DATA624 Spring 2021 HW9 - Regression Trees and Rule-Based Models
John K. Hancock
5/2/2021
8.1
##Recreate the simulated data from Exercise 7.2
## Warning: package 'mlbench' was built under R version 3.6.3 set.seed(200)
simulated <- mlbench.friedman1(200, sd = 1)
simulated <- cbind(simulated$x, simulated$y)
simulated <- as.data.frame(simulated)
colnames(simulated)[ncol(simulated)] <- "y"
head(simulated)## V1 V2 V3 V4 V5 V6 V7
## 1 0.5337724 0.6478064 0.85078526 0.18159957 0.92903976 0.36179060 0.8266609
## 2 0.5837650 0.4381528 0.67272659 0.66924914 0.16379784 0.45305931 0.6489601
## 3 0.5895783 0.5879065 0.40967108 0.33812728 0.89409334 0.02681911 0.1785614
## 4 0.6910399 0.2259548 0.03335447 0.06691274 0.63744519 0.52500637 0.5133614
## 5 0.6673315 0.8188985 0.71676079 0.80324287 0.08306864 0.22344157 0.6644906
## 6 0.8392937 0.3862983 0.64618857 0.86105431 0.63038947 0.43703891 0.3360117
## V8 V9 V10 y
## 1 0.4214081 0.59111440 0.5886216 18.46398
## 2 0.8446239 0.92819306 0.7584008 16.09836
## 3 0.3495908 0.01759542 0.4441185 17.76165
## 4 0.7970260 0.68986918 0.4450716 13.78730
## 5 0.9038919 0.39696995 0.5500808 18.42984
## 6 0.6489177 0.53116033 0.9066182 20.85817##(a)
Fit a random forest model to all of the predictors, then estimate the variable importance scores Did the random forest model significantly use the uninformative predictors (V6 - V10)?
No. Looking at the top ten predictors, V6-V10 are in the bottom half of the top ten predictors.
model1 <- randomForest(y ~ ., data = simulated, importance = TRUE, ntree = 1000)
rfImp1 <- varImp(model1, scale = FALSE)
rfImp1 <- rfImp1 %>%
arrange(desc(Overall))
rfImp1## Overall
## V1 8.732235404
## V4 7.615118809
## V2 6.415369387
## V5 2.023524577
## V3 0.763591825
## V6 0.165111172
## V7 -0.005961659
## V10 -0.074944788
## V9 -0.095292651
## V8 -0.166362581rfImp1_df <- as.data.frame(rfImp1)
rfImp1_df['Predictors'] <- rownames(rfImp1_df)
colnames(rfImp1_df) <- c("Overall", "Predictors")
rfImp1_df <- rfImp1_df[, c("Predictors", "Overall") ]
rownames(rfImp1_df) <- 1:nrow(rfImp1_df)
rfImp1_df## Predictors Overall
## 1 V1 8.732235404
## 2 V4 7.615118809
## 3 V2 6.415369387
## 4 V5 2.023524577
## 5 V3 0.763591825
## 6 V6 0.165111172
## 7 V7 -0.005961659
## 8 V10 -0.074944788
## 9 V9 -0.095292651
## 10 V8 -0.166362581rfImp1_df %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "darkgoldenrod4") +
theme_minimal() +
coord_flip() +
labs(title="randomForest Predictor Variable Importance",
y="randomForest Importance", x="Predictors") +
scale_y_continuous()
(b)
Now add an additional predictor that is highly correlated with one of the informative predictors. For example:
Below another the variable “predictor” is created and correlated to existing predictor, “V1”.
set.seed(100)
simulated$predictor <- simulated$V1 + rnorm(200) * .1
cor(simulated$predictor, simulated$V1)## [1] 0.9509187model <- randomForest(y ~ ., data = simulated, importance = TRUE, ntree = 1000)
rfImp1 <- varImp(model, scale = FALSE)
rfImp1 <- rfImp1 %>%
arrange(desc(Overall))
rfImp1## Overall
## V4 7.20204040
## V1 6.49306066
## V2 6.21582190
## predictor 4.16423346
## V5 2.13524474
## V3 0.64839591
## V6 0.14024806
## V10 0.04098736
## V7 -0.04983958
## V9 -0.11410645
## V8 -0.19251042Fit another random forest model to these data. Did the importance score for V1 change? What happens when you add another predictor that is also highly correlated with V1?
The importance score for V1 declined from the most importamt to the 2nd most important. Adding another highly correlated predictor with V1 dropped its importance.
(c)
Use the cforest function in the party package to fit a random forest model using conditional inference trees. The party package function varimp can calculate predictor importance. The conditional argument of that function toggles between the traditional importance measure and the modified version described in Strobl et al. (2007). Do these importances show the same pattern as the traditional random forest model?
Yes. They do show the same patterns.
rfImp2 <- as.data.frame( varimp(model2, conditional = TRUE))
rfImp2['Predictors'] <- rownames(rfImp2)
colnames(rfImp2) <- c("Overall", "Predictors")
rownames(rfImp2) <- 1:nrow(rfImp2)
rfImp2 <- rfImp2 %>%
arrange(desc(Overall))rfImp2 %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "green") +
theme_gray() +
coord_flip() +
labs(title="cForest Predictor Variable Importance",
y="cForest Importance", x="Predictors") +
scale_y_continuous()
(d)
Repeat this process with different tree models, such as boosted trees and Cubist. Does the same pattern occur?
Boosted Trees
library(mlbench)
set.seed(200)
simulated2 <- mlbench.friedman1(200, sd = 1)
simulated2 <- cbind(simulated2$x, simulated2$y)
simulated2 <- as.data.frame(simulated2)
colnames(simulated2)[ncol(simulated2)] <- "y"gbmGrid <- expand.grid(interaction.depth = seq(1, 7, by = 2),
n.trees = seq(100, 1000, by = 50),
shrinkage = c(0.01, 0.1),
n.minobsinnode = 5)set.seed(100)
gbmTune <- train(simulated2[1:10], simulated2$y,
method = "gbm",
tuneGrid = gbmGrid,
verbose = FALSE)## Overall
## V1 100.0000000
## V4 98.1097981
## V2 88.2693765
## V5 38.4827377
## V3 24.8130798
## V7 5.0311729
## V6 3.6098923
## V8 1.0913383
## V10 0.8008837
## V9 0.0000000gbmTune1_df <- as.data.frame(gbmTune1$importance)
gbmTune1_df['Predictors'] <- rownames(gbmTune1_df)
colnames(gbmTune1_df) <- c("Overall", "Predictors")
rownames(gbmTune1_df) <- 1:nrow(gbmTune1_df)
gbmTune1_df## Overall Predictors
## 1 100.0000000 V1
## 2 88.2693765 V2
## 3 24.8130798 V3
## 4 98.1097981 V4
## 5 38.4827377 V5
## 6 3.6098923 V6
## 7 5.0311729 V7
## 8 1.0913383 V8
## 9 0.0000000 V9
## 10 0.8008837 V10gbmTune1_df %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "steelblue") +
theme_gray() +
coord_flip() +
labs(title="boosted Predictor Variable Importance",
y="boosted Importance", x="Predictors") +
scale_y_continuous()
Now add an additional predictor that is highly correlated with one of the informative predictors as was done in Part A:
set.seed(100)
simulated2$duplicate <- simulated2$V1 + rnorm(200) * .1
cor(simulated2$duplicate, simulated2$V1)## [1] 0.9509187col_order <- colnames(simulated2)
col_order <- c("V1","V2","V3","V4","V5","V6","V7","V8","V9","V10", "duplicate", "y")
simulated2 <- simulated2[, col_order]
simulated2## V1 V2 V3 V4 V5 V6
## 1 0.533772448 0.6478064333 0.850785258 0.181599574 0.929039760 0.361790597
## 2 0.583765033 0.4381527551 0.672726594 0.669249143 0.163797838 0.453059313
## 3 0.589578298 0.5879064940 0.409671080 0.338127280 0.894093335 0.026819108
## 4 0.691039888 0.2259547510 0.033354474 0.066912736 0.637445191 0.525006367
## 5 0.667331498 0.8188985116 0.716760786 0.803242873 0.083068641 0.223441572
## 6 0.839293735 0.3862983445 0.646188573 0.861054306 0.630389472 0.437038906
## 7 0.711600085 0.1162793254 0.767706224 0.859962373 0.520582290 0.990291612
## 8 0.096501224 0.8445782231 0.153528016 0.412814007 0.746725963 0.662056439
## 9 0.523824728 0.2514584265 0.285196133 0.452202451 0.506808798 0.019370317
## 10 0.235350536 0.4317718598 0.780373945 0.072122673 0.100005680 0.294671116
## 11 0.454364888 0.1192040211 0.220170008 0.351687343 0.001755818 0.149134940
## 12 0.649252912 0.0973321993 0.598340076 0.734892188 0.669684836 0.668878612
## 13 0.153727122 0.0128550101 0.608990930 0.633952646 0.094662402 0.616397752
## 14 0.649288674 0.1866738056 0.365308329 0.045665963 0.806304601 0.476613421
## 15 0.383213673 0.4608722613 0.345225364 0.735293760 0.217474412 0.350192171
## 16 0.307298063 0.4219112301 0.979319583 0.144514926 0.489620249 0.516859321
## 17 0.566767377 0.7811157859 0.890115921 0.995679246 0.413354418 0.379292418
## 18 0.131787853 0.1998720246 0.379945722 0.570354241 0.932332295 0.175180161
## 19 0.922177571 0.4675492314 0.010254486 0.008189635 0.789955666 0.846729845
## 20 0.646329618 0.7929329765 0.053864328 0.652274119 0.226417012 0.510733424
## 21 0.460360692 0.0697931792 0.784207606 0.686981049 0.379707196 0.434224161
## 22 0.098747006 0.2313314399 0.520667098 0.298788559 0.058919030 0.321473247
## 23 0.206593813 0.6473270494 0.606014522 0.086910314 0.536598262 0.592455531
## 24 0.922339834 0.6342856146 0.888005181 0.503549783 0.504815002 0.519335387
## 25 0.319426806 0.0545100805 0.381021996 0.999287510 0.982473919 0.515890769
## 26 0.265324291 0.8564205186 0.050943109 0.395974373 0.937435226 0.983467527
## 27 0.717369557 0.2948283439 0.736812766 0.919277884 0.128039610 0.414260471
## 28 0.380335360 0.0004408562 0.733275530 0.345613460 0.443263867 0.558792540
## 29 0.030620939 0.2731315538 0.903001443 0.758067884 0.147233479 0.146207562
## 30 0.521419376 0.3537345366 0.830735998 0.393664814 0.671653698 0.573219036
## 31 0.263748623 0.5057117699 0.140882633 0.678475745 0.562049805 0.812396222
## 32 0.166053713 0.2998292497 0.377729565 0.270103104 0.711894969 0.103405041
## 33 0.483074695 0.5088484667 0.636458001 0.654003645 0.616297887 0.399691042
## 34 0.325727710 0.9247118952 0.817825248 0.371338245 0.382548874 0.441881776
## 35 0.925363897 0.2371832319 0.010075368 0.345586454 0.547638883 0.201830557
## 36 0.560558849 0.4270182950 0.313384585 0.610149687 0.802779849 0.815573796
## 37 0.178553036 0.4352612651 0.153328084 0.549069691 0.356350074 0.094069178
## 38 0.972322052 0.6359792664 0.445975145 0.899534479 0.268725364 0.903799011
## 39 0.493773325 0.3447996511 0.445896353 0.449058379 0.003265168 0.759522119
## 40 0.485940594 0.8554888491 0.813352563 0.045685444 0.880070203 0.513183234
## 41 0.586856649 0.2803302526 0.037726685 0.018251117 0.150030803 0.053033940
## 42 0.720570024 0.9092058453 0.210796098 0.875075159 0.094086062 0.585604633
## 43 0.691673029 0.5930176671 0.420771204 0.247303587 0.983297946 0.427623936
## 44 0.176150461 0.7141316915 0.741954805 0.197583070 0.836461429 0.296208750
## 45 0.952475880 0.8493538222 0.317191089 0.925082660 0.607305124 0.803849567
## 46 0.689011891 0.7483011317 0.807849665 0.877950979 0.967313918 0.574638351
## 47 0.157799606 0.6691785671 0.353649540 0.368825636 0.377917988 0.298162997
## 48 0.576220999 0.8380715831 0.609410121 0.191988432 0.172759505 0.113711787
## 49 0.653276739 0.9181834545 0.893769723 0.622584245 0.327600596 0.832185488
## 50 0.832807913 0.2265766494 0.355865418 0.047708418 0.547652281 0.939744496
## 51 0.067187183 0.1867572814 0.053412318 0.788249273 0.069746084 0.175875548
## 52 0.118626094 0.4984532818 0.081841033 0.847314714 0.095897603 0.953105583
## 53 0.892374709 0.9191673915 0.179852584 0.484247719 0.850093837 0.771444682
## 54 0.557935121 0.9555177600 0.070927210 0.284588894 0.860588939 0.018207328
## 55 0.515005544 0.6027795288 0.491738453 0.258037420 0.287011503 0.054381748
## 56 0.134100055 0.7252116359 0.862601955 0.610891974 0.280598821 0.785266264
## 57 0.149258960 0.1695368735 0.566346588 0.563854012 0.273068628 0.328188200
## 58 0.161343819 0.2199983387 0.222847626 0.136463749 0.596218371 0.105031757
## 59 0.561064044 0.7804879546 0.169082082 0.368560432 0.294977250 0.618674891
## 60 0.671786989 0.5629266184 0.306758978 0.797413421 0.402194366 0.169488368
## 61 0.147402651 0.9183623586 0.999923422 0.435399952 0.960000194 0.746313307
## 62 0.570647350 0.8898196355 0.359521539 0.807744707 0.942994522 0.850621036
## 63 0.758280237 0.4162223253 0.651333184 0.088788726 0.318467662 0.789343349
## 64 0.565787035 0.2931080312 0.935225714 0.254972817 0.682191425 0.116470202
## 65 0.775718143 0.2964265901 0.815802228 0.778016577 0.345414489 0.608970067
## 66 0.677378375 0.2773598756 0.627044755 0.937812351 0.439045849 0.796132486
## 67 0.218266052 0.7430458625 0.370964498 0.678309920 0.850654966 0.108555941
## 68 0.281448058 0.2555278649 0.540702318 0.102928993 0.499993075 0.200114859
## 69 0.094555768 0.6770530874 0.857065403 0.147499445 0.190941744 0.593200353
## 70 0.593106887 0.6049814720 0.829584161 0.068155296 0.812524924 0.272600746
## 71 0.355217626 0.9024892272 0.162602290 0.167165469 0.786120466 0.253500610
## 72 0.153351908 0.5403167598 0.522081524 0.131646728 0.303439272 0.406195677
## 73 0.466252540 0.2189726466 0.649081210 0.876677948 0.373312224 0.500154867
## 74 0.275116619 0.5810471375 0.328282601 0.821013230 0.365157783 0.574757167
## 75 0.397941506 0.0506482811 0.736786507 0.069037383 0.465576746 0.526418373
## 76 0.311401952 0.8876241017 0.829994129 0.273672034 0.822258464 0.576108309
## 77 0.586229856 0.6614987573 0.510906287 0.863162806 0.946865431 0.895700728
## 78 0.150715668 0.0240218288 0.293724078 0.763388061 0.337483510 0.572278405
## 79 0.644267766 0.5393897707 0.438592263 0.678769260 0.816074158 0.739229684
## 80 0.006409079 0.3240858268 0.081627410 0.388581997 0.143550989 0.586718400
## 81 0.816851889 0.8537856233 0.217289788 0.442311989 0.143528348 0.926974642
## 82 0.742108528 0.2384303520 0.580422256 0.720915187 0.629143175 0.597393914
## 83 0.654247520 0.5939083034 0.994853858 0.936799756 0.912532976 0.215555561
## 84 0.440734623 0.8666409499 0.564446902 0.379492091 0.822953047 0.368613384
## 85 0.442322013 0.2467340643 0.826851101 0.198192747 0.346601916 0.981209712
## 86 0.786464168 0.9204477360 0.150473845 0.543170314 0.512502319 0.773290500
## 87 0.459340288 0.2267787226 0.645397100 0.169832431 0.382568107 0.076924091
## 88 0.984272037 0.7370369236 0.306019300 0.648133427 0.114868225 0.384680568
## 89 0.371441818 0.1517067349 0.995130365 0.887727774 0.512004345 0.986306011
## 90 0.997792503 0.6529070695 0.098833617 0.917166736 0.471261014 0.157362159
## 91 0.474391870 0.6010630331 0.278657043 0.790569007 0.927579608 0.305082921
## 92 0.220132116 0.6547463359 0.537419467 0.345841283 