686 0.817313494 0.027791464 0.16331902
## 14 0.674881998 0.602071855 0.460380431 0.13843190
## 15 0.200270209 0.735559979 0.385074523 0.98721485
## 16 0.416621240 0.798843008 0.108875749 0.27033643
## 17 0.219470031 0.899830600 0.050881227 0.27920775
## 18 0.024462509 0.273231871 0.730649507 0.94320639
## 19 0.113417720 0.081294403 0.270535129 0.18233773
## 20 0.269403405 0.028573310 0.016672264 0.87534791
## 21 0.507509401 0.531037571 0.325111343 0.18500999
## 22 0.368089530 0.909991686 0.930813524 0.42389120
## 23 0.085760597 0.042044079 0.912691443 0.29843064
## 24 0.983760030 0.441671153 0.051604795 0.12585046
## 25 0.023289470 0.779766544 0.070364622 0.60225732
## 26 0.628853515 0.241917522 0.840225938 0.33744177
## 27 0.015534221 0.562131148 0.540985850 0.41281517
## 28 0.145463925 0.537444780 0.755434505 0.92029751
## 29 0.526779035 0.304192940 0.578553233 0.93827130
## 30 0.542079985 0.333297051 0.119768048 0.50683327
## 31 0.805175351 0.602511128 0.330112497 0.10652000
## 32 0.603830589 0.972658257 0.900348216 0.25494851
## 33 0.216728884 0.885251973 0.228364848 0.89499939
## 34 0.622855653 0.195130018 0.309552277 0.02215039
## 35 0.289043740 0.668353434 0.770928348 0.40387515
## 36 0.667111522 0.909629349 0.969186244 0.38488114
## 37 0.760201452 0.626953554 0.682690960 0.26672760
## 38 0.306276659 0.725091803 0.356287191 0.05697585
## 39 0.575959667 0.867031560 0.596096553 0.15525083
## 40 0.112562534 0.605250908 0.818059862 0.41934226
## 41 0.949463940 0.991519130 0.604401364 0.47929818
## 42 0.642815416 0.865613346 0.387452040 0.41512030
## 43 0.430328859 0.769829959 0.949844583 0.18466981
## 44 0.546463419 0.535265125 0.341542759 0.20041463
## 45 0.358501132 0.183830237 0.838181524 0.17595943
## 46 0.087422671 0.890520570 0.017796835 0.17444989
## 47 0.984674800 0.775756790 0.364331119 0.89467241
## 48 0.019100138 0.066842066 0.814403104 0.04635594
## 49 0.448254399 0.904437319 0.441184822 0.96406679
## 50 0.270746778 0.837970049 0.262201776 0.24830761
## 51 0.094596345 0.672513192 0.391961331 0.26486956
## 52 0.472251823 0.029529553 0.498419254 0.42333859
## 53 0.745295167 0.197320959 0.891100391 0.42414993
## 54 0.284515948 0.138636800 0.551513068 0.32364933
## 55 0.536572802 0.147331451 0.341822796 0.10696917
## 56 0.766587721 0.929107272 0.454603689 0.20988725
## 57 0.672949492 0.501593275 0.137496739 0.42319477
## 58 0.846425449 0.638075882 0.870249459 0.56568094
## 59 0.706808023 0.077864381 0.720970028 0.66621206
## 60 0.073849637 0.392855044 0.728438452 0.51479998
## 61 0.947467309 0.689873585 0.834255048 0.55702420
## 62 0.416916390 0.585043649 0.660119302 0.73612886
## 63 0.906797833 0.832550942 0.752925019 0.39938269
## 64 0.186582500 0.308830366 0.203545092 0.81097958
## 65 0.461028991 0.696630936 0.852112657 0.23560434
## 66 0.262959693 0.715349178 0.121828631 0.60706410
## 67 0.649597318 0.133346610 0.565267840 0.55784525
## 68 0.250339519 0.324333993 0.831413461 0.07106832
## 69 0.780842539 0.384964663 0.041165304 0.02690782
## 70 0.927335711 0.745140525 0.094164828 0.16479830
## 71 0.657793317 0.972823951 0.640401705 0.21579645
## 72 0.752835202 0.886159773 0.681310798 0.09420056
## 73 0.489316358 0.009119899 0.865221020 0.78529847
## 74 0.146288695 0.662854066 0.283150569 0.35938743
## 75 0.910049457 0.335258069 0.762721385 0.22813485
## 76 0.527467078 0.525870716 0.414597108 0.55189396
## 77 0.771836714 0.420813468 0.247336797 0.00616404
## 78 0.054875824 0.902885072 0.468505195 0.12104151
## 79 0.327557079 0.860213075 0.785841775 0.05932572
## 80 0.416784130 0.852773713 0.216500955 0.30023706
## 81 0.230612763 0.280670691 0.907011286 0.93660453
## 82 0.126819404 0.793337702 0.490047599 0.73761397
## 83 0.197503181 0.416155240 0.977546369 0.96897149
## 84 0.473110297 0.390338759 0.267154379 0.26815712
## 85 0.090110623 0.340038632 0.900693230 0.03404227
## 86 0.544155086 0.043283253 0.271166093 0.77990895
## 87 0.744820195 0.653749314 0.546592726 0.71363126
## 88 0.567039451 0.597868659 0.846082093 0.14614631
## 89 0.360787387 0.090582484 0.825097040 0.35881884
## 90 0.284619912 0.716550993 0.847082068 0.06776624
## 91 0.519716365 0.989592345 0.908736693 0.27950657
## 92 0.849089800 0.681896214 0.944219138 0.70900997
## 93 0.138885293 0.362985108 0.836835295 0.72874107
## 94 0.777302523 0.890084096 0.258382139 0.51136605
## 95 0.514619100 0.374066044 0.744136567 0.70117740
## 96 0.132194049 0.785832419 0.240932147 0.35393372
## 97 0.004350274 0.333975584 0.843022753 0.36509085
## 98 0.317295935 0.608802983 0.808800563 0.02268890
## 99 0.015884194 0.409196929 0.053608424 0.25008597
## 100 0.139087579 0.007509888 0.181448287 0.29179884
## 101 0.862689710 0.477703559 0.399016606 0.38153617
## 102 0.608211681 0.404462601 0.826253708 0.45232278
## 103 0.046057765 0.354929513 0.971815727 0.28517984
## 104 0.569287466 0.224406119 0.003214312 0.62280540
## 105 0.306271997 0.682356996 0.758520066 0.06516503
## 106 0.841200964 0.339149828 0.496161843 0.55112740
## 107 0.098525061 0.475399029 0.246452654 0.88244969
## 108 0.588656687 0.079853043 0.479729257 0.41643242
## 109 0.254510878 0.016681439 0.367821925 0.10100328
## 110 0.131700506 0.435532929 0.094510626 0.70346273
## 111 0.544253852 0.158114555 0.153534471 0.24986157
## 112 0.631808481 0.581415591 0.014591817 0.77336959
## 113 0.954311827 0.302297337 0.950592794 0.33641084
## 114 0.337170245 0.272823381 0.474930371 0.33713784
## 115 0.925341691 0.986454699 0.039895779 0.10438304
## 116 0.094696180 0.017277270 0.024430142 0.93081034
## 117 0.582313555 0.627403576 0.964344572 0.21218051
## 118 0.742853694 0.324525492 0.054958584 0.22049566
## 119 0.296197230 0.100834867 0.081107785 0.87237779
## 120 0.758553318 0.903886507 0.117724924 0.55134324
## 121 0.599558291 0.981174148 0.936330438 0.76929477
## 122 0.990555514 0.597307998 0.296845898 0.91006884
## 123 0.166398281 0.709155346 0.987614575 0.94354428
## 124 0.293871503 0.369138327 0.294011623 0.72594850
## 125 0.520716531 0.977809820 0.673546284 0.86495126
## 126 0.690611549 0.364509288 0.244842791 0.97944961
## 127 0.898416971 0.386835697 0.558873612 0.16290420
## 128 0.329210850 0.344694509 0.382509190 0.62436052
## 129 0.320050030 0.684921451 0.379240430 0.79744511
## 130 0.473803067 0.981478553 0.678012634 0.62661137
## 131 0.296005070 0.084021010 0.915560311 0.05830434
## 132 0.643002406 0.230455835 0.966514423 0.17438099
## 133 0.797160555 0.821973091 0.939702642 0.90619485
## 134 0.825869921 0.030195964 0.191659973 0.27863216
## 135 0.638712386 0.206196191 0.483376691 0.93750371
## 136 0.837419800 0.513071402 0.373704539 0.01024639
## 137 0.674379544 0.258027048 0.158906203 0.49037360
## 138 0.276765654 0.648439016 0.949929616 0.68834352
## 139 0.810438509 0.931770058 0.879786302 0.27104623
## 140 0.298950831 0.080295094 0.659699649 0.07889023
## 141 0.456838721 0.173297388 0.551471281 0.54444402
## 142 0.321288927 0.366316877 0.966430146 0.98894156
## 143 0.007381912 0.120196523 0.467919978 0.64902200
## 144 0.909716415 0.148416507 0.838031981 0.47839375
## 145 0.768987017 0.786143693 0.596769295 0.17087334
## 146 0.006061933 0.515664329 0.173798819 0.92415953
## 147 0.070991962 0.212991755 0.320151337 0.90104810
## 148 0.800179963 0.716312152 0.287075342 0.37331177
## 149 0.646985629 0.838777959 0.519848649 0.80456948
## 150 0.438128093 0.367484299 0.961555571 0.24778541
## 151 0.746835746 0.982450001 0.999006775 0.83712868
## 152 0.488979346 0.376975365 0.211045375 0.49569960
## 153 0.478043541 0.966173188 0.841776328 0.37624073
## 154 0.826841164 0.302526494 0.880471145 0.09970006
## 155 0.567345741 0.652758237 0.320700991 0.51294791
## 156 0.978937840 0.154946083 0.888823475 0.74062765
## 157 0.884757184 0.461897084 0.691725780 0.78553874
## 158 0.465200315 0.167919053 0.658674212 0.32545758
## 159 0.796619675 0.770449555 0.128407827 0.63288218
## 160 0.674475601 0.294673672 0.246534493 0.65943052
## 161 0.903187802 0.871877405 0.097281488 0.82756963
## 162 0.542902389 0.689380216 0.869209955 0.61010627
## 163 0.100118157 0.786237354 0.186340844 0.71525160
## 164 0.784346248 0.408016088 0.464462581 0.22618543
## 165 0.174739727 0.775438312 0.255407970 0.60195737
## 166 0.631585635 0.839436400 0.263226770 0.67789917
## 167 0.643331339 0.377073922 0.394179333 0.40979585
## 168 0.156732715 0.150822544 0.674603045 0.82325484
## 169 0.495887927 0.006337214 0.033664247 0.62186762
## 170 0.364372640 0.491888058 0.686238499 0.49652771
## 171 0.277523597 0.470086427 0.590324672 0.05393087
## 172 0.375348588 0.857763752 0.822487635 0.28534711
## 173 0.822573777 0.176880998 0.757889478 0.18475002
## 174 0.197965225 0.560150238 0.829130032 0.37920090
## 175 0.462556834 0.891551466 0.900898176 0.80391692
## 176 0.733199941 0.774404618 0.457640583 0.53218362
## 177 0.836197246 0.572724013 0.087294348 0.02487760
## 178 0.936154180 0.228703533 0.724892642 0.96107675
## 179 0.184412231 0.799087411 0.526502711 0.82861872
## 180 0.243326853 0.279668061 0.621370952 0.76357934
## 181 0.593790459 0.748771413 0.712995128 0.54143675
## 182 0.457784649 0.370104011 0.386264323 0.57238973
## 183 0.239504271 0.086274267 0.571580363 0.14818318
## 184 0.253332703 0.298254313 0.147402499 0.51000744
## 185 0.095946862 0.747062177 0.029768271 0.76099910
## 186 0.506628082 0.894112278 0.761555608 0.96759758
## 187 0.795988215 0.766148844 0.990426548 0.56957543
## 188 0.056027012 0.869893295 0.437126803 0.11566349
## 189 0.719765122 0.615522658 0.791712536 0.14492068
## 190 0.731300485 0.829866405 0.176863548 0.61951845
## 191 0.087342019 0.174951121 0.485986336 0.24804533
## 192 0.934051532 0.787731918 0.689254847 0.49021188
## 193 0.625086517 0.894071775 0.187574663 0.15512992
## 194 0.902079907 0.942049130 0.209424594 0.75344942
## 195 0.396374685 0.045542070 0.680473472 0.99027040
## 196 0.749527853 0.593081933 0.403229168 0.28839843
## 197 0.118204677 0.930880038 0.955516678 0.12070897
## 198 0.167046419 0.145025169 0.618926044 0.29775204
## 199 0.574268748 0.862417075 0.952667466 0.01611978
## 200 0.592683082 0.229214831 0.150814822 0.67591271
##
## $y
## [1] 5.412931 16.107065 14.734981 6.438693 13.609284 19.845299 13.143850
## [8] 19.679598 10.461482 7.711547 20.414488 14.022134 8.975202 20.885686
## [15] 16.035929 18.824351 14.487765 12.851509 15.601036 6.710743 23.649362
## [22] 18.150911 15.248375 19.650156 14.032838 16.959527 9.067678 16.778267
## [29] 16.281117 9.548045 19.744999 20.571733 14.384335 16.421745 11.905151
## [36] 15.084022 9.749036 25.903291 10.513170 14.164439 10.963547 23.085620
## [43] 22.760801 14.115112 12.382109 16.439104 17.166042 11.352487 9.962025
## [50] 8.200079 18.420854 11.489933 12.521341 15.247312 23.623135 14.030571
## [57] 15.832329 9.533448 17.484499 11.658576 9.964464 16.795656 18.174662
## [64] 24.441106 19.321279 16.332620 17.406317 10.249545 17.627896 17.573675
## [71] 17.728574 12.132801 13.169593 14.616051 18.171810 18.775738 16.088949
## [78] 12.037695 12.998936 8.384363 16.149999 11.295923 8.463263 26.055761
## [85] 14.505635 14.601589 22.308580 23.323770 8.534946 16.728484 21.612579
## [92] 16.793512 7.806692 12.332253 16.281623 12.312873 19.109465 12.017466
## [99] 12.227140 21.026603 14.010512 15.334591 11.761436 11.050259 16.118431
## [106] 14.705824 17.750275 23.806200 12.503476 12.182241 12.910539 17.667627
## [113] 18.709627 13.369580 21.044270 9.822876 21.641835 17.949068 4.879676
## [120] 19.541344 9.536688 10.651929 19.241475 17.940051 16.869416 4.869868
## [127] 17.287718 27.633464 17.172544 18.792592 8.244520 12.273187 10.586850
## [134] 19.099129 15.527921 12.214835 11.167777 13.417991 21.808015 25.599270
## [141] 18.905871 15.567980 12.133341 17.111106 15.574497 15.292383 17.907712
## [148] 6.429899 5.344833 14.286670 6.578185 18.061577 12.579281 14.272613
## [155] 16.269971 13.410412 12.970064 12.531857 15.225756 12.189635 11.695549
## [162] 15.931632 19.887341 8.585073 10.019386 14.868546 7.294858 17.703092
## [169] 14.401072 20.731714 21.914313 11.868368 13.006875 20.380159 12.495023
## [176] 14.720069 15.477657 18.725184 10.316178 18.789921 13.682901 11.197201
## [183] 21.986591 6.715426 18.727588 19.689489 5.321106 8.949122 15.989939
## [190] 27.064190 17.015985 7.429268 9.006285 17.064426 17.300439 12.376388
## [197] 3.480930 10.842029 8.082849 18.296654
## k-Nearest Neighbors
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 200, 200, 200, 200, 200, 200, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 5 3.533185 0.4774870 2.898956
## 7 3.502551 0.4975106 2.862761
## 9 3.475184 0.5174104 2.832425
## 11 3.452285 0.5388618 2.811275
## 13 3.471341 0.5476062 2.815970
## 15 3.466663 0.5654287 2.815842
## 17 3.465845 0.5792474 2.816261
## 19 3.485848 0.5854602 2.826398
## 21 3.517061 0.5858064 2.858450
## 23 3.547849 0.5848372 2.878512
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was k = 21.