0.043483641 0.429867428
## 93 0.031105185 0.6107613579 0.025156959 0.909916925 0.158163789 0.016845753
## 94 0.229582377 0.6054298035 0.639548430 0.572823923 0.743228543 0.887359502
## 95 0.609273809 0.9123187338 0.725720419 0.461442270 0.011241655 0.763862459
## 96 0.370745452 0.0759057687 0.361935701 0.433070669 0.090679155 0.101371452
## 97 0.307162299 0.6478466513 0.830584273 0.446856117 0.350730690 0.442842154
## 98 0.157705784 0.3871437064 0.703486373 0.566900127 0.685163247 0.440206385
## 99 0.448205397 0.8644333375 0.422698680 0.633362517 0.233479040 0.103215690
## 100 0.683045527 0.9840194189 0.611699514 0.531140843 0.797903161 0.597651707
## 101 0.686627647 0.6046307203 0.167846072 0.456818942 0.607740600 0.314174908
## 102 0.831901784 0.2939653466 0.672954567 0.803079295 0.280210467 0.998987383
## 103 0.113058501 0.2546948988 0.218817725 0.057622184 0.279840802 0.239368085
## 104 0.556645789 0.8126982844 0.692510723 0.966434979 0.351036289 0.281969752
## 105 0.192172982 0.3423131080 0.496556215 0.413942024 0.088539597 0.727522285
## 106 0.048556563 0.9640056610 0.605707243 0.566484744 0.508386431 0.614031048
## 107 0.636388587 0.4812663090 0.156460918 0.863360892 0.745412975 0.765995033
## 108 0.002806243 0.9363095718 0.649450997 0.242205442 0.870268838 0.335062859
## 109 0.501964895 0.7322653499 0.968477561 0.455123628 0.558531469 0.644129353
## 110 0.479473393 0.8101365152 0.371763220 0.896207781 0.851932624 0.277587108
## 111 0.904642434 0.7766639574 0.927888780 0.170289954 0.499319865 0.493327187
## 112 0.076446557 0.3885678530 0.869672049 0.631985184 0.508797599 0.512153390
## 113 0.171706995 0.6642553948 0.447441930 0.109595960 0.687226565 0.990115111
## 114 0.598192136 0.8803027971 0.934215342 0.184075910 0.930016244 0.015515274
## 115 0.494660591 0.5270667071 0.165982118 0.279556816 0.548412474 0.006808892
## 116 0.822326746 0.0874312406 0.339381942 0.624753956 0.139959793 0.881927748
## 117 0.884809928 0.2049752097 0.351055704 0.772163214 0.897429584 0.373503622
## 118 0.195553894 0.1479548330 0.547592697 0.426198894 0.233539708 0.459527157
## 119 0.463013117 0.4677024283 0.079132932 0.123636657 0.209901525 0.249119067
## 120 0.007715050 0.9759014850 0.647108061 0.623121100 0.489483954 0.913406589
## 121 0.623211886 0.7964882990 0.725319422 0.268862381 0.873370248 0.629094972
## 122 0.632887607 0.6062786465 0.027653304 0.215499579 0.437937672 0.412266847
## 123 0.313287797 0.6479254356 0.003295714 0.679255102 0.590496615 0.988463188
## 124 0.775744612 0.1102327388 0.168523920 0.228762099 0.965724084 0.842011251
## 125 0.998992379 0.8608238841 0.913439707 0.130730744 0.663723183 0.934387672
## 126 0.751483215 0.3711484901 0.757779663 0.436154100 0.914117961 0.487309208
## 127 0.512864344 0.4433466932 0.777240771 0.131851328 0.666940580 0.893005643
## 128 0.594934646 0.6147596298 0.629629193 0.029415055 0.156732836 0.675986912
## 129 0.108193488 0.0456732074 0.553760919 0.836029727 0.991577258 0.029231649
## 130 0.213286245 0.6094768783 0.343689348 0.090614796 0.383258829 0.830723291
## 131 0.511472948 0.8676087293 0.542017557 0.964182970 0.315437378 0.805567415
## 132 0.653088958 0.0627070705 0.925106390 0.035819308 0.250788742 0.872808259
## 133 0.680070220 0.4819761757 0.543910673 0.283038010 0.721935218 0.261010709
## 134 0.594429644 0.9517888685 0.487364555 0.429615057 0.077726093 0.396774478
## 135 0.566119617 0.7702909564 0.283901030 0.481008470 0.085473549 0.392161391
## 136 0.292137912 0.4600951856 0.031411853 0.355790904 0.714166709 0.646736944
## 137 0.621721983 0.8975026356 0.486688155 0.237542561 0.754609415 0.993754126
## 138 0.734009909 0.7064418797 0.685221680 0.159361927 0.678954404 0.522533498
## 139 0.250146729 0.2166299177 0.828084011 0.759835896 0.783513594 0.528184886
## 140 0.725502808 0.3214482346 0.801824650 0.683726188 0.785781410 0.368117954
## 141 0.518633971 0.1892801912 0.636985009 0.216002044 0.823852410 0.130777703
## 142 0.353793057 0.1187343048 0.771915119 0.228639466 0.026823693 0.470881379
## 143 0.536732926 0.5057627214 0.544558276 0.408174795 0.220592264 0.716128180
## 144 0.827716813 0.1134541789 0.151092910 0.249067954 0.167421041 0.812992523
## 145 0.799086446 0.2226722005 0.314966519 0.644402519 0.296044190 0.010295009
## 146 0.121202702 0.5125092892 0.736546513 0.173788953 0.987242828 0.128936096
## 147 0.965792880 0.2959974960 0.281766439 0.181185599 0.460291081 0.428525911
## 148 0.655097562 0.9138811582 0.685150367 0.203402501 0.556077081 0.384476536
## 149 0.523663767 0.3619226965 0.790130149 0.296799039 0.181327148 0.809934170
## 150 0.406266008 0.1738398047 0.437415589 0.528837076 0.650578036 0.017366972
## 151 0.811131607 0.4745276461 0.736739275 0.090695082 0.734380059 0.640642888
## 152 0.195899217 0.1883440749 0.036628024 0.037811573 0.361777857 0.891157788
## 153 0.901721909 0.7641276480 0.975725230 0.649152147 0.125422492 0.843844815
## 154 0.419387562 0.7132732121 0.537194521 0.663290517 0.813946252 0.346468189
## 155 0.502626143 0.1582271636 0.926717208 0.752402752 0.534871275 0.519248105
## 156 0.505678876 0.5922643617 0.249804128 0.229866606 0.489065639 0.002901212
## 157 0.914411720 0.3216436969 0.149495436 0.232416035 0.057981907 0.278796293
## 158 0.148558215 0.5582501232 0.832446445 0.294442032 0.117299439 0.885807658
## 159 0.937065663 0.7175001081 0.341711296 0.826616130 0.589513207 0.927866664
## 160 0.975472900 0.4723303919 0.144815880 0.495536016 0.437703832 0.338820112
## 161 0.424515043 0.6310416884 0.783094346 0.510714823 0.314462922 0.086185409
## 162 0.812289485 0.6547854072 0.352954853 0.395277522 0.834191832 0.642550439
## 163 0.029440868 0.7336349678 0.287532780 0.481363036 0.646652654 0.586816839
## 164 0.917813970 0.6703584662 0.014808858 0.308127946 0.908841855 0.511950091
## 165 0.214090701 0.3539453736 0.441450395 0.704947843 0.190465599 0.788839862
## 166 0.553994835 0.3797423861 0.426848450 0.406387825 0.583469785 0.982102466
## 167 0.087216421 0.0444812854 0.887981009 0.334847389 0.958314174 0.631051316
## 168 0.051853288 0.5381637057 0.287162258 0.544222318 0.580674538 0.138133082
## 169 0.153477015 0.7609185344 0.588195231 0.726811070 0.869440276 0.140277030
## 170 0.585922012 0.6343205774 0.114031907 0.054257943 0.132969180 0.262855512
## 171 0.915327054 0.6440016078 0.582549772 0.953309200 0.661264660 0.182328664
## 172 0.021536301 0.3673074185 0.137482502 0.985332304 0.359814066 0.504694133
## 173 0.175545276 0.5064939184 0.364339191 0.650103795 0.942291794 0.238556437
## 174 0.083142271 0.1788396279 0.373116091 0.705161238 0.367621270 0.640988169
## 175 0.491874318 0.4900236735 0.297881532 0.331352153 0.870221517 0.530976141
## 176 0.665890210 0.6166888489 0.978142474 0.226049843 0.988691468 0.411653516
## 177 0.028172681 0.3769877132 0.719316378 0.022271170 0.711718217 0.537131623
## 178 0.879781784 0.7322189799 0.869278736 0.649725121 0.669133191 0.397410648
## 179 0.795590631 0.2757800566 0.781217543 0.406130929 0.115849692 0.363247100
## 180 0.066798607 0.4353600563 0.641473262 0.070881601 0.725632793 0.845899404
## 181 0.369471576 0.2884542705 0.375342084 0.381129961 0.752541286 0.080834012
## 182 0.111091629 0.5124843172 0.743466425 0.401846189 0.632692037 0.334856320
## 183 0.825969449 0.7803220809 0.425994063 0.961734195 0.726619251 0.637834937
## 184 0.612556007 0.9145965697 0.257388497 0.629601910 0.375935599 0.271460483
## 185 0.637976925 0.1076111828 0.280669488 0.654566472 0.932735895 0.974294363
## 186 0.722749287 0.4142492083 0.976476628 0.461700869 0.261488323 0.760588499
## 187 0.088224613 0.3651040641 0.112417366 0.427385604 0.630677684 0.064398194
## 188 0.206456413 0.6789903478 0.269728941 0.026255392 0.533788505 0.339906024
## 189 0.271994818 0.4532893968 0.732908373 0.710368193 0.555094344 0.429670967
## 190 0.520548412 0.3144283574 0.803517855 0.349941988 0.498034912 0.495041399
## 191 0.776805477 0.9616133086 0.754222457 0.091987771 0.551281321 0.733340201
## 192 0.289232634 0.8427688032 0.202012851 0.496472600 0.546778636 0.428116115
## 193 0.989449516 0.2357514210 0.704040867 0.447436986 0.046436282 0.493715242
## 194 0.310988950 0.4760307493 0.771920531 0.274742047 0.416478656 0.183150188
## 195 0.581546503 0.0395606223 0.147069360 0.853941998 0.729293162 0.166967576
## 196 0.701018440 0.7045858139 0.531901518 0.318705286 0.510770075 0.799619116
## 197 0.539472235 0.1585750368 0.654213027 0.492335809 0.606566809 0.903776626
## 198 0.011292625 0.9602364919 0.776298914 0.773416284 0.594650894 0.984942808
## 199 0.603909890 0.9586990301 0.875057548 0.093729714 0.825522528 0.624501048
## 200 0.089178660 0.6006974212 0.113622466 0.825916705 0.558199830 0.084706127
## V7 V8 V9 V10 duplicate y
## 1 0.8266608594 0.421408064 0.59111440 0.588621560 0.483553213 18.463980
## 2 0.6489600763 0.844623926 0.92819306 0.758400814 0.596918149 16.098360
## 3 0.1785614495 0.349590781 0.01759542 0.444118458 0.581686589 17.761647
## 4 0.5133613953 0.797025980 0.68986918 0.445071622 0.779718369 13.787300
## 5 0.6644906041 0.903891937 0.39696995 0.550080800 0.679028625 18.429836
## 6 0.3360117343 0.648917723 0.53116033 0.906618237 0.871156744 20.858166
## 7 0.0084998407 0.072795420 0.97395768 0.440172910 0.653421017 13.888401
## 8 0.4722572784 0.381633542 0.75877525 0.710887919 0.167954496 12.915431
## 9 0.3058403293 0.525661726 0.43136410 0.400128186 0.441298786 12.149448
## 10 0.3228343336 0.960311741 0.92426620 0.832559698 0.199364323 5.271123
## 11 0.1315679180 0.939230266 0.46228702 0.775593376 0.463353503 8.946052
## 12 0.7618696443 0.550847133 0.08637756 0.524860506 0.658880358 12.894078
## 13 0.4806034924 0.485595847 0.54158360 0.081258474 0.133563727 6.533292
## 14 0.4200604216 0.282479481 0.62596273 0.003172379 0.723272724 7.520004
## 15 0.6595693664 0.469818084 0.03909819 0.706367689 0.395551623 15.141730
## 16 0.6941591527 0.917750880 0.33898498 0.689810129 0.304366392 12.974733
## 17 0.1693497750 0.290054937 0.69159996 0.120331543 0.527881952 25.016165
## 18 0.1774999567 0.724190771 0.14320681 0.075203559 0.182873479 12.436690
## 19 0.6109301876 0.182253540 0.20626788 0.247241936 0.830796153 16.899482
## 20 0.1655056404 0.996789995 0.57239957 0.970613467 0.877359300 22.052472
## 21 0.8696455043 0.480284780 0.94174627 0.525216599 0.416551694 12.892896
## 22 0.2200369346 0.543487359 0.91963756 0.948926731 0.175153068 3.555960
## 23 0.6324701225 0.833171203 0.91811502 0.181142754 0.232789942 10.032559
## 24 0.6703429641 0.285668603 0.84918471 0.397776954 0.999680294 19.728886
## 25 0.0101521015 0.960430558 0.23506862 0.230721395 0.237988893 15.271168
## 26 0.2522400960 0.634320574 0.87522970 0.635452710 0.221479234 21.921927
## 27 0.6650384206 0.650785477 0.28744271 0.616526859 0.645347402 17.848795
## 28 0.0648198922 0.178094681 0.56876498 0.428627433 0.403429814 5.964147
## 29 0.6192647608 0.146737191 0.33908035 0.938806834 -0.085152007 13.254190
## 30 0.3292513283 0.042337252 0.86859891 0.880950373 0.546126975 15.181016
## 31 0.2824812313 0.332542812 0.95191869 0.763801782 0.254637267 18.021637
## 32 0.2051616914 0.785139066 0.04968553 0.968671421 0.341791275 8.385652
## 33 0.6479521065 0.175871460 0.67905283 0.730759681 0.469281733 17.967104
## 34 0.3500645757 0.635448656 0.89620270 0.575594178 0.314608361 14.097415
## 35 0.8686830916 0.324884567 0.03161212 0.849832683 0.856362465 17.352764
## 36 0.6281718945 0.651751797 0.69222388 0.442386812 0.538379426 17.608729
## 37 0.5401211150 0.802915463 0.51344968 0.959669129 0.196843804 13.136663
## 38 0.0954262505 0.271751555 0.91415621 0.535858047 1.014054381 21.879995
## 39 0.3189930974 0.487114596 0.38007261 0.068724414 0.600313558 9.980150
## 40 0.0987321541 0.398785473 0.70468780 0.814099950 0.582960796 18.002840
## 41 0.8256829928 0.274217872 0.24911536 0.363809015 0.576693725 9.489052
## 42 0.4254488801 0.543745558 0.56771488 0.586587886 0.860890373 19.991424
## 43 0.6002272039 0.303179812 0.30442762 0.996330470 0.513995466 17.766711
## 44 0.0993871398 0.726330749 0.51122937 0.574089565 0.238437201 13.299483
## 45 0.3573383761 0.659334866 0.82108557 0.880166529 0.900247544 18.828347
## 46 0.3369224169 0.171208087 0.58813299 0.298467441 0.821234986 26.945666
## 47 0.7216083466 0.347465995 0.45980972 0.522110901 0.121455573 9.358890
## 48 0.1637666794 0.465182498 0.67228512 0.549377529 0.708127573 12.133777
## 49 0.0661412831 0.662970975 0.67190601 0.712600555 0.657654646 22.132197
## 50 0.5044657106 0.684693513 0.23367805 0.853776497 0.644942325 8.886239
## 51 0.4450478635 0.954027392 0.87891811 0.228369326 0.022480965 13.343289
## 52 0.8620285194 0.258589442 0.96154879 0.437253388 -0.055233701 12.709052
## 53 0.0236228870 0.676012672 0.37005100 0.260396947 0.910261194 16.708610
## 54 0.1452215833 0.955375290 0.70495617 0.882332698 0.747681691 19.797593
## 55 0.3742820916 0.214503606 0.13091783 0.462896239 0.287812995 12.166608
## 56 0.5384509673 0.037968947 0.61604382 0.535041264 0.232146468 13.772781
## 57 0.2577628391 0.186539843 0.93924713 0.942935549 0.009376398 6.563014
## 58 0.2109247684 0.363152975 0.22155711 0.789319306 0.343831061 5.325261
## 59 0.4573113865 0.197379992 0.41096121 0.626259638 0.699193917 18.244465
## 60 0.2189239766 0.259368576 0.39850931 0.322176775 0.587901802 20.632950
## 61 0.9801436167 0.418736819 0.50638210 0.791115409 0.121203074 18.974731
## 62 0.2792056827 0.632583834 0.92330341 0.663045999 0.563762947 21.779238
## 63 0.6202754262 0.088279070 0.26778657 0.207211251 0.720391881 9.197490
## 64 0.6345477444 0.994484988 0.67288102 0.949158964 0.823982928 15.073224
## 65 0.1516102208 0.669617534 0.12557122 0.392013110 0.788701557 17.561914
## 66 0.0638373715 0.153521036 0.22166633 0.123506922 0.606075877 17.601765
## 67 0.3630222164 0.350279308 0.14200169 0.041529058 0.282065476 15.824533
## 68 0.0141349288 0.663475810 0.67553172 0.501539484 0.301617217 7.134264
## 69 0.5267603784 0.429941210 0.97828898 0.885561631 0.087564073 6.413136
## 70 0.6532241760 0.671208466 0.65576477 0.673768810 0.583857899 14.613611
## 71 0.2219880908 0.476079757 0.71183447 0.425648322 0.400107953 16.255757
## 72 0.1531321660 0.691954747 0.65801907 0.426056444 0.046916341 4.698295
## 73 0.5008657877 0.040073613 0.92800985 0.381413696 0.350010608 14.105578
## 74 0.9806543912 0.819187354 0.84159996 0.896280786 0.439968794 15.707841
## 75 0.9244000583 0.198013207 0.23337787 0.116631588 0.191731905 4.888355
## 76 0.0099979453 0.295807930 0.90356056 0.885416760 0.312676924 16.992321
## 77 0.2356902743 0.506900013 0.55981430 0.534760828 0.477477021 22.980799
## 78 0.3650656492 0.810620838 0.11388461 0.410755347 0.177769617 9.623636
## 79 0.7987873172 0.366785977 0.60186782 0.973480208 0.745112953 20.669432
## 80 0.5599248759 0.116578872 0.34580507 0.714962742 -0.201031396 7.096990
## 81 0.7522757188 0.026414874 0.34715430 0.836363711 0.906534116 13.593588
## 82 0.8865377689 0.061911004 0.97803556 0.612240904 0.737108952 15.468199
## 83 0.0590573207 0.684142034 0.71260502 0.255351776 0.519712589 28.381673
## 84 0.7768231640 0.850076108 0.17097505 0.408350330 0.247613470 17.977054
## 85 0.4138241454 0.755554634 0.92548457 0.945293089 0.513280171 10.694865
## 86 0.9818397635 0.945009324 0.68008657 0.510965007 0.770673665 17.640215
## 87 0.2916908523 0.702514261 0.85496045 0.604653787 0.480977075 7.138598
## 88 0.1587244619 0.582193831 0.05235641 0.486561552 1.066008245 15.656878
## 89 0.0014450864 0.128084549 0.47699398 0.679715703 0.544159394 18.363995
## 90 0.2105985023 0.884157248 0.18779775 0.402003791 0.987415473 23.572686
## 91 0.8245949268 0.793933963 0.53137582 0.756866812 0.418679640 21.330888
## 92 0.0445211111 0.460617797 0.58243842 0.944980194 0.362962259 8.631156
## 93 0.5918905353 0.485206415 0.77555244 0.542896184 -0.058190556 16.373575
## 94 0.0303562423 0.324637733 0.98245833 0.605254818 0.113825253 13.359596
## 95 0.6099704383 0.731502909 0.49410755 0.882788646 0.556244164 15.744177
## 96 0.0619420919 0.788262721 0.32567336 0.790985481 0.615313728 8.078082
## 97 0.6019777379 0.718690965 0.24367231 0.571871065 0.223912719 14.497672
## 98 0.7470110336 0.789140293 0.18306352 0.852484180 0.199057769 14.942224
## 99 0.5261754794 0.983355801 0.37887188 0.765290411 0.330337083 15.829082
## 100 0.4876051969 0.122928050 0.08177731 0.848134163 0.565642051 19.178018
## 101 0.9011508890 0.617960313 0.12460480 0.702702949 0.653335312 19.928981
## 102 0.0003387642 0.388927228 0.97821702 0.104494945 0.968213155 17.178817
## 103 0.9080805883 0.905519754 0.60285307 0.877587634 0.066143767 5.784234
## 104 0.4965877566 0.636728981 0.79705572 0.319453278 0.640933352 22.061638
## 105 0.8487957353 0.912640729 0.11477043 0.155581983 0.046373610 5.776771
## 106 0.0822484379 0.955071241 0.06021731 0.421584291 0.008525971 9.597466
## 107 0.1611803344 0.599529999 0.26890232 0.188167820 0.558746858 23.395596
## 108 0.1425062015 0.571244097 0.74935739 0.464775090 -0.034123408 7.444598
## 109 0.4653496440 0.651546226 0.95540449 0.564070737 0.625975040 19.434952
## 110 0.1981665948 0.999560626 0.57950670 0.127039001 0.468730012 21.911755
## 111 0.8408644302 0.437424371 0.93131402 0.133683814 0.921901785 16.718751
## 112 0.9164640335 0.395302785 0.63386223 0.888060797 0.101906684 10.227144
## 113 0.3355441941 0.030395976 0.20250656 0.053323140 0.110253612 8.500874
## 114 0.6774176396 0.696283764 0.75913311 0.809930917 0.455270626 20.114536
## 115 0.9650529190 0.449902425 0.57304399 0.753339031 0.461563047 13.443701
## 116 0.1141603340 0.863953833 0.95345440 0.380650506 0.835165353 8.789036
## 117 0.4158274462 0.713239111 0.60102539 0.635894833 0.986621928 18.291185
## 118 0.1791522284 0.834004079 0.20838605 0.592570851 0.169996525 5.901247
## 119 0.5624954123 0.710008362 0.18311621 0.394101708 0.432759016 12.337007
## 120 0.9726133470 0.842078145 0.93576851 0.956083941 0.169234118 8.710816
## 121 0.4887156698 0.887054311 0.31041901 0.510736341 0.545840551 18.395967
## 122 0.9838132532 0.585472636 0.14732752 0.086574405 0.675287847 19.595790
## 123 0.4743697466 0.242674318 0.42347788 0.868947359 0.254893099 20.525566
## 124 0.2407878560 0.447328788 0.66467369 0.494879879 0.817248180 11.827082
## 125 0.1783671109 0.503948929 0.16230501 0.187285239 0.844466213 13.071909
## 126 0.4367017439 0.344732890 0.42201320 0.437095925 0.699608265 17.164010
## 127 0.3784207169 0.273177421 0.11701698 0.547305345 0.484885189 12.604661
## 128 0.1147928145 0.103627008 0.16504249 0.275940885 0.695680384 9.364654
## 129 0.3586573373 0.238100665 0.68896641 0.177130092 0.061236492 12.350974
## 130 0.2376520939 0.312197204 0.25109129 0.997579731 0.243075949 6.692139
## 131 0.7941833863 0.433608739 0.76234330 0.569325565 0.469693505 19.390364
## 132 0.5684747580 0.312200866 0.11102144 0.240327878 0.568050881 8.216058
## 133 0.9834440248 0.023838794 0.16816803 0.999992477 0.748974840 14.163226
## 134 0.8681481183 0.755061130 0.16099688 0.581953628 0.548410025 14.852324
## 135 0.2529283839 0.309956316 0.35376172 0.576154274 0.700938055 14.960020
## 136 0.2954634046 0.686869082 0.23401367 0.743752910 0.336445050 14.371226
## 137 0.7287589125 0.934555566 0.27740693 0.256602708 0.606629364 16.171388
## 138 0.5105628674 0.330980633 0.32516244 0.474497675 0.779564795 17.728141
## 139 0.4536720926 0.385358283 0.03655417 0.171900066 0.246131261 16.347169
## 140 0.0308236629 0.654293299 0.92551144 0.435859671 0.771114912 18.929738
## 141 0.3351621642 0.409007091 0.67315717 0.996981804 0.477791468 9.388698
## 142 0.6144252147 0.651714271 0.12889572 0.633149029 0.140143672 5.393462
## 143 0.1153656312 0.793603583 0.55421117 0.356097830 0.552415117 12.775396
## 144 0.7361220436 0.177242560 0.03421274 0.872309444 0.893721703 8.442596
## 145 0.9072946333 0.738731097 0.26822183 0.173052300 0.700903005 13.267265
## 146 0.8854910310 0.688096952 0.75856509 0.669689639 0.009838331 8.941159
## 147 0.0388078641 0.214172413 0.61253457 0.207942491 0.922058112 14.353866
## 148 0.3260785770 0.810973278 0.39199971 0.370241001 0.603486438 15.394612
## 149 0.7807700243 0.578197747 0.70276752 0.123103430 0.565563366 9.084654
## 150 0.7907638911 0.208587777 0.05438854 0.766739978 0.419681552 11.312659
## 151 0.7937673274 0.208766474 0.83636350 0.858343330 0.914600252 16.299293
## 152 0.1613148297 0.654811297 0.66729678 0.115404263 0.361249539 5.839912
## 153 0.7080952730 0.903838935 0.31193910 0.969527644 0.899927228 19.525552
## 154 0.5305830529 0.004698141 0.48546810 0.259277162 0.416967229 17.824782
## 155 0.1885056335 0.079913177 0.57972754 0.905628399 0.527650833 15.534928
## 156 0.5161641990 0.466810009 0.76300679 0.944087471 0.471966423 14.460986
## 157 0.6012678132 0.025244068 0.19821959 0.402928842 0.903076350 13.992105
## 158 0.6169876396 0.499346328 0.32760646 0.266050707 0.138669923 9.634654
## 159 0.7895973460 0.786763847 0.07832531 0.312945329 0.963474345 20.360593
## 160 0.0390002122 0.015907055 0.57958929 0.502512869 0.989371268 21.628769
## 161 0.4199729285 0.538111618 0.94932648 0.535985540 0.400288093 17.995487
## 162 0.5129533098 0.613649708 0.26589918 0.269859831 0.818192624 19.648813
## 163 0.6883663596 0.515120720 0.64359538 0.473454136 0.011713681 8.728757
## 164 0.2867906420 0.219839853 0.16326702 0.120969625 0.997281997 22.293667
## 165 0.9943477523 0.381418612 0.81146453 0.136825552 0.214764480 10.776480
## 166 0.2593658050 0.461603611 0.68922230 0.171518739 0.491015806 12.980947
## 167 0.5809806921 0.810821845 0.21677497 0.741042868 0.061967443 13.200163
## 168 0.9927047875 0.928290160 0.48741662 0.881588204 -0.017188929 11.617543
## 169 0.3948761285 0.914971805 0.04233756 0.987049844 0.173731229 15.072437
## 170 0.9569103546 0.694013482 0.97705820 0.012435718 0.670560155 13.042415
## 171 0.5889326367 0.509478116 0.64141950 0.365601074 0.978534460 21.870618
## 172 0.6114409810 0.830605455 0.52658278 0.065911923 0.041677654 15.131138
## 173 0.4287582068 0.366665906 0.86474573 0.016379327 0.166438212 14.669672
## 174 0.1562757776 0.463090256 0.02956841 0.971855537 0.112090683 9.609650
## 175 0.0453625068 0.177558171 0.10203368 0.505838658 0.486405824 14.428173
## 176 0.6969831374 0.631295626 0.58758911 0.247838673 0.461705225 21.871572
## 177 0.1762444021 0.080035930 0.84510174 0.700015211 0.064009605 6.124100
## 178 0.2357786680 0.385391619 0.62558152 0.954732809 0.842521698 19.906736
## 179 0.5439273247 0.627847850 0.88854501 0.855865543 0.922421515 14.038694
## 180 0.8102693288 0.839098028 0.15944836 0.379626432 0.283658638 6.595364
## 181 0.0133081947 0.168556706 0.10525675 0.771278932 0.245499291 12.188266
## 182 0.6584848959 0.287486323 0.12728033 0.041241815 0.170079018 11.029138
## 183 0.3847984066 0.117578465 0.96804658 0.902288517 0.838371378 20.917170
## 184 0.1876184577 0.798065790 0.92881170 0.884292413 0.560185228 18.056711
## 185 0.0729941991 0.472175947 0.07752809 0.744791487 0.699999725 11.085355
## 186 0.7420141906 0.437308198 0.66531113 0.045803222 0.793571445 17.402036
## 187 0.4334616780 0.849088030 0.46642330 0.779457425 0.078904778 11.244792
## 188 0.6745903494 0.986013835 0.50686606 0.312909630 0.176936743 9.334814
## 189 0.3680351812 0.496575716 0.49428027 0.447099152 0.163413295 15.629095
## 190 0.6922219021 0.011549961 0.57885152 0.406213945 0.458066907 12.631487
## 191 0.0971158685 0.412869229 0.97960020 0.136601998 0.753504823 13.381026
## 192 0.1838154087 0.210182422 0.04580357 0.427214286 0.264150947 16.619825
## 193 0.5494235111 0.720276414 0.29912111 0.994646956 1.084839050 11.294074
## 194 0.7455740881 0.886575559 0.25383887 0.521175744 0.284391700 10.942370
## 195 0.8809142739 0.322509774 0.66346270 0.930126207 0.771074098 15.337523
## 196 0.6664053195 0.267326644 0.24159338 0.606167757 0.658019357 17.171795
## 197 0.8829731958 0.123415505 0.99102161 0.073506513 0.697026935 10.496627
## 198 0.2567906741 0.309302658 0.05267484 0.698478227 0.027486745 14.793806
## 199 0.5021552520 0.334554489 0.03080467 0.395422508 0.495364600 17.333764
## 200 0.6627391470 0.959779277 0.09184009 0.219858172 0.146872390 17.153588set.seed(100)
gbmTune <- train(simulated2[1:11], simulated2$y,
method = "gbm",
tuneGrid = gbmGrid,
verbose = FALSE)## Overall
## V4 100.0000000
## V2 88.1655792
## V1 69.8100063
## V5 40.2428779
## duplicate 39.1538947
## V3 34.0955154
## V7 4.3702618
## V6 3.6011033
## V10 0.7021740
## V8 0.5911246
## V9 0.0000000gbmTune1_df <- as.data.frame(gbmTune1$importance)
gbmTune1_df['Predictors'] <- rownames(gbmTune1_df)
colnames(gbmTune1_df) <- c("Overall", "Predictors")
rownames(gbmTune1_df) <- 1:nrow(gbmTune1_df)gbmTune1_df %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "orange") +
theme_gray() +
coord_flip() +
labs(title="boosted Predictor Variable Importance",
y="boosted Importance", x="Predictors") +
scale_y_continuous()
Cubist
library(mlbench)
set.seed(200)
simulated3 <- mlbench.friedman1(200, sd = 1)
simulated3 <- cbind(simulated3$x, simulated3$y)
simulated3 <- as.data.frame(simulated3)
colnames(simulated3)[ncol(simulated3)] <- "y"set.seed(100)
colnamesx <- c("V1","V2","V3","V4","V5","V6","V7","V8","V9","V10")
cubistTuned <- train(simulated3[, colnamesx], simulated3$y, method = "cubist")## Overall
## V1 100.00000
## V2 75.69444
## V4 68.05556
## V3 58.33333
## V5 55.55556
## V6 15.27778
## V7 0.00000
## V8 0.00000
## V9 0.00000
## V10 0.00000cubistTuned1_df <- as.data.frame(cubistTuned1$importance)
cubistTuned1_df['Predictors'] <- rownames(cubistTuned1_df)
colnames(cubistTuned1_df) <- c("Overall", "Predictors")
rownames(cubistTuned1_df) <- 1:nrow(cubistTuned1_df)
cubistTuned1_df## Overall Predictors
## 1 100.00000 V1
## 2 58.33333 V3
## 3 75.69444 V2
## 4 68.05556 V4
## 5 55.55556 V5
## 6 15.27778 V6
## 7 0.00000 V7
## 8 0.00000 V8
## 9 0.00000 V9
## 10 0.00000 V10cubistTuned1_df %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "seashell") +
theme_dark() +
coord_flip() +
labs(title="cubist Predictor Variable Importance",
y="cubist Importance", x="Predictors") +
scale_y_continuous()
Now add an additional predictor that is highly correlated with one of the informative predictors as was done in Part A:
set.seed(100)
simulated3$corr_pred <- simulated3$V1 + rnorm(200) * .1
cor(simulated3$corr_pred, simulated3$V1)## [1] 0.9509187col_order <- colnames(simulated3)
col_order <- c("V1","V2","V3","V4","V5","V6","V7","V8","V9","V10", "corr_pred", "y")
simulated3 <- simulated3[, col_order]
simulated3## V1 V2 V3 V4 V5 V6