## Multivariate Adaptive Regression Spline
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 200, 200, 200, 200, 200, 200, ...
## Resampling results across tuning parameters:
##
## nprune RMSE Rsquared MAE
## 2 3.868263 0.3842103 3.139259
## 3 3.494278 0.5012929 2.834597
## 4 2.812824 0.6764985 2.269004
## 5 2.511457 0.7370225 2.022915
## 6 2.323047 0.7765739 1.848667
## 7 1.902079 0.8495596 1.512605
## 8 1.798530 0.8647185 1.414294
## 9 1.761677 0.8699765 1.369170
## 10 1.766088 0.8691087 1.376501
## 11 1.795290 0.8655318 1.405872
## 12 1.794348 0.8657322 1.396193
## 13 1.811606 0.8636824 1.411689
## 14 1.820548 0.8619952 1.421489
## 15 1.840907 0.8588165 1.442058
##
## Tuning parameter 'degree' was held constant at a value of 1
## Rsquared was used to select the optimal model using the largest value.
## The final values used for the model were nprune = 9 and degree = 1.
## Support Vector Machines with Radial Basis Function Kernel
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 200, 200, 200, 200, 200, 200, ...
## Resampling results across tuning parameters:
##
## C RMSE Rsquared MAE
## 0.25 2.784809 0.7213081 2.217052
## 0.50 2.529132 0.7404709 1.971648
## 1.00 2.404085 0.7581877 1.857364
## 2.00 2.321131 0.7707435 1.787580
## 4.00 2.283035 0.7746800 1.767334
## 8.00 2.302382 0.7694434 1.790045
## 16.00 2.304461 0.7691002 1.793023
## 32.00 2.304429 0.7691082 1.793005
## 64.00 2.304429 0.7691082 1.793005
## 128.00 2.304429 0.7691082 1.793005
##
## Tuning parameter 'sigma' was held constant at a value of 0.07271678
## Rsquared was used to select the optimal model using the largest value.
## The final values used for the model were sigma = 0.07271678 and C = 4.
## Neural Network
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 180, 180, 180, 180, 180, 180, ...
## Resampling results across tuning parameters:
##
## decay size RMSE Rsquared MAE
## 0.00 1 3.275870 0.5473129 2.614373
## 0.00 2 3.126371 0.5805436 2.538043
## 0.00 3 2.961602 0.6515118 2.418079
## 0.00 4 2.842680 0.6569294 2.288869
## 0.00 5 2.637831 0.6998895 2.175161
## 0.00 6 2.964566 0.6390744 2.315150
## 0.00 7 3.299544 0.5857268 2.536560
## 0.00 8 3.101541 0.6321648 2.483226
## 0.00 9 3.390979 0.5828986 2.593775
## 0.00 10 3.002307 0.6526483 2.363519
## 0.01 1 3.637995 0.4410715 2.876707
## 0.01 2 3.108337 0.5823112 2.482011
## 0.01 3 3.066785 0.6255759 2.444426
## 0.01 4 2.970730 0.6606864 2.412843
## 0.01 5 2.980371 0.6486312 2.408681
## 0.01 6 3.391528 0.5871446 2.654474
## 0.01 7 3.334556 0.5104528 2.786251
## 0.01 8 3.463918 0.4903223 2.812249
## 0.01 9 3.118473 0.5715230 2.516713
## 0.01 10 2.970755 0.6586950 2.299721
## 0.10 1 3.499455 0.4757066 2.759936
## 0.10 2 3.146231 0.5898302 2.543551
## 0.10 3 2.782354 0.6808048 2.225033
## 0.10 4 3.002455 0.6527479 2.379126
## 0.10 5 2.760992 0.7047623 2.196737
## 0.10 6 2.957029 0.6531646 2.360793
## 0.10 7 3.679163 0.4623846 2.979758
## 0.10 8 3.040999 0.6721390 2.398991
## 0.10 9 3.216753 0.6161458 2.504509
## 0.10 10 3.037704 0.6143997 2.469785
##
## Rsquared was used to select the optimal model using the largest value.
## The final values used for the model were size = 5 and decay = 0.1.
## RMSE Rsquared MAE
## KNN 3.467175 0.6741064 2.811834
## MARS 1.868228 0.8591140 1.410758
## SVM 2.033144 0.8315281 1.566636
## NNET 3.349946 0.5910171 2.606147
Based on the performance values on the test set, MARS was the best model for this data base on the Rsquared. It also had the lowest RMSE, indicaticating that it far out preforms the other models trained here.