## 1 0.533772448 0.6478064333 0.850785258 0.181599574 0.929039760 0.361790597
## 2 0.583765033 0.4381527551 0.672726594 0.669249143 0.163797838 0.453059313
## 3 0.589578298 0.5879064940 0.409671080 0.338127280 0.894093335 0.026819108
## 4 0.691039888 0.2259547510 0.033354474 0.066912736 0.637445191 0.525006367
## 5 0.667331498 0.8188985116 0.716760786 0.803242873 0.083068641 0.223441572
## 6 0.839293735 0.3862983445 0.646188573 0.861054306 0.630389472 0.437038906
## 7 0.711600085 0.1162793254 0.767706224 0.859962373 0.520582290 0.990291612
## 8 0.096501224 0.8445782231 0.153528016 0.412814007 0.746725963 0.662056439
## 9 0.523824728 0.2514584265 0.285196133 0.452202451 0.506808798 0.019370317
## 10 0.235350536 0.4317718598 0.780373945 0.072122673 0.100005680 0.294671116
## 11 0.454364888 0.1192040211 0.220170008 0.351687343 0.001755818 0.149134940
## 12 0.649252912 0.0973321993 0.598340076 0.734892188 0.669684836 0.668878612
## 13 0.153727122 0.0128550101 0.608990930 0.633952646 0.094662402 0.616397752
## 14 0.649288674 0.1866738056 0.365308329 0.045665963 0.806304601 0.476613421
## 15 0.383213673 0.4608722613 0.345225364 0.735293760 0.217474412 0.350192171
## 16 0.307298063 0.4219112301 0.979319583 0.144514926 0.489620249 0.516859321
## 17 0.566767377 0.7811157859 0.890115921 0.995679246 0.413354418 0.379292418
## 18 0.131787853 0.1998720246 0.379945722 0.570354241 0.932332295 0.175180161
## 19 0.922177571 0.4675492314 0.010254486 0.008189635 0.789955666 0.846729845
## 20 0.646329618 0.7929329765 0.053864328 0.652274119 0.226417012 0.510733424
## 21 0.460360692 0.0697931792 0.784207606 0.686981049 0.379707196 0.434224161
## 22 0.098747006 0.2313314399 0.520667098 0.298788559 0.058919030 0.321473247
## 23 0.206593813 0.6473270494 0.606014522 0.086910314 0.536598262 0.592455531
## 24 0.922339834 0.6342856146 0.888005181 0.503549783 0.504815002 0.519335387
## 25 0.319426806 0.0545100805 0.381021996 0.999287510 0.982473919 0.515890769
## 26 0.265324291 0.8564205186 0.050943109 0.395974373 0.937435226 0.983467527
## 27 0.717369557 0.2948283439 0.736812766 0.919277884 0.128039610 0.414260471
## 28 0.380335360 0.0004408562 0.733275530 0.345613460 0.443263867 0.558792540
## 29 0.030620939 0.2731315538 0.903001443 0.758067884 0.147233479 0.146207562
## 30 0.521419376 0.3537345366 0.830735998 0.393664814 0.671653698 0.573219036
## 31 0.263748623 0.5057117699 0.140882633 0.678475745 0.562049805 0.812396222
## 32 0.166053713 0.2998292497 0.377729565 0.270103104 0.711894969 0.103405041
## 33 0.483074695 0.5088484667 0.636458001 0.654003645 0.616297887 0.399691042
## 34 0.325727710 0.9247118952 0.817825248 0.371338245 0.382548874 0.441881776
## 35 0.925363897 0.2371832319 0.010075368 0.345586454 0.547638883 0.201830557
## 36 0.560558849 0.4270182950 0.313384585 0.610149687 0.802779849 0.815573796
## 37 0.178553036 0.4352612651 0.153328084 0.549069691 0.356350074 0.094069178
## 38 0.972322052 0.6359792664 0.445975145 0.899534479 0.268725364 0.903799011
## 39 0.493773325 0.3447996511 0.445896353 0.449058379 0.003265168 0.759522119
## 40 0.485940594 0.8554888491 0.813352563 0.045685444 0.880070203 0.513183234
## 41 0.586856649 0.2803302526 0.037726685 0.018251117 0.150030803 0.053033940
## 42 0.720570024 0.9092058453 0.210796098 0.875075159 0.094086062 0.585604633
## 43 0.691673029 0.5930176671 0.420771204 0.247303587 0.983297946 0.427623936
## 44 0.176150461 0.7141316915 0.741954805 0.197583070 0.836461429 0.296208750
## 45 0.952475880 0.8493538222 0.317191089 0.925082660 0.607305124 0.803849567
## 46 0.689011891 0.7483011317 0.807849665 0.877950979 0.967313918 0.574638351
## 47 0.157799606 0.6691785671 0.353649540 0.368825636 0.377917988 0.298162997
## 48 0.576220999 0.8380715831 0.609410121 0.191988432 0.172759505 0.113711787
## 49 0.653276739 0.9181834545 0.893769723 0.622584245 0.327600596 0.832185488
## 50 0.832807913 0.2265766494 0.355865418 0.047708418 0.547652281 0.939744496
## 51 0.067187183 0.1867572814 0.053412318 0.788249273 0.069746084 0.175875548
## 52 0.118626094 0.4984532818 0.081841033 0.847314714 0.095897603 0.953105583
## 53 0.892374709 0.9191673915 0.179852584 0.484247719 0.850093837 0.771444682
## 54 0.557935121 0.9555177600 0.070927210 0.284588894 0.860588939 0.018207328
## 55 0.515005544 0.6027795288 0.491738453 0.258037420 0.287011503 0.054381748
## 56 0.134100055 0.7252116359 0.862601955 0.610891974 0.280598821 0.785266264
## 57 0.149258960 0.1695368735 0.566346588 0.563854012 0.273068628 0.328188200
## 58 0.161343819 0.2199983387 0.222847626 0.136463749 0.596218371 0.105031757
## 59 0.561064044 0.7804879546 0.169082082 0.368560432 0.294977250 0.618674891
## 60 0.671786989 0.5629266184 0.306758978 0.797413421 0.402194366 0.169488368
## 61 0.147402651 0.9183623586 0.999923422 0.435399952 0.960000194 0.746313307
## 62 0.570647350 0.8898196355 0.359521539 0.807744707 0.942994522 0.850621036
## 63 0.758280237 0.4162223253 0.651333184 0.088788726 0.318467662 0.789343349
## 64 0.565787035 0.2931080312 0.935225714 0.254972817 0.682191425 0.116470202
## 65 0.775718143 0.2964265901 0.815802228 0.778016577 0.345414489 0.608970067
## 66 0.677378375 0.2773598756 0.627044755 0.937812351 0.439045849 0.796132486
## 67 0.218266052 0.7430458625 0.370964498 0.678309920 0.850654966 0.108555941
## 68 0.281448058 0.2555278649 0.540702318 0.102928993 0.499993075 0.200114859
## 69 0.094555768 0.6770530874 0.857065403 0.147499445 0.190941744 0.593200353
## 70 0.593106887 0.6049814720 0.829584161 0.068155296 0.812524924 0.272600746
## 71 0.355217626 0.9024892272 0.162602290 0.167165469 0.786120466 0.253500610
## 72 0.153351908 0.5403167598 0.522081524 0.131646728 0.303439272 0.406195677
## 73 0.466252540 0.2189726466 0.649081210 0.876677948 0.373312224 0.500154867
## 74 0.275116619 0.5810471375 0.328282601 0.821013230 0.365157783 0.574757167
## 75 0.397941506 0.0506482811 0.736786507 0.069037383 0.465576746 0.526418373
## 76 0.311401952 0.8876241017 0.829994129 0.273672034 0.822258464 0.576108309
## 77 0.586229856 0.6614987573 0.510906287 0.863162806 0.946865431 0.895700728
## 78 0.150715668 0.0240218288 0.293724078 0.763388061 0.337483510 0.572278405
## 79 0.644267766 0.5393897707 0.438592263 0.678769260 0.816074158 0.739229684
## 80 0.006409079 0.3240858268 0.081627410 0.388581997 0.143550989 0.586718400
## 81 0.816851889 0.8537856233 0.217289788 0.442311989 0.143528348 0.926974642
## 82 0.742108528 0.2384303520 0.580422256 0.720915187 0.629143175 0.597393914
## 83 0.654247520 0.5939083034 0.994853858 0.936799756 0.912532976 0.215555561
## 84 0.440734623 0.8666409499 0.564446902 0.379492091 0.822953047 0.368613384
## 85 0.442322013 0.2467340643 0.826851101 0.198192747 0.346601916 0.981209712
## 86 0.786464168 0.9204477360 0.150473845 0.543170314 0.512502319 0.773290500
## 87 0.459340288 0.2267787226 0.645397100 0.169832431 0.382568107 0.076924091
## 88 0.984272037 0.7370369236 0.306019300 0.648133427 0.114868225 0.384680568
## 89 0.371441818 0.1517067349 0.995130365 0.887727774 0.512004345 0.986306011
## 90 0.997792503 0.6529070695 0.098833617 0.917166736 0.471261014 0.157362159
## 91 0.474391870 0.6010630331 0.278657043 0.790569007 0.927579608 0.305082921
## 92 0.220132116 0.6547463359 0.537419467 0.345841283 0.043483641 0.429867428
## 93 0.031105185 0.6107613579 0.025156959 0.909916925 0.158163789 0.016845753
## 94 0.229582377 0.6054298035 0.639548430 0.572823923 0.743228543 0.887359502
## 95 0.609273809 0.9123187338 0.725720419 0.461442270 0.011241655 0.763862459
## 96 0.370745452 0.0759057687 0.361935701 0.433070669 0.090679155 0.101371452
## 97 0.307162299 0.6478466513 0.830584273 0.446856117 0.350730690 0.442842154
## 98 0.157705784 0.3871437064 0.703486373 0.566900127 0.685163247 0.440206385
## 99 0.448205397 0.8644333375 0.422698680 0.633362517 0.233479040 0.103215690
## 100 0.683045527 0.9840194189 0.611699514 0.531140843 0.797903161 0.597651707
## 101 0.686627647 0.6046307203 0.167846072 0.456818942 0.607740600 0.314174908
## 102 0.831901784 0.2939653466 0.672954567 0.803079295 0.280210467 0.998987383
## 103 0.113058501 0.2546948988 0.218817725 0.057622184 0.279840802 0.239368085
## 104 0.556645789 0.8126982844 0.692510723 0.966434979 0.351036289 0.281969752
## 105 0.192172982 0.3423131080 0.496556215 0.413942024 0.088539597 0.727522285
## 106 0.048556563 0.9640056610 0.605707243 0.566484744 0.508386431 0.614031048
## 107 0.636388587 0.4812663090 0.156460918 0.863360892 0.745412975 0.765995033
## 108 0.002806243 0.9363095718 0.649450997 0.242205442 0.870268838 0.335062859
## 109 0.501964895 0.7322653499 0.968477561 0.455123628 0.558531469 0.644129353
## 110 0.479473393 0.8101365152 0.371763220 0.896207781 0.851932624 0.277587108
## 111 0.904642434 0.7766639574 0.927888780 0.170289954 0.499319865 0.493327187
## 112 0.076446557 0.3885678530 0.869672049 0.631985184 0.508797599 0.512153390
## 113 0.171706995 0.6642553948 0.447441930 0.109595960 0.687226565 0.990115111
## 114 0.598192136 0.8803027971 0.934215342 0.184075910 0.930016244 0.015515274
## 115 0.494660591 0.5270667071 0.165982118 0.279556816 0.548412474 0.006808892
## 116 0.822326746 0.0874312406 0.339381942 0.624753956 0.139959793 0.881927748
## 117 0.884809928 0.2049752097 0.351055704 0.772163214 0.897429584 0.373503622
## 118 0.195553894 0.1479548330 0.547592697 0.426198894 0.233539708 0.459527157
## 119 0.463013117 0.4677024283 0.079132932 0.123636657 0.209901525 0.249119067
## 120 0.007715050 0.9759014850 0.647108061 0.623121100 0.489483954 0.913406589
## 121 0.623211886 0.7964882990 0.725319422 0.268862381 0.873370248 0.629094972
## 122 0.632887607 0.6062786465 0.027653304 0.215499579 0.437937672 0.412266847
## 123 0.313287797 0.6479254356 0.003295714 0.679255102 0.590496615 0.988463188
## 124 0.775744612 0.1102327388 0.168523920 0.228762099 0.965724084 0.842011251
## 125 0.998992379 0.8608238841 0.913439707 0.130730744 0.663723183 0.934387672
## 126 0.751483215 0.3711484901 0.757779663 0.436154100 0.914117961 0.487309208
## 127 0.512864344 0.4433466932 0.777240771 0.131851328 0.666940580 0.893005643
## 128 0.594934646 0.6147596298 0.629629193 0.029415055 0.156732836 0.675986912
## 129 0.108193488 0.0456732074 0.553760919 0.836029727 0.991577258 0.029231649
## 130 0.213286245 0.6094768783 0.343689348 0.090614796 0.383258829 0.830723291
## 131 0.511472948 0.8676087293 0.542017557 0.964182970 0.315437378 0.805567415
## 132 0.653088958 0.0627070705 0.925106390 0.035819308 0.250788742 0.872808259
## 133 0.680070220 0.4819761757 0.543910673 0.283038010 0.721935218 0.261010709
## 134 0.594429644 0.9517888685 0.487364555 0.429615057 0.077726093 0.396774478
## 135 0.566119617 0.7702909564 0.283901030 0.481008470 0.085473549 0.392161391
## 136 0.292137912 0.4600951856 0.031411853 0.355790904 0.714166709 0.646736944
## 137 0.621721983 0.8975026356 0.486688155 0.237542561 0.754609415 0.993754126
## 138 0.734009909 0.7064418797 0.685221680 0.159361927 0.678954404 0.522533498
## 139 0.250146729 0.2166299177 0.828084011 0.759835896 0.783513594 0.528184886
## 140 0.725502808 0.3214482346 0.801824650 0.683726188 0.785781410 0.368117954
## 141 0.518633971 0.1892801912 0.636985009 0.216002044 0.823852410 0.130777703
## 142 0.353793057 0.1187343048 0.771915119 0.228639466 0.026823693 0.470881379
## 143 0.536732926 0.5057627214 0.544558276 0.408174795 0.220592264 0.716128180
## 144 0.827716813 0.1134541789 0.151092910 0.249067954 0.167421041 0.812992523
## 145 0.799086446 0.2226722005 0.314966519 0.644402519 0.296044190 0.010295009
## 146 0.121202702 0.5125092892 0.736546513 0.173788953 0.987242828 0.128936096
## 147 0.965792880 0.2959974960 0.281766439 0.181185599 0.460291081 0.428525911
## 148 0.655097562 0.9138811582 0.685150367 0.203402501 0.556077081 0.384476536
## 149 0.523663767 0.3619226965 0.790130149 0.296799039 0.181327148 0.809934170
## 150 0.406266008 0.1738398047 0.437415589 0.528837076 0.650578036 0.017366972
## 151 0.811131607 0.4745276461 0.736739275 0.090695082 0.734380059 0.640642888
## 152 0.195899217 0.1883440749 0.036628024 0.037811573 0.361777857 0.891157788
## 153 0.901721909 0.7641276480 0.975725230 0.649152147 0.125422492 0.843844815
## 154 0.419387562 0.7132732121 0.537194521 0.663290517 0.813946252 0.346468189
## 155 0.502626143 0.1582271636 0.926717208 0.752402752 0.534871275 0.519248105
## 156 0.505678876 0.5922643617 0.249804128 0.229866606 0.489065639 0.002901212
## 157 0.914411720 0.3216436969 0.149495436 0.232416035 0.057981907 0.278796293
## 158 0.148558215 0.5582501232 0.832446445 0.294442032 0.117299439 0.885807658
## 159 0.937065663 0.7175001081 0.341711296 0.826616130 0.589513207 0.927866664
## 160 0.975472900 0.4723303919 0.144815880 0.495536016 0.437703832 0.338820112
## 161 0.424515043 0.6310416884 0.783094346 0.510714823 0.314462922 0.086185409
## 162 0.812289485 0.6547854072 0.352954853 0.395277522 0.834191832 0.642550439
## 163 0.029440868 0.7336349678 0.287532780 0.481363036 0.646652654 0.586816839
## 164 0.917813970 0.6703584662 0.014808858 0.308127946 0.908841855 0.511950091
## 165 0.214090701 0.3539453736 0.441450395 0.704947843 0.190465599 0.788839862
## 166 0.553994835 0.3797423861 0.426848450 0.406387825 0.583469785 0.982102466
## 167 0.087216421 0.0444812854 0.887981009 0.334847389 0.958314174 0.631051316
## 168 0.051853288 0.5381637057 0.287162258 0.544222318 0.580674538 0.138133082
## 169 0.153477015 0.7609185344 0.588195231 0.726811070 0.869440276 0.140277030
## 170 0.585922012 0.6343205774 0.114031907 0.054257943 0.132969180 0.262855512
## 171 0.915327054 0.6440016078 0.582549772 0.953309200 0.661264660 0.182328664
## 172 0.021536301 0.3673074185 0.137482502 0.985332304 0.359814066 0.504694133
## 173 0.175545276 0.5064939184 0.364339191 0.650103795 0.942291794 0.238556437
## 174 0.083142271 0.1788396279 0.373116091 0.705161238 0.367621270 0.640988169
## 175 0.491874318 0.4900236735 0.297881532 0.331352153 0.870221517 0.530976141
## 176 0.665890210 0.6166888489 0.978142474 0.226049843 0.988691468 0.411653516
## 177 0.028172681 0.3769877132 0.719316378 0.022271170 0.711718217 0.537131623
## 178 0.879781784 0.7322189799 0.869278736 0.649725121 0.669133191 0.397410648
## 179 0.795590631 0.2757800566 0.781217543 0.406130929 0.115849692 0.363247100
## 180 0.066798607 0.4353600563 0.641473262 0.070881601 0.725632793 0.845899404
## 181 0.369471576 0.2884542705 0.375342084 0.381129961 0.752541286 0.080834012
## 182 0.111091629 0.5124843172 