## $KNN
## Length Class Mode
## learn 2 -none- list
## k 1 -none- numeric
## theDots 0 -none- list
## xNames 10 -none- character
## problemType 1 -none- character
## tuneValue 1 data.frame list
## obsLevels 1 -none- logical
## param 0 -none- list
##
## $MARS
## Call: earth(x=data.frame[200,10], y=c(5.413,16.11,1...), keepxy=TRUE, degree=1,
## nprune=9)
##
## coefficients
## (Intercept) 22.921198
## h(X1- -0.901364) -3.774019
## h(0.430044-X1) -6.033602
## h(X1-0.430044) 4.039842
## h(0.14566-X2) -3.605096
## h(-0.404554-X3) 4.066603
## h(X3- -0.404554) 2.475100
## h(1.37736-X4) -2.931072
## h(X5- -1.25848) 1.539441
##
## Selected 9 of 18 terms, and 5 of 10 predictors (nprune=9)
## Termination condition: Reached nk 21
## Importance: X4, X1, X2, X5, X3, X6-unused, X7-unused, X8-unused, X9-unused, ...
## Number of terms at each degree of interaction: 1 8 (additive model)
## GCV 2.587705 RSS 433.2982 GRSq 0.8880058 RSq 0.9052909
##
## $SVM
## Length Class Mode
## 1 ksvm S4
##
## $NNET
## a 10-5-1 network with 61 weights
## options were - linear output units decay=0.1
## b->h1 i1->h1 i2->h1 i3->h1 i4->h1 i5->h1 i6->h1 i7->h1 i8->h1 i9->h1
## -6.25 0.07 0.31 1.16 2.51 0.92 -0.54 -0.94 1.60 -0.28
## i10->h1
## -0.43
## b->h2 i1->h2 i2->h2 i3->h2 i4->h2 i5->h2 i6->h2 i7->h2 i8->h2 i9->h2
## -0.26 2.25 0.30 -3.21 0.05 0.25 -0.68 -0.68 -0.39 -0.17
## i10->h2
## -1.21
## b->h3 i1->h3 i2->h3 i3->h3 i4->h3 i5->h3 i6->h3 i7->h3 i8->h3 i9->h3
## 3.09 3.82 8.50 -0.38 4.26 -0.31 1.18 2.36 -1.50 0.33
## i10->h3
## 1.88
## b->h4 i1->h4 i2->h4 i3->h4 i4->h4 i5->h4 i6->h4 i7->h4 i8->h4 i9->h4
## -7.11 0.75 0.34 -2.54 2.47 0.71 0.81 0.59 -0.66 -0.33
## i10->h4
## -0.20
## b->h5 i1->h5 i2->h5 i3->h5 i4->h5 i5->h5 i6->h5 i7->h5 i8->h5 i9->h5
## -1.76 -0.15 0.44 3.89 0.79 1.75 0.64 -0.22 0.85 0.46
## i10->h5
## 0.53
## b->o h1->o h2->o h3->o h4->o h5->o
## 4.70 13.63 7.61 4.66 9.73 7.04
The Mars model did correctly select X1- X5.
7.5. Exercise 6.3 describes data for a chemical manufacturing process. Use the same data imputation, data splitting, and pre-processing steps as before and train several nonlinear regression models.
## [1] 176 57
## Yield BiologicalMaterial01 BiologicalMaterial02 BiologicalMaterial03
## 3 1.00422585 2.23914983 1.308996029 -0.05623504
## 4 0.67372192 2.23914983 1.308996029 -0.05623504
## 5 1.25345832 1.48276526 1.893939107 1.13594780
## 6 1.83861281 -0.40819618 0.662088642 -0.59859075
## 7 1.59479844 1.49677238 2.176496356 1.17593716
## 8 1.56228986 0.74038780 1.960860560 1.08846043
## 13 1.76817755 1.06255161 1.373438911 0.57609674
## 16 0.55994187 1.00652312 1.142931681 0.11871842
## 17 0.38656276 2.01503588 0.627388629 -0.18869980
## 19 -0.47491469 1.53879374 1.004131628 -0.10622174
## 21 0.02355025 1.53879374 1.004131628 -0.10622174
## 22 0.54368758 0.93648751 1.522153252 0.74605152
## 24 0.92837248 -0.19808935 0.134152729 -0.68106881
## 25 1.73566897 2.46326378 1.975731995 1.43336867
## 26 -1.81318470 0.26414567 0.012702683 -0.36365326
## 27 -2.66924406 0.68435932 -0.354126026 -1.67830351
## 28 -2.19786960 0.62833083 -0.007125896 -1.06846575
## 30 -0.98963392 0.16609581 1.484974667 2.36062199
## 31 -0.10648408 0.67035220 1.450274654 2.09069380
## 32 0.91753629 1.00652312 1.413096068 1.59832479
## 33 1.86570330 0.60031659 1.430446075 1.55083742
## 34 -0.85418149 -1.73887275 1.358567476 2.17067252
## 38 1.34556597 -1.52876592 0.855417287 0.83602759
## 39 1.11258779 -1.52876592 0.855417287 0.83602759
## 40 0.67914001 -0.98248817 0.493545722 0.41613929
## 41 0.70081240 0.26414567 0.771145826 0.86601961
## 44 2.15828055 0.48825961 -0.066611632 0.52361070
## 45 1.70857848 0.50226674 0.761231537 1.25841522
## 46 1.31847548 0.75439493 1.145410253 1.56583343
## 47 1.50810889 0.75439493 1.145410253 1.56583343
## 48 1.98490144 0.75439493 1.145410253 1.56583343
## 49 3.33942574 2.18312135 2.245896382 1.59832479
## 50 -0.23651841 0.74038780 0.329959946 0.45112998
## 51 0.51117900 0.74038780 0.329959946 0.45112998
## 52 -0.01979453 0.74038780 0.329959946 0.45112998
## 53 1.36182026 1.60882935 1.470103233 1.11595312
## 54 -0.01437643 0.64233795 0.406795689 0.95349634
## 55 -0.22026412 0.64233795 0.406795689 0.95349634
## 56 -0.42073372 0.64233795 0.406795689 0.95349634
## 57 -0.56160425 0.33418127 -0.019518757 0.30616855
## 58 0.09940361 0.33418127 -0.019518757 0.30616855
## 59 1.15593257 0.33418127 -0.019518757 0.30616855
## 61 0.21318365 0.22212430 0.059795558 0.44363198
## 62 -1.07090538 -0.35216769 -0.252504559 -0.18869980
## 65 0.93379058 -0.05801813 -0.748219032 -0.84102626
## 66 1.00422585 -0.05801813 -0.748219032 -0.84102626
## 67 0.96629917 -0.05801813 -0.748219032 -0.84102626
## 69 -0.25277271 -0.19808935 -0.540018954 -0.29617121
## 70 -0.43156991 -0.19808935 -0.540018954 -0.29617121
## 72 -0.43156991 0.23613142 -0.790354762 -1.10345644
## 73 -0.05230311 0.05403884 -0.621811842 -0.68106881
## 74 -0.54534995 -0.03000389 0.783538688 1.43586801
## 75 -0.97879773 -0.03000389 0.783538688 1.43586801
## 76 -0.76749194 -0.03000389 0.783538688 1.43586801
## 79 0.12649410 0.78240917 0.617474340 1.03597439
## 82 0.58161426 3.35971957 2.057524883 2.63554885
## 85 0.39739896 0.54428810 0.377052821 0.65857480
## 86 -0.64287570 -0.15606799 -0.924197670 -0.90850830
## 87 -0.74040145 -0.15606799 -0.924197670 -0.90850830
## 88 -0.47491469 -0.15606799 -0.924197670 -0.90850830
## 91 -0.06313930 0.05403884 -0.148404520 0.36865193
## 92 -0.54534995 -0.18408223 -0.336776020 0.14871044
## 93 -0.10648408 1.28666555 0.292781360 0.61608610
## 94 -0.14441076 1.13258721 0.404317117 0.82852958
## 95 0.32154560 -0.31014633 -0.520190375 -0.32616323
## 96 -0.17150125 -0.60429588 -0.393783184 -0.30116988
## 97 -0.07939359 -0.60429588 -0.393783184 -0.30116988
## 100 -1.32555595 -0.78638847 -0.976247689 -0.92100498
## 101 -1.55853413 -0.78638847 -0.976247689 -0.92100498
## 102 -1.25512069 -0.56227452 -0.956419110 -0.97599035
## 103 -1.15217684 -0.73035998 -1.092740590 -0.91600631
## 104 -1.24970259 -0.71635286 -1.053083433 -1.02347772
## 106 -0.94087105 -0.71635286 -1.053083433 -1.02347772
## 112 0.00729596 -0.01599677 0.753795820 0.95099700
## 114 -0.20942793 -0.43621042 0.166374170 0.45362932
## 115 0.91211819 -0.88443832 -0.492926079 -0.12121775
## 117 2.00657383 -0.01599677 -0.760611894 1.17093849
## 118 -0.32320797 -1.13656651 -1.050604860 -1.06596641
## 119 0.00729596 -1.13656651 -1.050604860 -1.06596641
## 120 -0.18233744 -1.13656651 -1.050604860 -1.06596641
## 121 0.22401985 -1.37468758 -1.633069365 -1.40587599
## 122 0.26194653 -0.54826740 -1.407519280 -1.72079221
## 123 1.30222119 -0.53426027 -0.770526183 -0.66357347
## 125 0.68997621 -0.91245256 -0.733347598 -0.95599567
## 126 0.61412285 -0.87043120 -0.740783315 -0.84352559
## 127 1.13967828 -0.25411784 -0.678819006 -0.24868384
## 128 0.78208386 -0.25411784 -0.678819006 -0.24868384
## 129 1.38349265 -0.25411784 -0.678819006 -0.24868384
## 130 0.80375625 -0.21209647 0.062274131 0.37864927
## 133 -0.22026412 -0.07202526 -0.621811842 -0.28367453
## 135 -1.25512069 -1.72486562 -1.756997984 -1.66580684
## 136 -1.16301303 -1.72486562 -1.756997984 -1.66580684
## 138 -0.55076805 -0.17007511 -1.251369222 -0.94599833
## 139 -1.37431883 -0.43621042 -1.261283511 -1.08346176
## 140 -0.22026412 -1.55678016 -2.185791002 -2.53557545
## 142 0.07231313 -0.22610360 -0.277290283 -0.03624036
## 143 0.19692936 -0.22610360 -0.277290283 -0.03624036
## 144 0.25111033 -0.22610360 -0.277290283 -0.03624036
## 145 -0.85418149 -0.57628164 -0.594547546 -0.55110339
## 146 -1.10883206 -0.57628164 -0.594547546 -0.55110339
## 148 -0.56160425 -1.29064485 -1.898276608 -2.17817053
## 149 -0.83792720 -1.55678016 -2.185791002 -2.53557545
## 150 0.67914001 -1.22060924 -0.795311907 -0.68106881
## 152 -1.23886640 -0.22610360 -0.745740460 -0.64607812
## 153 -1.49351696 -0.22610360 -0.745740460 -0.64607812
## 154 -1.44475409 -0.22610360 -0.745740460 -0.64607812
## 155 -1.22261210 -0.26812496 -0.725911881 -0.64357878
## 156 -1.84569328 -0.71635286 -1.070433439 -1.01348038
## 157 -1.64522369 -0.71635286 -1.070433439 -1.01348038
## 158 -1.32555595 -0.71635286 -1.070433439 -1.01348038
## 159 -1.16301303 -0.99649529 -0.723433308 -0.36365326
## 161 -1.01130631 -0.99649529 -0.723433308 -0.36365326
## 163 -0.82709101 -0.03000389 -0.487968934 -0.14371177
## 164 -0.81625481 -1.47273743 -0.569761822 -0.60109009
## 166 -0.55618615 -2.56529293 -1.519055037 -1.65580949
## 167 -0.73498336 -2.56529293 -1.519055037 -1.65580949
## 169 -0.69163858 1.80492906 1.792317640 2.05070444
## 170 -0.30153558 -0.03000389 0.845502997 0.83352825
## 171 -0.22026412 0.30616703 1.021481635 1.05846841
## 172 -0.27986319 0.41822400 0.156459880 -0.37864927
## 173 -0.26902700 0.64233795 0.260559920 -0.27367719
## 174 1.11258779 1.52478662 0.674481504 0.14871044
## 175 -0.91919866 1.56680799 0.662088642 0.38614727
## 176 -0.37197084 1.56680799 0.662088642 0.38614727
## BiologicalMaterial04 BiologicalMaterial05 BiologicalMaterial06
## 3 1.2964386029 0.412855482 1.129076662
## 4 1.2964386029 0.412855482 1.129076662
## 5 0.9414411656 -0.373418540 1.534835032
## 6 1.5894523607 1.730542291 0.619209236
## 7 0.8287435665 -0.481870129 1.478776310
## 8 1.8881009984 0.445390958 1.550851810
## 13 0.5695390884 0.038697499 1.046323310
## 16 0.8174738065 1.150326288 0.955561569
## 17 1.7077848398 1.226242401 0.515100180
## 19 1.8993707583 1.735964870 0.904841773
## 21 1.8993707583 1.735964870 0.904841773
## 22 0.6089832481 -0.476447550 1.163779680
## 24 -0.4954532235 0.179684565 0.373618643
## 25 3.3926139470 2.798790445 2.063388699
## 26 -0.2925975451 2.126390591 0.010571680
## 27 -0.0728372267 0.846661839 -0.448575950
## 28 0.1018440520 0.971381166 0.007902217
## 30 -0.3038673050 1.367229467 2.794821551
## 31 0.0342254925 1.378074626 2.397071570
## 32 0.5188251688 1.280468196 1.879195755
## 33 0.4681112492 1.177439186 1.996652125
## 34 0.0905742920 0.933423110 2.471816533
## 38 0.3779531699 1.394342364 0.979586736
## 39 0.3779531699 1.394342364 0.979586736
## 40 -0.0502977069 1.475681056 0.501752865
## 41 0.0285906125 1.920332572 0.888824995
## 44 -0.6194205826 -0.243276633 0.261501199
## 45 -0.1291860263 1.112368232 1.137085051
## 46 0.0398603724 0.244755518 0.907511236
## 47 0.0398603724 0.244755518 0.907511236
## 48 0.0398603724 0.244755518 0.907511236
## 49 1.5556430809 2.202306704 1.951271255
## 50 0.6202530080 -0.086021829 0.333576699
## 51 0.6202530080 -0.086021829 0.333576699
## 52 0.6202530080 -0.086021829 0.333576699
## 53 1.1893758837 1.313003672 1.299922292
## 54 0.4906507690 -1.615189237 0.517769643
## 55 0.4906507690 -1.615189237 0.517769643
## 56 0.4906507690 -1.615189237 0.517769643
## 57 0.2089067711 -1.457934432 -0.072181672
## 58 0.2089067711 -1.457934432 -0.072181672
## 59 0.2089067711 -1.457934432 -0.072181672
## 61 -0.2249789856 -0.324615325 0.424338439
## 62 -0.6757693822 -0.731308785 -0.210993746
## 65 -0.1855348259 -0.649970093 -0.638107820
## 66 -0.1855348259 -0.649970093 -0.638107820
## 67 -0.1855348259 -0.649970093 -0.638107820
## 69 -0.2925975451 -0.893986168 -0.611413191
## 70 -0.2925975451 -0.893986168 -0.611413191
## 72 -0.0615674668 -0.172783100 -0.766242042
## 73 -0.1348209063 0.092923293 -0.563362857
## 74 0.1920021313 -0.910253907 0.624548162
## 75 0.1920021313 -0.910253907 0.624548162
## 76 0.1920021313 -0.910253907 0.624548162
## 79 1.0710434046 -0.823492635 0.306882069
## 82 6.0522772869 0.738210249 1.323947458
## 85 0.9189016458 -0.969902281 -0.120232005
## 86 0.1694626114 0.342361949 -1.134627931
## 87 0.1694626114 0.342361949 -1.134627931
## 88 0.1694626114 0.342361949 -1.134627931
## 91 -0.2080743457 -0.747576523 -0.477940042
## 92 0.0116859726 -1.701950508 -0.584718561
## 93 1.0428690048 0.846661839 0.039935773
## 94 0.9583458055 0.304403892 0.079977717
## 95 -0.2024394657 0.071232976 -0.400525616
## 96 -0.3489463446 0.109191032 -0.248366227
## 97 -0.3489463446 0.109191032 -0.248366227
## 100 -1.0927504990 0.976803746 -1.230728598
## 101 -1.0927504990 0.976803746 -1.230728598
## 102 -0.6363252225 0.591800604 -1.158653098
## 103 -1.3294154572 -0.921099066 -1.113272228
## 104 -1.0476714593 -0.302925007 -1.115941691
## 106 -1.0476714593 -0.302925007 -1.115941691
## 112 -0.0333930670 -0.818070056 0.456371995
## 114 -0.3602161045 -1.219340936 0.050613624
## 115 -0.6644996222 -1.712795667 -0.421881320
## 117 -0.0052186672 -0.660815252 0.763360236
## 118 -1.0420365794 0.309826472 -1.027849413
## 119 -1.0420365794 0.309826472 -1.027849413
## 120 -1.0420365794 0.309826472 -1.027849413
## 121 -1.2617968977 0.266445836 -1.190686654
## 122 -0.3151370649 0.450813538 -1.513691672
## 123 -0.5067229834 0.277290995 -0.760903117
## 125 -0.9913226598 1.025606961 -0.432559172
## 126 -0.9293389802 0.808703782 -0.453914876
## 127 0.2258114110 -1.241031254 -0.819631302
## 128 0.2258114110 -1.241031254 -0.819631302
## 129 0.2258114110 -1.241031254 -0.819631302
## 130 -0.1573604261 -0.281234689 0.002563291
## 133 -0.1573604261 -1.289834469 -0.640777283
## 135 -1.6731431346 -1.246453833 -1.369540672
## 136 -1.6731431346 -1.246453833 -1.369540672
## 138 -0.5010881035 -2.905763149 -1.444285635
## 139 -0.8166413811 0.244755518 -1.262762154
## 140 -1.3632247369 -0.286657269 -2.218429895
## 142 -0.1404557862 -0.508983027 -0.296416561
## 143 -0.1404557862 -0.508983027 -0.296416561
## 144 -0.1404557862 -0.508983027 -0.296416561
## 145 -0.3602161045 0.109191032 -0.686158154
## 146 -0.3602161045 0.109191032 -0.686158154
## 148 -1.1885434583 -0.161937941 -1.978178228
## 149 -1.3632247369 -0.286657269 -2.218429895
## 150 -1.1547341785 -0.194473418 -0.814292376
## 152 -0.3996602642 -0.264966951 -0.931748746
## 153 -0.3996602642 -0.264966951 -0.931748746
## 154 -0.3996602642 -0.264966951 -0.931748746
## 155 -0.4785485836 -0.026373455 -0.915731968
## 156 -0.8955297005 0.705674773 -1.025179950
## 157 -0.8955297005 0.705674773 -1.025179950
## 158 -0.8955297005 0.705674773 -1.025179950
## 159 -1.0420365794 -1.853782733 -0.491287357
## 161 -1.0420365794 -1.853782733 -0.491287357
## 163 -0.3376765847 0.006162022 -0.691497079
## 164 -0.1686301860 -0.015528296 -0.533998765
## 166 -1.4139386566 0.044120078 -1.436277246
## 167 -1.4139386566 0.044120078 -1.436277246
## 169 0.6427925279 -1.354905423 1.703011199
## 170 -0.4672788237 1.746810029 1.233185717
## 171 -0.2587882653 1.172016606 1.321277995
## 172 0.0004162127 0.770745726 0.360271328
## 173 0.1131138119 0.857506998 0.504422328
## 174 0.5526344485 1.199129504 1.081026329
## 175 1.1273922042 1.068987597 0.640564940
## 176 1.1273922042 1.068987597 0.640564940
## BiologicalMaterial08 BiologicalMaterial09 BiologicalMaterial10
## 3 2.28261904 -0.72272251 1.100529620
## 4 2.28261904 -0.72272251 1.100529620
## 5 1.07131010 -0.12056780 0.416219259
## 6 1.18948658 -1.73434244 1.634625512
## 7 1.80991311 0.24072503 0.399528763
## 8 2.00194989 0.67427643 1.751458988
## 13 0.56906005 -0.55411919 0.165861810
## 16 1.75082487 -0.24099874 0.750029192
## 17 1.49969985 -0.36142968 2.018506934
## 19 1.94286165 0.31298360 2.402388356
## 21 1.94286165 0.31298360 2.402388356
## 22 2.43033964 1.27643114 0.366147769
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## 2 2.34626280 -0.054722649 -0.01374656
## 9 -0.44058781 0.099788359 -0.01374656
## 10 -0.44058781 0.048284690 -0.12895579
## 11 -0.44058781 -0.106226318 0.10146268
## 12 -0.44058781 -0.003218979 -0.12895579
## 14 -0.44058781 0.254299367 -0.35937426
## 15 -0.44058781 0.202795698 -0.12895579
## 18 -0.44058781 0.254299367 0.90792731
## 20 -0.44058781 0.099788359 0.67750884
## 23 -0.44058781 0.202795698 -0.12895579
## 29 3.27521300 0.254299367 -0.12895579
## 35 -0.44058781 0.254299367 -0.35937426
## 36 3.27521300 -0.106226318 -0.01374656
## 37 -0.44058781 -0.003218979 0.21667191
## 42 -0.44058781 0.099788359 -0.24416502
## 43 1.41731259 0.099788359 -0.24416502
## 60 -0.44058781 0.151292029 -0.24416502
## 63 -0.44058781 0.202795698 -0.12895579
## 64 -0.44058781 0.151292029 -0.24416502
## 68 -0.44058781 -0.003218979 0.33188114
## 71 -0.44058781 0.151292029 0.90792731
## 77 -0.44058781 0.202795698 -0.35937426
## 78 -0.44058781 0.099788359 0.44709038
## 80 -0.44058781 0.048284690 -0.01374656
## 81 -0.44058781 0.048284690 0.10146268
## 83 -0.44058781 0.151292029 0.79271808
## 84 -0.44058781 0.151292029 0.67750884
## 89 -0.44058781 0.151292029 0.21667191
## 90 -0.44058781 0.048284690 -0.12895579
## 98 -0.44058781 0.151292029 -0.01374656
## 99 1.41731259 0.254299367 0.21667191
## 105 -0.44058781 0.254299367 -0.12895579
## 107 -0.44058781 0.254299367 -0.12895579
## 108 -0.44058781 0.202795698 -0.12895579
## 109 1.41731259 0.254299367 -0.12895579
## 110 -0.44058781 0.151292029 -0.01374656
## 111 -0.44058781 0.202795698 0.90792731
## 113 1.41731259 0.048284690 -0.01374656
## 116 -0.44058781 0.305803036 -0.35937426
## 124 -0.44058781 0.202795698 -0.24416502
## 131 -0.44058781 0.099788359 -0.58979272
## 132 -0.44058781 0.202795698 -0.35937426
## 134 -0.44058781 0.305803036 -0.58979272
## 137 1.41731259 0.254299367 -0.47458349
## 141 1.41731259 0.254299367 -0.47458349
## 147 -0.44058781 0.254299367 -0.47458349
## 151 -0.44058781 0.254299367 -0.35937426
## 160 -0.44058781 0.460314044 -0.24416502
## 162 -0.44058781 0.254299367 -0.70500195
## 165 -0.44058781 0.202795698 -0.58979272
## 168 -0.44058781 0.048284690 -0.47458349
## ManufacturingProcess44 ManufacturingProcess45
## 1 -0.01588055 0.64371849
## 2 0.29467248 0.15220242
## 9 0.29467248 -0.09355562
## 10 0.29467248 0.64371849
## 11 0.29467248 -0.83082972
## 12 0.60522552 -0.83082972
## 14 -0.32643359 -0.58507169
## 15 0.29467248 -0.33931365
## 18 -0.01588055 0.15220242
## 20 -0.94753966 -0.33931365
## 23 0.29467248 0.64371849
## 29 -0.32643359 0.15220242
## 35 0.29467248 1.13523456
## 36 0.60522552 -0.09355562
## 37 0.29467248 0.64371849
## 42 -0.01588055 0.64371849
## 43 0.60522552 0.64371849
## 60 -0.01588055 0.39796046
## 63 -0.01588055 -0.33931365
## 64 0.29467248 0.39796046
## 68 0.29467248 -0.83082972
## 71 0.29467248 0.15220242
## 77 0.60522552 0.39796046
## 78 0.29467248 0.15220242
## 80 0.91577855 0.15220242
## 81 0.29467248 -0.09355562
## 83 0.29467248 0.64371849
## 84 0.29467248 0.64371849
## 89 0.29467248 0.39796046
## 90 0.29467248 -0.09355562
## 98 0.29467248 -0.09355562
## 99 0.29467248 0.15220242
## 105 0.29467248 -0.33931365
## 107 0.29467248 -0.58507169
## 108 0.29467248 0.64371849
## 109 0.29467248 -0.58507169
## 110 -0.01588055 0.64371849
## 111 -0.01588055 0.15220242
## 113 -0.01588055 0.39796046
## 116 0.29467248 0.15220242
## 124 -0.01588055 0.15220242
## 131 0.29467248 0.15220242
## 132 -0.01588055 -0.09355562
## 134 0.29467248 0.15220242
## 137 0.29467248 0.64371849
## 141 -0.01588055 0.39796046
## 147 -0.01588055 -0.58507169
## 151 -0.32643359 0.39796046
## 160 -0.01588055 -0.09355562
## 162 0.29467248 -0.83082972
## 165 -0.01588055 0.39796046
## 168 -0.32643359 -0.09355562
## k-Nearest Neighbors
##
## 124 samples
## 56 predictor
##
## Pre-processing: centered (56), scaled (56)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 112, 112, 111, 112, 112, 112, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 5 0.7331985 0.5390202 0.5872201
## 7 0.7495777 0.5081141 0.6134293
## 9 0.7539743 0.5048775 0.6142058
## 11 0.7692892 0.4934248 0.6296052
## 13 0.7749992 0.4906569 0.6386534
## 15 0.7796738 0.4945717 0.6413171
## 17 0.8008349 0.4658446 0.6563732
## 19 0.8005706 0.4634039 0.6560027
## 21 0.8076917 0.4607728 0.6614042
## 23 0.8097771 0.4681025 0.6596785
## 25 0.8226214 0.4550624 0.6691038
## 27 0.8282965 0.4511624 0.6736881
## 29 0.8300861 0.4644303 0.6740676
## 31 0.8441553 0.4474153 0.6821483
## 33 0.8513937 0.4551148 0.6862595
## 35 0.8550559 0.4533600 0.6900227
## 37 0.8608531 0.4479458 0.6961920
## 39 0.8584946 0.4655464 0.6927552
## 41 0.8667824 0.4623245 0.7023725
## 43 0.8713728 0.4561548 0.7072131
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was k = 5.
## Partial Least Squares
##
## 124 samples
## 56 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 111, 111, 112, 112, 112, 112, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 0.7717822 0.4757553 0.6429452
## 2 0.6944841 0.5622464 0.5775583
## 3 0.6562379 0.6174017 0.5526675
## 4 0.6607017 0.6267252 0.5623003
## 5 0.6717716 0.6285520 0.5681390
## 6 0.6907795 0.6207983 0.5813630
## 7 0.7230514 0.6120486 0.5996732
## 8 0.7439499 0.6059499 0.6159466
## 9 0.7550069 0.6069699 0.6305237
## 10 0.7627294 0.6034252 0.6366891
## 11 0.7832391 0.5947809 0.6498214
## 12 0.7970844 0.5814125 0.6575522
## 13 0.8162926 0.5769007 0.6643552
## 14 0.8268635 0.5688058 0.6705877
## 15 0.8270035 0.5704065 0.6724572
## 16 0.8377279 0.5639058 0.6793361
## 17 0.8494510 0.5552573 0.6885689
## 18 0.8575688 0.5473096 0.6950498
## 19 0.8706284 0.5427714 0.7020860
## 20 0.8782051 0.5423162 0.7074147
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was ncomp = 5.
## Support Vector Machines with Radial Basis Function Kernel
##
## 124 samples
## 56 predictor
##
## Pre-processing: centered (56), scaled (56)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 112, 112, 111, 111, 112, 112, ...
## Resampling results across tuning parameters:
##
## C RMSE Rsquared MAE
## 0.25 0.8206841 0.4698489 0.6631817
## 0.50 0.7482548 0.5374628 0.6046570
## 1.00 0.6658502 0.6374008 0.5343725
## 2.00 0.6171673 0.6802396 0.4944881
## 4.00 0.6024390 0.6823679 0.4760243
## 8.00 0.6053784 0.6767094 0.4773850
## 16.00 0.6043757 0.6782157 0.4765995
## 32.00 0.6043757 0.6782157 0.4765995
## 64.00 0.6043757 0.6782157 0.4765995
## 128.00 0.6043757 0.6782157 0.4765995
## 256.00 0.6043757 0.6782157 0.4765995
## 512.00 0.6043757 0.6782157 0.4765995
## 1024.00 0.6043757 0.6782157 0.4765995
## 2048.00 0.6043757 0.6782157 0.4765995
## 4096.00 0.6043757 0.6782157 0.4765995
## 8192.00 0.6043757 0.6782157 0.4765995
## 16384.00 0.6043757 0.6782157 0.4765995
## 32768.00 0.6043757 0.6782157 0.4765995
## 65536.00 0.6043757 0.6782157 0.4765995
## 131072.00 0.6043757 0.6782157 0.4765995
##
## Tuning parameter 'sigma' was held constant at a value of 0.01439414
## Rsquared was used to select the optimal model using the largest value.
## The final values used for the model were sigma = 0.01439414 and C = 4.
## Multivariate Adaptive Regression Spline
##
## 124 samples
## 56 predictor
##
## Pre-processing: centered (56), scaled (56)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 112, 111, 112, 112, 111, 111, ...