0.743466425 0.401846189 0.632692037 0.334856320
## 183 0.825969449 0.7803220809 0.425994063 0.961734195 0.726619251 0.637834937
## 184 0.612556007 0.9145965697 0.257388497 0.629601910 0.375935599 0.271460483
## 185 0.637976925 0.1076111828 0.280669488 0.654566472 0.932735895 0.974294363
## 186 0.722749287 0.4142492083 0.976476628 0.461700869 0.261488323 0.760588499
## 187 0.088224613 0.3651040641 0.112417366 0.427385604 0.630677684 0.064398194
## 188 0.206456413 0.6789903478 0.269728941 0.026255392 0.533788505 0.339906024
## 189 0.271994818 0.4532893968 0.732908373 0.710368193 0.555094344 0.429670967
## 190 0.520548412 0.3144283574 0.803517855 0.349941988 0.498034912 0.495041399
## 191 0.776805477 0.9616133086 0.754222457 0.091987771 0.551281321 0.733340201
## 192 0.289232634 0.8427688032 0.202012851 0.496472600 0.546778636 0.428116115
## 193 0.989449516 0.2357514210 0.704040867 0.447436986 0.046436282 0.493715242
## 194 0.310988950 0.4760307493 0.771920531 0.274742047 0.416478656 0.183150188
## 195 0.581546503 0.0395606223 0.147069360 0.853941998 0.729293162 0.166967576
## 196 0.701018440 0.7045858139 0.531901518 0.318705286 0.510770075 0.799619116
## 197 0.539472235 0.1585750368 0.654213027 0.492335809 0.606566809 0.903776626
## 198 0.011292625 0.9602364919 0.776298914 0.773416284 0.594650894 0.984942808
## 199 0.603909890 0.9586990301 0.875057548 0.093729714 0.825522528 0.624501048
## 200 0.089178660 0.6006974212 0.113622466 0.825916705 0.558199830 0.084706127
## V7 V8 V9 V10 corr_pred y
## 1 0.8266608594 0.421408064 0.59111440 0.588621560 0.483553213 18.463980
## 2 0.6489600763 0.844623926 0.92819306 0.758400814 0.596918149 16.098360
## 3 0.1785614495 0.349590781 0.01759542 0.444118458 0.581686589 17.761647
## 4 0.5133613953 0.797025980 0.68986918 0.445071622 0.779718369 13.787300
## 5 0.6644906041 0.903891937 0.39696995 0.550080800 0.679028625 18.429836
## 6 0.3360117343 0.648917723 0.53116033 0.906618237 0.871156744 20.858166
## 7 0.0084998407 0.072795420 0.97395768 0.440172910 0.653421017 13.888401
## 8 0.4722572784 0.381633542 0.75877525 0.710887919 0.167954496 12.915431
## 9 0.3058403293 0.525661726 0.43136410 0.400128186 0.441298786 12.149448
## 10 0.3228343336 0.960311741 0.92426620 0.832559698 0.199364323 5.271123
## 11 0.1315679180 0.939230266 0.46228702 0.775593376 0.463353503 8.946052
## 12 0.7618696443 0.550847133 0.08637756 0.524860506 0.658880358 12.894078
## 13 0.4806034924 0.485595847 0.54158360 0.081258474 0.133563727 6.533292
## 14 0.4200604216 0.282479481 0.62596273 0.003172379 0.723272724 7.520004
## 15 0.6595693664 0.469818084 0.03909819 0.706367689 0.395551623 15.141730
## 16 0.6941591527 0.917750880 0.33898498 0.689810129 0.304366392 12.974733
## 17 0.1693497750 0.290054937 0.69159996 0.120331543 0.527881952 25.016165
## 18 0.1774999567 0.724190771 0.14320681 0.075203559 0.182873479 12.436690
## 19 0.6109301876 0.182253540 0.20626788 0.247241936 0.830796153 16.899482
## 20 0.1655056404 0.996789995 0.57239957 0.970613467 0.877359300 22.052472
## 21 0.8696455043 0.480284780 0.94174627 0.525216599 0.416551694 12.892896
## 22 0.2200369346 0.543487359 0.91963756 0.948926731 0.175153068 3.555960
## 23 0.6324701225 0.833171203 0.91811502 0.181142754 0.232789942 10.032559
## 24 0.6703429641 0.285668603 0.84918471 0.397776954 0.999680294 19.728886
## 25 0.0101521015 0.960430558 0.23506862 0.230721395 0.237988893 15.271168
## 26 0.2522400960 0.634320574 0.87522970 0.635452710 0.221479234 21.921927
## 27 0.6650384206 0.650785477 0.28744271 0.616526859 0.645347402 17.848795
## 28 0.0648198922 0.178094681 0.56876498 0.428627433 0.403429814 5.964147
## 29 0.6192647608 0.146737191 0.33908035 0.938806834 -0.085152007 13.254190
## 30 0.3292513283 0.042337252 0.86859891 0.880950373 0.546126975 15.181016
## 31 0.2824812313 0.332542812 0.95191869 0.763801782 0.254637267 18.021637
## 32 0.2051616914 0.785139066 0.04968553 0.968671421 0.341791275 8.385652
## 33 0.6479521065 0.175871460 0.67905283 0.730759681 0.469281733 17.967104
## 34 0.3500645757 0.635448656 0.89620270 0.575594178 0.314608361 14.097415
## 35 0.8686830916 0.324884567 0.03161212 0.849832683 0.856362465 17.352764
## 36 0.6281718945 0.651751797 0.69222388 0.442386812 0.538379426 17.608729
## 37 0.5401211150 0.802915463 0.51344968 0.959669129 0.196843804 13.136663
## 38 0.0954262505 0.271751555 0.91415621 0.535858047 1.014054381 21.879995
## 39 0.3189930974 0.487114596 0.38007261 0.068724414 0.600313558 9.980150
## 40 0.0987321541 0.398785473 0.70468780 0.814099950 0.582960796 18.002840
## 41 0.8256829928 0.274217872 0.24911536 0.363809015 0.576693725 9.489052
## 42 0.4254488801 0.543745558 0.56771488 0.586587886 0.860890373 19.991424
## 43 0.6002272039 0.303179812 0.30442762 0.996330470 0.513995466 17.766711
## 44 0.0993871398 0.726330749 0.51122937 0.574089565 0.238437201 13.299483
## 45 0.3573383761 0.659334866 0.82108557 0.880166529 0.900247544 18.828347
## 46 0.3369224169 0.171208087 0.58813299 0.298467441 0.821234986 26.945666
## 47 0.7216083466 0.347465995 0.45980972 0.522110901 0.121455573 9.358890
## 48 0.1637666794 0.465182498 0.67228512 0.549377529 0.708127573 12.133777
## 49 0.0661412831 0.662970975 0.67190601 0.712600555 0.657654646 22.132197
## 50 0.5044657106 0.684693513 0.23367805 0.853776497 0.644942325 8.886239
## 51 0.4450478635 0.954027392 0.87891811 0.228369326 0.022480965 13.343289
## 52 0.8620285194 0.258589442 0.96154879 0.437253388 -0.055233701 12.709052
## 53 0.0236228870 0.676012672 0.37005100 0.260396947 0.910261194 16.708610
## 54 0.1452215833 0.955375290 0.70495617 0.882332698 0.747681691 19.797593
## 55 0.3742820916 0.214503606 0.13091783 0.462896239 0.287812995 12.166608
## 56 0.5384509673 0.037968947 0.61604382 0.535041264 0.232146468 13.772781
## 57 0.2577628391 0.186539843 0.93924713 0.942935549 0.009376398 6.563014
## 58 0.2109247684 0.363152975 0.22155711 0.789319306 0.343831061 5.325261
## 59 0.4573113865 0.197379992 0.41096121 0.626259638 0.699193917 18.244465
## 60 0.2189239766 0.259368576 0.39850931 0.322176775 0.587901802 20.632950
## 61 0.9801436167 0.418736819 0.50638210 0.791115409 0.121203074 18.974731
## 62 0.2792056827 0.632583834 0.92330341 0.663045999 0.563762947 21.779238
## 63 0.6202754262 0.088279070 0.26778657 0.207211251 0.720391881 9.197490
## 64 0.6345477444 0.994484988 0.67288102 0.949158964 0.823982928 15.073224
## 65 0.1516102208 0.669617534 0.12557122 0.392013110 0.788701557 17.561914
## 66 0.0638373715 0.153521036 0.22166633 0.123506922 0.606075877 17.601765
## 67 0.3630222164 0.350279308 0.14200169 0.041529058 0.282065476 15.824533
## 68 0.0141349288 0.663475810 0.67553172 0.501539484 0.301617217 7.134264
## 69 0.5267603784 0.429941210 0.97828898 0.885561631 0.087564073 6.413136
## 70 0.6532241760 0.671208466 0.65576477 0.673768810 0.583857899 14.613611
## 71 0.2219880908 0.476079757 0.71183447 0.425648322 0.400107953 16.255757
## 72 0.1531321660 0.691954747 0.65801907 0.426056444 0.046916341 4.698295
## 73 0.5008657877 0.040073613 0.92800985 0.381413696 0.350010608 14.105578
## 74 0.9806543912 0.819187354 0.84159996 0.896280786 0.439968794 15.707841
## 75 0.9244000583 0.198013207 0.23337787 0.116631588 0.191731905 4.888355
## 76 0.0099979453 0.295807930 0.90356056 0.885416760 0.312676924 16.992321
## 77 0.2356902743 0.506900013 0.55981430 0.534760828 0.477477021 22.980799
## 78 0.3650656492 0.810620838 0.11388461 0.410755347 0.177769617 9.623636
## 79 0.7987873172 0.366785977 0.60186782 0.973480208 0.745112953 20.669432
## 80 0.5599248759 0.116578872 0.34580507 0.714962742 -0.201031396 7.096990
## 81 0.7522757188 0.026414874 0.34715430 0.836363711 0.906534116 13.593588
## 82 0.8865377689 0.061911004 0.97803556 0.612240904 0.737108952 15.468199
## 83 0.0590573207 0.684142034 0.71260502 0.255351776 0.519712589 28.381673
## 84 0.7768231640 0.850076108 0.17097505 0.408350330 0.247613470 17.977054
## 85 0.4138241454 0.755554634 0.92548457 0.945293089 0.513280171 10.694865
## 86 0.9818397635 0.945009324 0.68008657 0.510965007 0.770673665 17.640215
## 87 0.2916908523 0.702514261 0.85496045 0.604653787 0.480977075 7.138598
## 88 0.1587244619 0.582193831 0.05235641 0.486561552 1.066008245 15.656878
## 89 0.0014450864 0.128084549 0.47699398 0.679715703 0.544159394 18.363995
## 90 0.2105985023 0.884157248 0.18779775 0.402003791 0.987415473 23.572686
## 91 0.8245949268 0.793933963 0.53137582 0.756866812 0.418679640 21.330888
## 92 0.0445211111 0.460617797 0.58243842 0.944980194 0.362962259 8.631156
## 93 0.5918905353 0.485206415 0.77555244 0.542896184 -0.058190556 16.373575
## 94 0.0303562423 0.324637733 0.98245833 0.605254818 0.113825253 13.359596
## 95 0.6099704383 0.731502909 0.49410755 0.882788646 0.556244164 15.744177
## 96 0.0619420919 0.788262721 0.32567336 0.790985481 0.615313728 8.078082
## 97 0.6019777379 0.718690965 0.24367231 0.571871065 0.223912719 14.497672
## 98 0.7470110336 0.789140293 0.18306352 0.852484180 0.199057769 14.942224
## 99 0.5261754794 0.983355801 0.37887188 0.765290411 0.330337083 15.829082
## 100 0.4876051969 0.122928050 0.08177731 0.848134163 0.565642051 19.178018
## 101 0.9011508890 0.617960313 0.12460480 0.702702949 0.653335312 19.928981
## 102 0.0003387642 0.388927228 0.97821702 0.104494945 0.968213155 17.178817
## 103 0.9080805883 0.905519754 0.60285307 0.877587634 0.066143767 5.784234
## 104 0.4965877566 0.636728981 0.79705572 0.319453278 0.640933352 22.061638
## 105 0.8487957353 0.912640729 0.11477043 0.155581983 0.046373610 5.776771
## 106 0.0822484379 0.955071241 0.06021731 0.421584291 0.008525971 9.597466
## 107 0.1611803344 0.599529999 0.26890232 0.188167820 0.558746858 23.395596
## 108 0.1425062015 0.571244097 0.74935739 0.464775090 -0.034123408 7.444598
## 109 0.4653496440 0.651546226 0.95540449 0.564070737 0.625975040 19.434952
## 110 0.1981665948 0.999560626 0.57950670 0.127039001 0.468730012 21.911755
## 111 0.8408644302 0.437424371 0.93131402 0.133683814 0.921901785 16.718751
## 112 0.9164640335 0.395302785 0.63386223 0.888060797 0.101906684 10.227144
## 113 0.3355441941 0.030395976 0.20250656 0.053323140 0.110253612 8.500874
## 114 0.6774176396 0.696283764 0.75913311 0.809930917 0.455270626 20.114536
## 115 0.9650529190 0.449902425 0.57304399 0.753339031 0.461563047 13.443701
## 116 0.1141603340 0.863953833 0.95345440 0.380650506 0.835165353 8.789036
## 117 0.4158274462 0.713239111 0.60102539 0.635894833 0.986621928 18.291185
## 118 0.1791522284 0.834004079 0.20838605 0.592570851 0.169996525 5.901247
## 119 0.5624954123 0.710008362 0.18311621 0.394101708 0.432759016 12.337007
## 120 0.9726133470 0.842078145 0.93576851 0.956083941 0.169234118 8.710816
## 121 0.4887156698 0.887054311 0.31041901 0.510736341 0.545840551 18.395967
## 122 0.9838132532 0.585472636 0.14732752 0.086574405 0.675287847 19.595790
## 123 0.4743697466 0.242674318 0.42347788 0.868947359 0.254893099 20.525566
## 124 0.2407878560 0.447328788 0.66467369 0.494879879 0.817248180 11.827082
## 125 0.1783671109 0.503948929 0.16230501 0.187285239 0.844466213 13.071909
## 126 0.4367017439 0.344732890 0.42201320 0.437095925 0.699608265 17.164010
## 127 0.3784207169 0.273177421 0.11701698 0.547305345 0.484885189 12.604661
## 128 0.1147928145 0.103627008 0.16504249 0.275940885 0.695680384 9.364654
## 129 0.3586573373 0.238100665 0.68896641 0.177130092 0.061236492 12.350974
## 130 0.2376520939 0.312197204 0.25109129 0.997579731 0.243075949 6.692139
## 131 0.7941833863 0.433608739 0.76234330 0.569325565 0.469693505 19.390364
## 132 0.5684747580 0.312200866 0.11102144 0.240327878 0.568050881 8.216058
## 133 0.9834440248 0.023838794 0.16816803 0.999992477 0.748974840 14.163226
## 134 0.8681481183 0.755061130 0.16099688 0.581953628 0.548410025 14.852324
## 135 0.2529283839 0.309956316 0.35376172 0.576154274 0.700938055 14.960020
## 136 0.2954634046 0.686869082 0.23401367 0.743752910 0.336445050 14.371226
## 137 0.7287589125 0.934555566 0.27740693 0.256602708 0.606629364 16.171388
## 138 0.5105628674 0.330980633 0.32516244 0.474497675 0.779564795 17.728141
## 139 0.4536720926 0.385358283 0.03655417 0.171900066 0.246131261 16.347169
## 140 0.0308236629 0.654293299 0.92551144 0.435859671 0.771114912 18.929738
## 141 0.3351621642 0.409007091 0.67315717 0.996981804 0.477791468 9.388698
## 142 0.6144252147 0.651714271 0.12889572 0.633149029 0.140143672 5.393462
## 143 0.1153656312 0.793603583 0.55421117 0.356097830 0.552415117 12.775396
## 144 0.7361220436 0.177242560 0.03421274 0.872309444 0.893721703 8.442596
## 145 0.9072946333 0.738731097 0.26822183 0.173052300 0.700903005 13.267265
## 146 0.8854910310 0.688096952 0.75856509 0.669689639 0.009838331 8.941159
## 147 0.0388078641 0.214172413 0.61253457 0.207942491 0.922058112 14.353866
## 148 0.3260785770 0.810973278 0.39199971 0.370241001 0.603486438 15.394612
## 149 0.7807700243 0.578197747 0.70276752 0.123103430 0.565563366 9.084654
## 150 0.7907638911 0.208587777 0.05438854 0.766739978 0.419681552 11.312659
## 151 0.7937673274 0.208766474 0.83636350 0.858343330 0.914600252 16.299293
## 152 0.1613148297 0.654811297 0.66729678 0.115404263 0.361249539 5.839912
## 153 0.7080952730 0.903838935 0.31193910 0.969527644 0.899927228 19.525552
## 154 0.5305830529 0.004698141 0.48546810 0.259277162 0.416967229 17.824782
## 155 0.1885056335 0.079913177 0.57972754 0.905628399 0.527650833 15.534928
## 156 0.5161641990 0.466810009 0.76300679 0.944087471 0.471966423 14.460986
## 157 0.6012678132 0.025244068 0.19821959 0.402928842 0.903076350 13.992105
## 158 0.6169876396 0.499346328 0.32760646 0.266050707 0.138669923 9.634654
## 159 0.7895973460 0.786763847 