## Resampling results across tuning parameters:
##
## nprune RMSE Rsquared MAE
## 2 0.8154544 0.4720160 0.6587037
## 3 0.7130644 0.5741567 0.5873824
## 4 0.6514306 0.6428340 0.5452651
## 5 0.6545428 0.6481032 0.5400096
## 6 0.6457563 0.6513140 0.5255786
## 7 0.6461546 0.6630352 0.5201329
## 8 0.6556009 0.6531376 0.5359745
## 9 0.6744509 0.6328709 0.5524364
## 10 0.6815064 0.6204259 0.5545490
## 11 0.6871669 0.6087856 0.5575379
## 12 0.6747233 0.6230402 0.5389567
## 13 0.6636080 0.6315013 0.5343202
## 14 0.6632792 0.6152898 0.5232999
## 15 0.6576001 0.6250993 0.5170064
## 16 0.6549971 0.6245939 0.5193456
## 17 0.6576019 0.6228212 0.5215179
##
## Tuning parameter 'degree' was held constant at a value of 1
## Rsquared was used to select the optimal model using the largest value.
## The final values used for the model were nprune = 7 and degree = 1.
## Neural Network
##
## 176 samples
## 56 predictor
##
## Pre-processing: centered (56), scaled (56)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 159, 158, 158, 158, 156, 158, ...
## Resampling results across tuning parameters:
##
## size decay RMSE Rsquared MAE
## 1 0.0000000000 0.7733361 0.4359341 0.6178509
## 1 0.0001000000 0.7361748 0.4916011 0.6038343
## 1 0.0001467799 0.7883505 0.4234944 0.6323070
## 1 0.0002154435 0.7666251 0.4453828 0.6045113
## 1 0.0003162278 0.7390739 0.4848626 0.5852972
## 1 0.0004641589 0.7516727 0.4603698 0.6112549
## 1 0.0006812921 0.7268926 0.4899206 0.5838684
## 1 0.0010000000 0.7416230 0.4891885 0.5990619
## 1 0.0014677993 0.7853660 0.4320965 0.6393634
## 1 0.0021544347 0.7846231 0.4161316 0.6177282
## 1 0.0031622777 0.7797749 0.4364165 0.6313108
## 1 0.0046415888 0.7838140 0.4218816 0.6207221
## 1 0.0068129207 0.7998903 0.4111267 0.6414881
## 1 0.0100000000 0.7651401 0.4731201 0.6072512
## 1 0.0146779927 0.7430733 0.4648457 0.6123035
## 1 0.0215443469 0.7475622 0.4570689 0.5969587
## 1 0.0316227766 0.7797138 0.4195511 0.6157066
## 1 0.0464158883 0.7705100 0.4346861 0.6178038
## 1 0.0681292069 0.7352786 0.4981942 0.5953988
## 1 0.1000000000 0.7806364 0.4318419 0.6337328
## 3 0.0000000000 NaN NaN NaN
## 3 0.0001000000 NaN NaN NaN
## 3 0.0001467799 NaN NaN NaN
## 3 0.0002154435 NaN NaN NaN
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## 3 0.1000000000 NaN NaN NaN
## 5 0.0000000000 NaN NaN NaN
## 5 0.0001000000 NaN NaN NaN
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## 5 0.0010000000 NaN NaN NaN
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## 7 0.1000000000 NaN NaN NaN
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## 9 0.0001000000 NaN NaN NaN
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## 9 0.0002154435 NaN NaN NaN
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## 9 0.0010000000 NaN NaN NaN
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## 9 0.0031622777 NaN NaN NaN
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## 9 0.0100000000 NaN NaN NaN
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## 9 0.0316227766 NaN NaN NaN
## 9 0.0464158883 NaN NaN NaN
## 9 0.0681292069 NaN NaN NaN
## 9 0.1000000000 NaN NaN NaN
## 11 0.0000000000 NaN NaN NaN
## 11 0.0001000000 NaN NaN NaN
## 11 0.0001467799 NaN NaN NaN
## 11 0.0002154435 NaN NaN NaN
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## 11 0.0010000000 NaN NaN NaN
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## 11 0.0031622777 NaN NaN NaN
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## 13 0.0000000000 NaN NaN NaN
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## 13 0.1000000000 NaN NaN NaN
## 15 0.0000000000 NaN NaN NaN
## 15 0.0001000000 NaN NaN NaN
## 15 0.0001467799 NaN NaN NaN
## 15 0.0002154435 NaN NaN NaN
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## 15 0.0010000000 NaN NaN NaN
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##
## Rsquared was used to select the optimal model using the largest value.
## The final values used for the model were size = 1 and decay = 0.06812921.
Which nonlinear regression model gives the optimal resampling and test set performance?
## RMSE Rsquared MAE
## KNN 0.6302989 0.4581004 0.4824190
## MARS 0.6126259 0.5046110 0.4675212
## SVM 0.4869395 0.6792380 0.3922497
## NNET 0.5489011 0.5902603 0.4585941
## PLS 0.5816102 0.5648120 0.4522781
Best Model Overall: SVM performs best in terms of explaining variance (highest R-squared) and has competitive RMSE and MAE values, making it a strong choice.
Which predictors are most important in the optimal nonlinear regression model?
Both the SVM and PLS models agree that the top 2 most important variables are ManufacturingProcess32, ManufacturingProcess13, showing that these processes are major predictors. In the SVM model’s top 10, there are six manufacturing process variables and four biological materials. For the PLS model, there are seven manufacturing processes and three biological materials. Even though each model has a different mix, those key manufacturing processes consistently come out on top.
Explore the relationships between the top predictors and the response for the predictors that are unique to the optimal nonlinear regression model. Do these plots reveal intuition about the biological or process predictors and their relationship with yield?
ManufacturingProcess32: It looks like ManufacturingProcess32 has a bit of a sweet spot for yield. When values are low, Yield dips slightly, but once ManufacturingProcess32 crosses zero, yield steadily improves. This suggests that higher levels of this process might be helping to boost yield, but only once it reaches a certain point.
ManufacturingProcess13: With ManufacturingProcess13, the story’s a bit different. Here, yield starts off high but steadily drops as ManufacturingProcess13 increases. This implies that keeping ManufacturingProcess13 lower might actually be better for yield.
BiologicalMaterial06: The relationship between BiologicalMaterial06 and yield is more subtle. There’s a slight upward trend, hinting that a bit more of BiologicalMaterial06 might nudge yields up, but the effect isn’t as strong as with the manufacturing processes. This could mean that biological factors play a smaller role here, or perhaps they’re just harder to optimize for yield.