0.07832531 0.312945329 0.963474345 20.360593
## 160 0.0390002122 0.015907055 0.57958929 0.502512869 0.989371268 21.628769
## 161 0.4199729285 0.538111618 0.94932648 0.535985540 0.400288093 17.995487
## 162 0.5129533098 0.613649708 0.26589918 0.269859831 0.818192624 19.648813
## 163 0.6883663596 0.515120720 0.64359538 0.473454136 0.011713681 8.728757
## 164 0.2867906420 0.219839853 0.16326702 0.120969625 0.997281997 22.293667
## 165 0.9943477523 0.381418612 0.81146453 0.136825552 0.214764480 10.776480
## 166 0.2593658050 0.461603611 0.68922230 0.171518739 0.491015806 12.980947
## 167 0.5809806921 0.810821845 0.21677497 0.741042868 0.061967443 13.200163
## 168 0.9927047875 0.928290160 0.48741662 0.881588204 -0.017188929 11.617543
## 169 0.3948761285 0.914971805 0.04233756 0.987049844 0.173731229 15.072437
## 170 0.9569103546 0.694013482 0.97705820 0.012435718 0.670560155 13.042415
## 171 0.5889326367 0.509478116 0.64141950 0.365601074 0.978534460 21.870618
## 172 0.6114409810 0.830605455 0.52658278 0.065911923 0.041677654 15.131138
## 173 0.4287582068 0.366665906 0.86474573 0.016379327 0.166438212 14.669672
## 174 0.1562757776 0.463090256 0.02956841 0.971855537 0.112090683 9.609650
## 175 0.0453625068 0.177558171 0.10203368 0.505838658 0.486405824 14.428173
## 176 0.6969831374 0.631295626 0.58758911 0.247838673 0.461705225 21.871572
## 177 0.1762444021 0.080035930 0.84510174 0.700015211 0.064009605 6.124100
## 178 0.2357786680 0.385391619 0.62558152 0.954732809 0.842521698 19.906736
## 179 0.5439273247 0.627847850 0.88854501 0.855865543 0.922421515 14.038694
## 180 0.8102693288 0.839098028 0.15944836 0.379626432 0.283658638 6.595364
## 181 0.0133081947 0.168556706 0.10525675 0.771278932 0.245499291 12.188266
## 182 0.6584848959 0.287486323 0.12728033 0.041241815 0.170079018 11.029138
## 183 0.3847984066 0.117578465 0.96804658 0.902288517 0.838371378 20.917170
## 184 0.1876184577 0.798065790 0.92881170 0.884292413 0.560185228 18.056711
## 185 0.0729941991 0.472175947 0.07752809 0.744791487 0.699999725 11.085355
## 186 0.7420141906 0.437308198 0.66531113 0.045803222 0.793571445 17.402036
## 187 0.4334616780 0.849088030 0.46642330 0.779457425 0.078904778 11.244792
## 188 0.6745903494 0.986013835 0.50686606 0.312909630 0.176936743 9.334814
## 189 0.3680351812 0.496575716 0.49428027 0.447099152 0.163413295 15.629095
## 190 0.6922219021 0.011549961 0.57885152 0.406213945 0.458066907 12.631487
## 191 0.0971158685 0.412869229 0.97960020 0.136601998 0.753504823 13.381026
## 192 0.1838154087 0.210182422 0.04580357 0.427214286 0.264150947 16.619825
## 193 0.5494235111 0.720276414 0.29912111 0.994646956 1.084839050 11.294074
## 194 0.7455740881 0.886575559 0.25383887 0.521175744 0.284391700 10.942370
## 195 0.8809142739 0.322509774 0.66346270 0.930126207 0.771074098 15.337523
## 196 0.6664053195 0.267326644 0.24159338 0.606167757 0.658019357 17.171795
## 197 0.8829731958 0.123415505 0.99102161 0.073506513 0.697026935 10.496627
## 198 0.2567906741 0.309302658 0.05267484 0.698478227 0.027486745 14.793806
## 199 0.5021552520 0.334554489 0.03080467 0.395422508 0.495364600 17.333764
## 200 0.6627391470 0.959779277 0.09184009 0.219858172 0.146872390 17.153588set.seed(100)
colnamesx <- c("V1","V2","V3","V4","V5","V6","V7","V8","V9","V10", "corr_pred")
cubistTuned <- train(simulated3[, colnamesx], simulated3$y, method = "cubist")## V1 V2 V3 V4 V5 V6
## 1 0.533772448 0.6478064333 0.850785258 0.181599574 0.929039760 0.361790597
## 2 0.583765033 0.4381527551 0.672726594 0.669249143 0.163797838 0.453059313
## 3 0.589578298 0.5879064940 0.409671080 0.338127280 0.894093335 0.026819108
## 4 0.691039888 0.2259547510 0.033354474 0.066912736 0.637445191 0.525006367
## 5 0.667331498 0.8188985116 0.716760786 0.803242873 0.083068641 0.223441572
## 6 0.839293735 0.3862983445 0.646188573 0.861054306 0.630389472 0.437038906
## 7 0.711600085 0.1162793254 0.767706224 0.859962373 0.520582290 0.990291612
## 8 0.096501224 0.8445782231 0.153528016 0.412814007 0.746725963 0.662056439
## 9 0.523824728 0.2514584265 0.285196133 0.452202451 0.506808798 0.019370317
## 10 0.235350536 0.4317718598 0.780373945 0.072122673 0.100005680 0.294671116
## 11 0.454364888 0.1192040211 0.220170008 0.351687343 0.001755818 0.149134940
## 12 0.649252912 0.0973321993 0.598340076 0.734892188 0.669684836 0.668878612
## 13 0.153727122 0.0128550101 0.608990930 0.633952646 0.094662402 0.616397752
## 14 0.649288674 0.1866738056 0.365308329 0.045665963 0.806304601 0.476613421
## 15 0.383213673 0.4608722613 0.345225364 0.735293760 0.217474412 0.350192171
## 16 0.307298063 0.4219112301 0.979319583 0.144514926 0.489620249 0.516859321
## 17 0.566767377 0.7811157859 0.890115921 0.995679246 0.413354418 0.379292418
## 18 0.131787853 0.1998720246 0.379945722 0.570354241 0.932332295 0.175180161
## 19 0.922177571 0.4675492314 0.010254486 0.008189635 0.789955666 0.846729845
## 20 0.646329618 0.7929329765 0.053864328 0.652274119 0.226417012 0.510733424
## 21 0.460360692 0.0697931792 0.784207606 0.686981049 0.379707196 0.434224161
## 22 0.098747006 0.2313314399 0.520667098 0.298788559 0.058919030 0.321473247
## 23 0.206593813 0.6473270494 0.606014522 0.086910314 0.536598262 0.592455531
## 24 0.922339834 0.6342856146 0.888005181 0.503549783 0.504815002 0.519335387
## 25 0.319426806 0.0545100805 0.381021996 0.999287510 0.982473919 0.515890769
## 26 0.265324291 0.8564205186 0.050943109 0.395974373 0.937435226 0.983467527
## 27 0.717369557 0.2948283439 0.736812766 0.919277884 0.128039610 0.414260471
## 28 0.380335360 0.0004408562 0.733275530 0.345613460 0.443263867 0.558792540
## 29 0.030620939 0.2731315538 0.903001443 0.758067884 0.147233479 0.146207562
## 30 0.521419376 0.3537345366 0.830735998 0.393664814 0.671653698 0.573219036
## 31 0.263748623 0.5057117699 0.140882633 0.678475745 0.562049805 0.812396222
## 32 0.166053713 0.2998292497 0.377729565 0.270103104 0.711894969 0.103405041
## 33 0.483074695 0.5088484667 0.636458001 0.654003645 0.616297887 0.399691042
## 34 0.325727710 0.9247118952 0.817825248 0.371338245 0.382548874 0.441881776
## 35 0.925363897 0.2371832319 0.010075368 0.345586454 0.547638883 0.201830557
## 36 0.560558849 0.4270182950 0.313384585 0.610149687 0.802779849 0.815573796
## 37 0.178553036 0.4352612651 0.153328084 0.549069691 0.356350074 0.094069178
## 38 0.972322052 0.6359792664 0.445975145 0.899534479 0.268725364 0.903799011
## 39 0.493773325 0.3447996511 0.445896353 0.449058379 0.003265168 0.759522119
## 40 0.485940594 0.8554888491 0.813352563 0.045685444 0.880070203 0.513183234
## 41 0.586856649 0.2803302526 0.037726685 0.018251117 0.150030803 0.053033940
## 42 0.720570024 0.9092058453 0.210796098 0.875075159 0.094086062 0.585604633
## 43 0.691673029 0.5930176671 0.420771204 0.247303587 0.983297946 0.427623936
## 44 0.176150461 0.7141316915 0.741954805 0.197583070 0.836461429 0.296208750
## 45 0.952475880 0.8493538222 0.317191089 0.925082660 0.607305124 0.803849567
## 46 0.689011891 0.7483011317 0.807849665 0.877950979 0.967313918 0.574638351
## 47 0.157799606 0.6691785671 0.353649540 0.368825636 0.377917988 0.298162997
## 48 0.576220999 0.8380715831 0.609410121 0.191988432 0.172759505 0.113711787
## 49 0.653276739 0.9181834545 0.893769723 0.622584245 0.327600596 0.832185488
## 50 0.832807913 0.2265766494 0.355865418 0.047708418 0.547652281 0.939744496
## 51 0.067187183 0.1867572814 0.053412318 0.788249273 0.069746084 0.175875548
## 52 0.118626094 0.4984532818 0.081841033 0.847314714 0.095897603 0.953105583
## 53 0.892374709 0.9191673915 0.179852584 0.484247719 0.850093837 0.771444682
## 54 0.557935121 0.9555177600 0.070927210 0.284588894 0.860588939 0.018207328
## 55 0.515005544 0.6027795288 0.491738453 0.258037420 0.287011503 0.054381748
## 56 0.134100055 0.7252116359 0.862601955 0.610891974 0.280598821 0.785266264
## 57 0.149258960 0.1695368735 0.566346588 0.563854012 0.273068628 0.328188200
## 58 0.161343819 0.2199983387 0.222847626 0.136463749 0.596218371 0.105031757
## 59 0.561064044 0.7804879546 0.169082082 0.368560432 0.294977250 0.618674891
## 60 0.671786989 0.5629266184 0.306758978 0.797413421 0.402194366 0.169488368
## 61 0.147402651 0.9183623586 0.999923422 0.435399952 0.960000194 0.746313307
## 62 0.570647350 0.8898196355 0.359521539 0.807744707 0.942994522 0.850621036
## 63 0.758280237 0.4162223253 0.651333184 0.088788726 0.318467662 0.789343349
## 64 0.565787035 0.2931080312 0.935225714 0.254972817 0.682191425 0.116470202
## 65 0.775718143 0.2964265901 0.815802228 0.778016577 0.345414489 0.608970067
## 66 0.677378375 0.2773598756 0.627044755 0.937812351 0.439045849 0.796132486
## 67 0.218266052 0.7430458625 0.370964498 0.678309920 0.850654966 0.108555941
## 68 0.281448058 0.2555278649 0.540702318 0.102928993 0.499993075 0.200114859
## 69 0.094555768 0.6770530874 0.857065403 0.147499445 0.190941744 0.593200353
## 70 0.593106887 0.6049814720 0.829584161 0.068155296 0.812524924 0.272600746
## 71 0.355217626 0.9024892272 0.162602290 0.167165469 0.786120466 0.253500610
## 72 0.153351908 0.5403167598 0.522081524 0.131646728 0.303439272 0.406195677
## 73 0.466252540 0.2189726466 0.649081210 0.876677948 0.373312224 0.500154867
## 74 0.275116619 0.5810471375 0.328282601 0.821013230 0.365157783 0.574757167
## 75 0.397941506 0.0506482811 0.736786507 0.069037383 0.465576746 0.526418373
## 76 0.311401952 0.8876241017 0.829994129 0.273672034 0.822258464 0.576108309
## 77 0.586229856 0.6614987573 0.510906287 0.863162806 0.946865431 0.895700728
## 78 0.150715668 0.0240218288 0.293724078 0.763388061 0.337483510 0.572278405
## 79 0.644267766 0.5393897707 0.438592263 0.678769260 0.816074158 0.739229684
## 80 0.006409079 0.3240858268 0.081627410 0.388581997 0.143550989 0.586718400
## 81 0.816851889 0.8537856233 0.217289788 0.442311989 0.143528348 0.926974642
## 82 0.742108528 0.2384303520 0.580422256 0.720915187 0.629143175 0.597393914
## 83 0.654247520 0.5939083034 0.994853858 0.936799756 0.912532976 0.215555561
## 84 0.440734623 0.8666409499 0.564446902 0.379492091 0.822953047 0.368613384
## 85 0.442322013 0.2467340643 0.826851101 0.198192747 0.346601916 0.981209712
## 86 0.786464168 0.9204477360 0.150473845 0.543170314 0.512502319 0.773290500
## 87 0.459340288 0.2267787226 0.645397100 0.169832431 0.382568107 0.076924091
## 88 0.984272037 0.7370369236 0.306019300 0.648133427 0.114868225 0.384680568
## 89 0.371441818 0.1517067349 0.995130365 0.887727774 0.512004345 0.986306011
## 90 0.997792503 0.6529070695 0.098833617 0.917166736 0.471261014 0.157362159
## 91 0.474391870 0.6010630331 0.278657043 0.790569007 0.927579608 0.305082921
## 92 0.220132116 0.6547463359 0.537419467 0.345841283 0.043483641 0.429867428
## 93 0.031105185 0.6107613579 0.025156959 0.909916925 0.158163789 0.016845753
## 94 0.229582377 0.6054298035 0.639548430 0.572823923 0.743228543 0.887359502
## 95 0.609273809 0.9123187338 0.725720419 0.461442270 0.011241655 0.763862459
## 96 0.370745452 0.0759057687 0.361935701 0.433070669 0.090679155 0.101371452
## 97 0.307162299 0.6478466513 0.830584273 0.446856117 0.350730690 0.442842154
## 98 0.157705784 0.3871437064 0.703486373 0.566900127 0.685163247 0.440206385
## 99 0.448205397 0.8644333375 0.422698680 0.633362517 0.233479040 0.103215690
## 100 0.683045527 0.9840194189 0.611699514 0.531140843 0.797903161 0.597651707
## 101 0.686627647 0.6046307203 0.167846072 0.456818942 0.607740600 0.314174908
## 102 0.831901784 0.2939653466 0.672954567 0.803079295 0.280210467 0.998987383
## 103 0.113058501 0.2546948988 0.218817725 0.057622184 0.279840802 0.239368085
## 104 0.556645789 0.8126982844 0.692510723 0.966434979 0.351036289 0.281969752
## 105 0.192172982 0.3423131080 0.496556215 0.413942024 0.088539597 0.727522285
## 106 0.048556563 0.9640056610 0.605707243 0.566484744 0.508386431 0.614031048
## 107 0.636388587 0.4812663090 0.156460918 0.863360892 0.745412975 0.765995033
## 108 0.002806243 0.9363095718 0.649450997 0.242205442 0.870268838 0.335062859
## 109 0.501964895 0.7322653499 0.968477561 0.455123628 0.558531469 0.644129353
## 110 0.479473393 0.8101365152 0.371763220 0.896207781 0.851932624 0.277587108
## 111 0.904642434 0.7766639574 0.927888780 0.170289954 0.499319865 0.493327187
## 112 0.076446557 0.3885678530 0.869672049 0.631985184 0.508797599 0.512153390
## 113 0.171706995 0.6642553948 0.447441930 0.109595960 0.687226565 0.990115111
## 114 0.598192136 0.8803027971 0.934215342 0.184075910 0.930016244 0.015515274
## 115 0.494660591 0.5270667071 0.165982118 0.279556816 0.548412474 0.006808892
## 116 0.822326746 0.0874312406 0.339381942 0.624753956 0.139959793 0.881927748
## 117 0.884809928 0.2049752097 0.351055704 0.772163214 0.897429584 0.373503622
## 118 0.195553894 0.1479548330 0.547592697 0.426198894 0.233539708 0.459527157
## 119 0.463013117 0.4677024283 0.079132932 0.123636657 0.209901525 0.249119067
## 120 0.007715050 0.9759014850 0.647108061 0.623121100 0.489483954 0.913406589
## 121 0.623211886 0.7964882990 0.725319422 0.268862381 0.873370248 0.629094972
## 122 0.632887607 0.6062786465 0.027653304 0.215499579 0.437937672 0.412266847
## 123 0.313287797 0.6479254356 0.003295714 0.679255102 0.590496615 0.988463188
## 124 0.775744612 0.1102327388 0.168523920 0.228762099 0.965724084 0.842011251
## 125 0.998992379 0.8608238841 0.913439707 0.130730744 0.663723183 0.934387672
## 126 0.751483215 0.3711484901 0.757779663 0.436154100 0.914117961 0.487309208
## 127 0.512864344 0.4433466932 0.777240771 0.131851328 0.666940580 0.893005643
## 128 0.594934646 0.6147596298 0.629629193 0.029415055 0.156732836 0.675986912
## 129 0.108193488 0.0456732074 0.553760919 0.836029727 0.991577258 0.029231649
## 130 0.213286245 0.6094768783 0.343689348 0.090614796 0.383258829 0.830723291
## 131 0.511472948 0.8676087293 0.542017557 0.964182970 0.315437378 0.805567415
## 132 0.653088958 0.0627070705 0.925106390 0.035819308 0.250788742 0.872808259
## 133 0.680070220 0.4819761757 0.543910673 0.283038010 0.721935218 0.261010709
## 134 0.594429644 0.9517888685 0.487364555 0.429615057 0.077726093 0.396774478
## 135 0.566119617 0.7702909564 0.283901030 0.481008470 0.085473549 0.392161391
## 136 0.292137912 0.4600951856 0.031411853 0.355790904 0.714166709 0.646736944
## 137 0.621721983 0.8975026356 0.486688155 0.237542561 0.754609415 0.993754126
## 138 0.734009909 0.7064418797 0.685221680 0.159361927 0.678954404 0.522533498
## 139 0.250146729 0.2166299177 0.828084011 0.759835896 0.783513594 0.528184886
## 140 0.725502808 0.3214482346 0.801824650 0.683726188 0.785781410 0.368117954
## 141 0.518633971 0.1892801912 0.636985009 0.216002044 0.823852410 0.130777703
## 142 0.353793057 0.1187343048 0.771915119 0.228639466 0.026823693 0.470881379
## 143 0.536732926 0.5057627214 0.544558276 0.408174795 0.220592264 0.716128180
## 144 0.827716813 0.1134541789 0.151092910 0.249067954 0.167421041 0.812992523
## 145 0.799086446 0.2226722005 0.314966519 0.644402519 0.296044190 0.010295009
## 146 0.121202702 0.5125092892 0.736546513 0.173788953 0.987242828 0.128936096
## 147 0.965792880 0.2959974960 0.281766439 0.181185599 0.460291081 0.428525911
## 148 0.655097562 0.9138811582 0.685150367 0.203402501 0.556077081 0.384476536
## 149 0.523663767 0.3619226965 0.790130149 0.296799039 0.181327148 0.809934170
## 150 0.406266008 0.1738398047 0.437415589 0.528837076 0.650578036 0.017366972
## 151 0.811131607 0.4745276461 0.736739275 0.090695082 0.734380059 0.640642888
## 152 0.195899217 0.1883440749 0.036628024 0.037811573 0.361777857 0.891157788
## 153 0.901721909 0.7641276480 0.975725230 0.649152147 0.125422492 0.843844815
## 154 0.419387562 0.7132732121 0.537194521 0.663290517 0.813946252 0.346468189
## 155 0.502626143 0.1582271636 0.926717208 0.752402752 0.534871275 0.519248105
## 156 0.505678876 0.5922643617 0.249804128 0.229866606 0.489065639 0.002901212
## 157 0.914411720 0.3216436969 0.149495436 0.232416035 0.057981907 0.278796293
## 158 0.148558215 0.5582501232 0.832446445 0.294442032 0.117299439 0.885807658
## 159 0.937065663 0.7175001081 0.341711296 0.826616130 0.589513207 0.927866664
## 160 0.975472900 0.4723303919 0.144815880 0.495536016 0.437703832 0.338820112
## 161 0.424515043 0.6310416884 0.783094346 0.510714823 0.314462922 0.086185409
## 162 0.812289485 0.6547854072 0.352954853 0.395277522 0.834191832 0.642550439
## 163 0.029440868 0.7336349678 0.287532780 0.481363036 0.646652654 0.586816839
## 164 0.917813970 0.6703584662 0.014808858 0.308127946 0.908841855 0.511950091
## 165 0.214090701 0.3539453736 0.441450395 0.704947843 0.190465599 0.788839862
## 166 0.553994835 0.3797423861 0.426848450 0.406387825 0.583469785 0.982102466
## 167 0.087216421 0.0444812854 0.887981009 0.334847389 0.958314174 0.631051316
## 168 0.051853288 0.5381637057 0.287162258 0.544222318 0.580674538 0.138133082
## 169 0.153477015 0.7609185344 0.588195231 0.726811070 0.869440276 0.140277030
## 170 0.585922012 0.6343205774 0.114031907 0.054257943 0.132969180 0.262855512
## 171 0.915327054 0.6440016078 0.582549772 0.953309200 0.661264660 0.182328664
## 172 0.021536301 0.3673074185 0.137482502 0.985332304 0.359814066 0.504694133
## 173 0.175545276 0.5064939184 0.364339191 0.650103795 0.942291794 0.238556437
## 174 0.083142271 0.1788396279 0.373116091 0.705161238 0.367621270 0.640988169
## 175 0.491874318 0.4900236735 0.297881532 0.331352153 0.870221517 0.530976141
## 176 0.665890210 0.6166888489 0.978142474 0.226049843 0.988691468 0.411653516
## 177 0.028172681 0.3769877132 0.719316378 0.022271170 0.711718217 0.537131623
## 178 0.879781784 0.7322189799 0.869278736 0.649725121 0.669133191 0.397410648
## 179 0.795590631 0.2757800566 0.781217543 0.406130929 0.115849692 0.363247100
## 180 0.066798607 0.4353600563 0.641473262 0.070881601 0.725632793 0.845899404
## 181 0.369471576 0.2884542705 0.375342084 0.381129961 0.752541286 0.080834012
## 182 0.111091629 0.5124843172 0.743466425 0.401846189 0.632692037 0.334856320
## 183 0.825969449 0.7803220809 0.425994063 0.961734195 0.726619251 0.637834937
## 184 0.612556007 0.9145965697 0.257388497 0.629601910 0.375935599 0.271460483
## 185 0.637976925 0.1076111828 0.280669488 0.654566472 0.932735895 0.974294363
## 186 0.722749287 0.4142492083 0.976476628 0.461700869 0.261488323 0.760588499
## 187 0.088224613 0.3651040641 0.112417366 0.427385604 0.630677684 0.064398194
## 188 0.206456413 0.6789903478 0.269728941 0.026255392 0.533788505 0.339906024
## 189 0.271994818 0.4532893968 0.732908373 0.710368193 0.555094344 0.429670967
## 190 0.520548412 0.3144283574 0.803517855 0.349941988 0.498034912 0.495041399
## 191 0.776805477 0.9616133086 0.754222457 0.091987771 0.551281321 0.733340201
## 192 0.289232634 0.8427688032 0.202012851 0.496472600 0.546778636 0.428116115
## 193 0.989449516 0.2357514210 0.704040867 0.447436986 0.046436282 0.493715242
## 194 0.310988950 0.4760307493 0.771920531 0.274742047 0.416478656 0.183150188
## 195 0.581546503 0.0395606223 0.147069360 0.853941998 0.729293162 0.166967576
## 196 0.701018440 0.7045858139 0.531901518 0.318705286 0.510770075 0.799619116
## 197 0.539472235 0.1585750368 0.654213027 0.492335809 0.606566809 0.903776626
## 198 0.011292625 0.9602364919 0.776298914 0.773416284 0.594650894 0.984942808
## 199 0.603909890 0.9586990301 0.875057548 0.093729714 0.825522528 0.624501048
## 200 0.089178660 0.6006974212 0.113622466 0.825916705 0.558199830 0.084706127
## V7 V8 V9 V10 corr_pred
## 1 0.8266608594 0.421408064 0.59111440 0.588621560 0.483553213
## 2 0.6489600763 0.844623926 0.92819306 0.758400814 0.596918149
## 3 0.1785614495 0.349590781 0.01759542 0.444118458 0.581686589
## 4 0.5133613953 0.797025980 0.68986918 0.445071622 0.779718369
## 5 0.6644906041 0.903891937 0.39696995 0.550080800 0.679028625
## 6 0.3360117343 0.648917723 0.53116033 0.906618237 0.871156744
## 7 0.0084998407 0.072795420 0.97395768 0.440172910 0.653421017
## 8 0.4722572784 0.381633542 0.75877525 0.710887919 0.167954496
## 9 0.3058403293 0.525661726 0.43136410 0.400128186 0.441298786
## 10 0.3228343336 0.960311741 0.92426620 0.832559698 0.199364323
## 11 0.1315679180 0.939230266 0.46228702 0.775593376 0.463353503
## 12 0.7618696443 0.550847133 0.08637756 0.524860506 0.658880358
## 13 0.4806034924 0.485595847 0.54158360 0.081258474 0.133563727
## 14 0.4200604216 0.282479481 0.62596273 0.003172379 0.723272724
## 15 0.6595693664 0.469818084 0.03909819 0.706367689 0.395551623
## 16 0.6941591527 0.917750880 0.33898498 0.689810129 0.304366392
## 17 0.1693497750 0.290054937 0.69159996 0.120331543 0.527881952
## 18 0.1774999567 0.724190771 0.14320681 0.075203559 0.182873479
## 19 0.6109301876 0.182253540 0.20626788 0.247241936 0.830796153
## 20 0.1655056404 0.996789995 0.57239957 0.970613467 0.877359300
## 21 0.8696455043 0.480284780 0.94174627 0.525216599 0.416551694
## 22 0.2200369346 0.543487359 0.91963756 0.948926731 0.175153068
## 23 0.6324701225 0.833171203 0.91811502 0.181142754 0.232789942
## 24 0.6703429641 0.285668603 0.84918471 0.397776954 0.999680294
## 25 0.0101521015 0.960430558 0.23506862 0.230721395 0.237988893
## 26 0.2522400960 0.634320574 0.87522970 0.635452710 0.221479234
## 27 0.6650384206 0.650785477 0.28744271 0.616526859 0.645347402
## 28 0.0648198922 0.178094681 0.56876498 0.428627433 0.403429814
## 29 0.6192647608 0.146737191 0.33908035 0.938806834 -0.085152007
## 30 0.3292513283 0.042337252 0.86859891 0.880950373 0.546126975
## 31 0.2824812313 0.332542812 0.95191869 0.763801782 0.254637267
## 32 0.2051616914 0.785139066 0.04968553 0.968671421 0.341791275
## 33 0.6479521065 0.175871460 0.67905283 0.730759681 0.469281733
## 34 0.3500645757 0.635448656 0.89620270 0.575594178 0.314608361
## 35 0.8686830916 0.324884567 0.03161212 0.849832683 0.856362465
## 36 0.6281718945 0.651751797 0.69222388 0.442386812 0.538379426
## 37 0.5401211150 0.802915463 0.51344968 0.959669129 0.196843804
## 38 0.0954262505 0.271751555 0.91415621 0.535858047 1.014054381
## 39 0.3189930974 0.487114596 0.38007261 0.068724414 0.600313558
## 40 0.0987321541 0.398785473 0.70468780 0.814099950 0.582960796
## 41 0.8256829928 0.274217872 0.24911536 0.363809015 0.576693725
## 42 0.4254488801 0.543745558 0.56771488 0.586587886 0.860890373
## 43 0.6002272039 0.303179812 0.30442762 0.996330470 0.513995466
## 44 0.0993871398 0.726330749 0.51122937 0.574089565 0.238437201
## 45 0.3573383761 0.659334866 0.82108557 0.880166529 0.900247544
## 46 0.3369224169 0.171208087 0.58813299 0.298467441 0.821234986
## 47 0.7216083466 0.347465995 0.45980972 0.522110901 0.121455573
## 48 0.1637666794 0.465182498 0.67228512 0.549377529 0.708127573
## 49 0.0661412831 0.662970975 0.67190601 0.712600555 0.657654646
## 50 0.5044657106 0.684693513 0.23367805 0.853776497 0.644942325
## 51 0.4450478635 0.954027392 0.87891811 0.228369326 0.022480965
## 52 0.8620285194 0.258589442 0.96154879 0.437253388 -0.055233701
## 53 0.0236228870 0.676012672 0.37005100 0.260396947 0.910261194
## 54 0.1452215833 0.955375290 0.70495617 0.882332698 0.747681691
## 55 0.3742820916 0.214503606 0.13091783 0.462896239 0.287812995
## 56 0.5384509673 0.037968947 0.61604382 0.535041264 0.232146468
## 57 0.2577628391 0.186539843 0.93924713 0.942935549 0.009376398
## 58 0.2109247684 0.363152975 0.22155711 0.789319306 0.343831061
## 59 0.4573113865 0.197379992 0.41096121 0.626259638 0.699193917
## 60 0.2189239766 0.259368576 0.39850931 0.322176775 0.587901802
## 61 0.9801436167 0.418736819 0.50638210 0.791115409 0.121203074
## 62 0.2792056827 0.632583834 0.92330341 0.663045999 0.563762947
## 63 0.6202754262 0.088279070 0.26778657 0.207211251 0.720391881
## 64 0.6345477444 0.994484988 0.67288102 0.949158964 0.823982928
## 65 0.1516102208 0.669617534 0.12557122 0.392013110 0.788701557
## 66 0.0638373715 0.153521036 0.22166633 0.123506922 0.606075877
## 67 0.3630222164 0.350279308 0.14200169 0.041529058 0.282065476
## 68 0.0141349288 0.663475810 0.67553172 0.501539484 0.301617217
## 69 0.5267603784 0.429941210 0.97828898 0.885561631 0.087564073
## 70 0.6532241760 0.671208466 0.65576477 0.673768810 0.583857899
## 71 0.2219880908 0.476079757 0.71183447 0.425648322 0.400107953
## 72 0.1531321660 0.691954747 0.65801907 0.426056444 0.046916341
## 73 0.5008657877 0.040073613 0.92800985 0.381413696 0.350010608
## 74 0.9806543912 0.819187354 0.84159996 0.896280786 0.439968794
## 75 0.9244000583 0.198013207 0.23337787 0.116631588 0.191731905
## 76 0.0099979453 0.295807930 0.90356056 0.885416760 0.312676924
## 77 0.2356902743 0.506900013 0.55981430 0.534760828 0.477477021
## 78 0.3650656492 0.810620838 0.11388461 0.410755347 0.177769617
## 79 0.7987873172 0.366785977 0.60186782 0.973480208 0.745112953
## 80 0.5599248759 0.116578872 0.34580507 0.714962742 -0.201031396
## 81 0.7522757188 0.026414874 0.34715430 0.836363711 0.906534116
## 82 0.8865377689 0.061911004 0.97803556 0.612240904 0.737108952
## 83 0.0590573207 0.684142034 0.71260502 0.255351776 0.519712589
## 84 0.7768231640 0.850076108 0.17097505 0.408350330 0.247613470
## 85 0.4138241454 0.755554634 0.92548457 0.945293089 0.513280171
## 86 0.9818397635 0.945009324 0.68008657 0.510965007 0.770673665
## 87 0.2916908523 0.702514261 0.85496045 0.604653787 0.480977075
## 88 0.1587244619 0.582193831 0.05235641 0.486561552 1.066008245
## 89 0.0014450864 0.128084549 0.47699398 0.679715703 0.544159394
## 90 0.2105985023 0.884157248 0.18779775 0.402003791 0.987415473
## 91 0.8245949268 0.793933963 0.53137582 0.756866812 0.418679640
## 92 0.0445211111 0.460617797 0.58243842 0.944980194 0.362962259
## 93 0.5918905353 0.485206415 0.77555244 0.542896184 -0.058190556
## 94 0.0303562423 0.324637733 0.98245833 0.605254818 0.113825253
## 95 0.6099704383 0.731502909 0.49410755 0.882788646 0.556244164
## 96 0.0619420919 0.788262721 0.32567336 0.790985481 0.615313728
## 97 0.6019777379 0.718690965 0.24367231 0.571871065 0.223912719
## 98 0.7470110336 0.789140293 0.18306352 0.852484180 0.199057769
## 99 0.5261754794 0.983355801 0.37887188 0.765290411 0.330337083
## 100 0.4876051969 0.122928050 0.08177731 0.848134163 0.565642051
## 101 0.9011508890 0.617960313 0.12460480 0.702702949 0.653335312
## 102 0.0003387642 0.388927228 0.97821702 0.104494945 0.968213155
## 103 0.9080805883 0.905519754 0.60285307 0.877587634 0.066143767
## 104 0.4965877566 0.636728981 0.79705572 0.319453278 0.640933352
## 105 0.8487957353 0.912640729 0.11477043 0.155581983 0.046373610
## 106 0.0822484379 0.955071241 0.06021731 0.421584291 0.008525971
## 107 0.1611803344 0.599529999 0.26890232 0.188167820 0.558746858
## 108 0.1425062015 0.571244097 0.74935739 0.464775090 -0.034123408
## 109 0.4653496440 0.651546226 0.95540449 0.564070737 0.625975040
## 110 0.1981665948 0.999560626 0.57950670 0.127039001 0.468730012
## 111 0.8408644302 0.437424371 0.93131402 0.133683814 0.921901785
## 112 0.9164640335 0.395302785 0.63386223 0.888060797 0.101906684
## 113 0.3355441941 0.030395976 0.20250656 0.053323140 0.110253612
## 114 0.6774176396 0.696283764 0.75913311 0.809930917 0.455270626
## 115 0.9650529190 0.449902425 0.57304399 0.753339031 0.461563047
## 116 0.1141603340 0.863953833 0.95345440 0.380650506 0.835165353
## 117 0.4158274462 0.713239111 0.60102539 0.635894833 0.986621928
## 118 0.1791522284 0.834004079 0.20838605 0.592570851 0.169996525
## 119 0.5624954123 0.710008362 0.18311621 0.394101708 0.432759016
## 120 0.9726133470 0.842078145 0.93576851 0.956083941 0.169234118
## 121 0.4887156698 0.887054311 0.31041901 0.510736341 0.545840551
## 122 0.9838132532 0.585472636 0.14732752 0.086574405 0.675287847
## 123 0.4743697466 0.242674318 0.42347788 0.868947359 0.254893099
## 124 0.2407878560 0.447328788 0.66467369 0.494879879 0.817248180
## 125 0.1783671109 0.503948929 0.16230501 0.187285239 0.844466213
## 126 0.4367017439 0.344732890 0.42201320 0.437095925 0.699608265
## 127 0.3784207169 0.273177421 0.11701698 0.547305345 0.484885189
## 128 0.1147928145 0.103627008 0.16504249 0.275940885 0.695680384
## 129 0.3586573373 0.238100665 0.68896641 0.177130092 0.061236492
## 130 0.2376520939 0.312197204 0.25109129 0.997579731 0.243075949
## 131 0.7941833863 0.433608739 0.76234330 0.569325565 0.469693505
## 132 0.5684747580 0.312200866 0.11102144 0.240327878 0.568050881
## 133 0.9834440248 0.023838794 0.16816803 0.999992477 0.748974840
## 134 0.8681481183 0.755061130 0.16099688 0.581953628 0.548410025
## 135 0.2529283839 0.309956316 0.35376172 0.576154274 0.700938055
## 136 0.2954634046 0.686869082 0.23401367 0.743752910 0.336445050
## 137 0.7287589125 0.934555566 0.27740693 0.256602708 0.606629364
## 138 0.5105628674 0.330980633 0.32516244 0.474497675 0.779564795
## 139 0.4536720926 0.385358283 0.03655417 0.171900066 0.246131261
## 140 0.0308236629 0.654293299 0.92551144 0.435859671 0.771114912
## 141 0.3351621642 0.409007091 0.67315717 0.996981804 0.477791468
## 142 0.6144252147 0.651714271 0.12889572 0.633149029 0.140143672
## 143 0.1153656312 0.793603583 0.55421117 0.356097830 0.552415117
## 144 0.7361220436 0.177242560 0.03421274 0.872309444 0.893721703
## 145 0.9072946333 0.738731097 0.26822183 0.173052300 0.700903005
## 146 0.8854910310 0.688096952 0.75856509 0.669689639 0.009838331
## 147 0.0388078641 0.214172413 0.61253457 0.207942491 0.922058112
## 148 0.3260785770 0.810973278 0.39199971 0.370241001 0.603486438
## 149 0.7807700243 0.578197747 0.70276752 0.123103430 0.565563366
## 150 0.7907638911 0.208587777 0.05438854 0.766739978 0.419681552
## 151 0.7937673274 0.208766474 0.83636350 0.858343330 0.914600252
## 152 0.1613148297 0.654811297 0.66729678 0.115404263 0.361249539
## 153 0.7080952730 0.903838935 0.31193910 0.969527644 0.899927228
## 154 0.5305830529 0.004698141 0.48546810 0.259277162 0.416967229
## 155 0.1885056335 0.079913177 0.57972754 0.905628399 0.527650833
## 156 0.5161641990 0.466810009 0.76300679 0.944087471 0.471966423
## 157 0.6012678132 0.025244068 0.19821959 0.402928842 0.903076350
## 158 0.6169876396 0.499346328 0.32760646 0.266050707 0.138669923
## 159 0.7895973460 0.786763847 0.07832531 0.312945329 0.963474345
## 160 0.0390002122 0.015907055 0.57958929 0.502512869 0.989371268
## 161 0.4199729285 0.538111618 0.94932648 0.535985540 0.400288093
## 162 0.5129533098 0.613649708 0.26589918 0.269859831 0.818192624
## 163 0.6883663596 0.515120720 0.64359538 0.473454136 0.011713681
## 164 0.2867906420 0.219839853 0.16326702 0.120969625 0.997281997
## 165 0.9943477523 0.381418612 0.81146453 0.136825552 0.214764480
## 166 0.2593658050 0.461603611 0.68922230 0.171518739 0.491015806
## 167 0.5809806921 0.810821845 0.21677497 0.741042868 0.061967443
## 168 0.9927047875 0.928290160 0.48741662 0.881588204 -0.017188929
## 169 0.3948761285 0.914971805 0.04233756 0.987049844 0.173731229
## 170 0.9569103546 0.694013482 0.97705820 0.012435718 0.670560155
## 171 0.5889326367 0.509478116 0.64141950 0.365601074 0.978534460
## 172 0.6114409810 0.830605455 0.52658278 0.065911923 0.041677654
## 173 0.4287582068 0.366665906 0.86474573 0.016379327 0.166438212
## 174 0.1562757776 0.463090256 0.02956841 0.971855537 0.112090683
## 175 0.0453625068 0.177558171 0.10203368 0.505838658 0.486405824
## 176 0.6969831374 0.631295626 0.58758911 0.247838673 0.461705225
## 177 0.1762444021 0.080035930 0.84510174 0.700015211 0.064009605
## 178 0.2357786680 0.385391619 0.62558152 0.954732809 0.842521698
## 179 0.5439273247 0.627847850 0.88854501 0.855865543 0.922421515
## 180 0.8102693288 0.839098028 0.15944836 0.379626432 0.283658638
## 181 0.0133081947 0.168556706 0.10525675 0.771278932 0.245499291
## 182 0.6584848959 0.287486323 0.12728033 0.041241815 0.170079018
## 183 0.3847984066 0.117578465 0.96804658 0.902288517 0.838371378
## 184 0.1876184577 0.798065790 0.92881170 0.884292413 0.560185228
## 185 0.0729941991 0.472175947 0.07752809 0.744791487 0.699999725
## 186 0.7420141906 0.437308198 0.66531113 0.045803222 0.793571445
## 187 0.4334616780 0.849088030 0.46642330 0.779457425 0.078904778
## 188 0.6745903494 0.986013835 0.50686606 0.312909630 0.176936743
## 189 0.3680351812 0.496575716 0.49428027 0.447099152 0.163413295
## 190 0.6922219021 0.011549961 0.57885152 0.406213945 0.458066907
## 191 0.0971158685 0.412869229 0.97960020 0.136601998 0.753504823
## 192 0.1838154087 0.210182422 0.04580357 0.427214286 0.264150947
## 193 0.5494235111 0.720276414 0.29912111 0.994646956 1.084839050
## 194 0.7455740881 0.886575559 0.25383887 0.521175744 0.284391700
## 195 0.8809142739 0.322509774 0.66346270 0.930126207 0.771074098
## 196 0.6664053195 0.267326644 0.24159338 0.606167757 0.658019357
## 197 0.8829731958 0.123415505 0.99102161 0.073506513 0.697026935
## 198 0.2567906741 0.309302658 0.05267484 0.698478227 0.027486745
## 199 0.5021552520 0.334554489 0.03080467 0.395422508 0.495364600
## 200 0.6627391470 0.959779277 0.09184009 0.219858172 0.146872390## Overall
## V1 100.000000
## V2 79.861111
## V4 68.055556
## V3 58.333333
## V5 51.388889
## V6 25.694444
## corr_pred 4.166667
## V7 0.000000
## V8 0.000000
## V9 0.000000
## V10 0.000000cubistTuned1_df <- as.data.frame(cubistTuned1$importance)
cubistTuned1_df['Predictors'] <- rownames(cubistTuned1_df)
colnames(cubistTuned1_df) <- c("Overall", "Predictors")
rownames(cubistTuned1_df) <- 1:nrow(cubistTuned1_df)
cubistTuned1_df## Overall Predictors
## 1 100.000000 V1
## 2 58.333333 V3
## 3 79.861111 V2
## 4 4.166667 corr_pred
## 5 68.055556 V4
## 6 51.388889 V5
## 7 25.694444 V6
## 8 0.000000 V7
## 9 0.000000 V8
## 10 0.000000 V9
## 11 0.000000 V10cubistTuned1_df %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "gold") +
theme_minimal() +
coord_flip() +
labs(title="cubist Predictor Variable Importance",
y="cubist Importance", x="Predictors") +
scale_y_continuous()
8.2.
Use a simulation to show tree bias with different granularities.
After creating a simulated dataset using 8 samples and a dependent variable that is the summation of all of the variables except for gran5. After appling the tree models, cforest and boost, I found that the variables with the most granularity, gran1 and gran2, were the most important to the model.
set.seed(100)
gran1 <- c(sample(1:100, 100, replace=TRUE))
gran2 <- c(sample(1:90, 100, replace=TRUE))
gran3 <- c(sample(1:80, 100, replace=TRUE))
gran4 <- c(sample(1:70, 100, replace=TRUE))
gran5 <- c(sample(1:30, 100, replace=TRUE))
gran6 <- c(sample(1:15, 100, replace=TRUE))
gran7 <- c(sample(1:8, 100, replace=TRUE))
gran8 <- c(sample(1:3, 100, replace=TRUE))
y <- gran1 + gran2 + gran3 + gran4 + gran6 + gran7 + gran8 + rnorm(100)*.1
custom_simulation <- as.data.frame(cbind(gran1, gran2, gran3, gran4, gran5, gran6, gran7, gran8, y))
head(custom_simulation)## gran1 gran2 gran3 gran4 gran5 gran6 gran7 gran8 y
## 1 74 58 28 40 28 8 6 2 216.0582
## 2 89 26 16 37 20 2 8 1 178.9297
## 3 78 48 69 16 9 14 3 2 229.9529
## 4 23 80 7 51 13 8 7 1 177.0412
## 5 86 37 56 21 24 4 2 1 206.9312
## 6 70 18 37 18 13 8 1 3 154.9305cforest
custImp <- as.data.frame( varimp(custom_model, conditional = TRUE))
custImp ['Predictors'] <- rownames(custImp)
colnames(custImp ) <- c("Overall", "Predictors")
rownames(custImp ) <- 1:nrow(custImp)
custImp <- custImp %>%
arrange(desc(Overall))custImp %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "black") +
theme_minimal() +
coord_flip() +
labs(title="cforest Predictor Variable Importance",
y="cforest Importance", x="Predictors") +
scale_y_continuous()
Boosted Trees
gbmGrid <- expand.grid(interaction.depth = seq(1, 7, by = 2),
n.trees = seq(100, 1000, by = 50),
shrinkage = c(0.01, 0.1),
n.minobsinnode = 5)set.seed(100)
gbmTune <- train(custom_simulation[1:8], custom_simulation$y,
method = "gbm",
tuneGrid = gbmGrid,
verbose = FALSE)## Overall
## gran2 100.000000
## gran1 62.861725
## gran3 49.452449
## gran4 42.352176
## gran6 2.967537
## gran7 1.326973
## gran5 1.208729
## gran8 0.000000gbmTune1_df <- as.data.frame(gbmTune1$importance)
gbmTune1_df['Predictors'] <- rownames(gbmTune1_df)
colnames(gbmTune1_df) <- c("Overall", "Predictors")
rownames(gbmTune1_df) <- 1:nrow(gbmTune1_df)gbmTune1_df %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "purple") +
theme_minimal() +
coord_flip() +
labs(title="boostPredictor Variable Importance",
y="boost Importance", x="Predictors") +
scale_y_continuous()
8.3.
In stochastic gradient boosting the bagging fraction and learning rate will govern the construction of the trees as they are guided by the gradient. Although the optimal values of these parameters should be obtained through the tuning process, it is helpful to understand how the magnitudes of these parameters affect magnitudes of variable importance. Figure 8.24 provides the variable importance plots for boosting using two extreme values for the bagging fraction (0.1 and 0.9) and the learning rate (0.1 and 0.9) for the solubility data. The left-hand plot has both parameters set to 0.1, and the right-hand plot has both set to 0.9:
Fig. 8.24
(a)
Why does the model on the right focus its importance on just the first few of predictors, whereas the model on the left spreads importance across more predictors?
First, let’s define what a boosting algorithm does. Gradient boosting works by creating a combination of weak learners into an ensemble which is used to make predictions. Specifically:
“Given a loss function (e.g., squared error for regression) and a weak learner (e.g., regression trees), the algorithm seeks to find an additive model that minimizes the loss function. The algorithm is typically initialized with the best guess of the response (e.g., the mean of the response in regression). The gradient (e.g., residual) is calculated, and a model is then fit to the residuals to minimize the loss function. The current model is added to the previous model, and the procedure continues for a user-specified number of iteration”
Max Kuhn, Kjell Johnson, Applied Predictive Modeling, New York, NY:Springer Science+Business Media LLC New York, 2013, p. 204
Second, Trees-because they have the flexibility to be weak learners by restricting their depth, and they can be created easily and added together-are suitable for the additive modeling process. In boosting, Trees are dependent on past trees and unequally contribute to the model.
Third, the learner in gradient boosting is susceptible to over fitting since the learner is using the greedy strategy of choosing the optimal weak learner at each stage. To address this, the learner is constrained by regularization, or shrinkage, where a fraction of the current predicted value is added to the previous iteration’s predicted value. This fraction is known as the learning rate which is another parameter to tune in the model. The learning rate is set between 0 and 1.
Fourth, Stochastic Gradient Boosting involves fitting a base learner on a subsample of the training set drawn at random without replacement. This fraction is known as the bagging fraction.The suggested fraction is set to 0.5.
Given these four points, the reasons why the right hand diagram places more importance on the first few predictors is that the model is over fitting the data. The parameters, learning rate and bagging fraction, which are both set close to one at .9. In this instance the learning rate will not be constrained and the model is using the greedy strategy when choosing the optimal weak learner. Also, given the bagging fraction at .9, the model is using practically the entire training set instead of a subsample.
(b)
Which model do you think would be more predictive of other samples?
Since the right hand model overfits on training data, the left hand model would be more predicitive when generalizing to unseen data.
(c)
How would increasing interaction depth affect the slope of predictor importancefor either model in Fig. 8.24?
The interaction depth parameter is the number of splits it has to perform on a tree (starting from a single node).
I re-created the output using interaction.depth = 1 with the learning rate and bagging fractions set to .1 and then set at .9. Then I increased the interaction.depth=10 with the learning rate and bagging fractions set to .1 and then set at .9
The model with the interaction.depth = 1 with higher learning rate and bagging fractions over fit the data. When I increased the interaction.depth = 10, the model with the lower learning rate and bagging fractions had more predictive power because they did not over fit.
## Warning: package 'AppliedPredictiveModeling' was built under R version 3.6.3data(solubility)
set.seed(100)
gbmTune1 <- gbm(solTrainY ~ ., data = solTrainXtrans,
distribution = "gaussian",
bag.fraction = 0.1,
n.trees = 100,
interaction.depth=1,
shrinkage = 0.1,
n.minobsinnode = 10)
gbmTune1A <- gbm(solTrainY ~ ., data = solTrainXtrans,
distribution = "gaussian",
bag.fraction = 0.9,
n.trees = 100,
interaction.depth=1,
shrinkage = 0.9,
n.minobsinnode = 10)interaction_depth_1 <- as.data.frame(varImp(gbmTune1, numTrees = 100))
interaction_depth_1 <- interaction_depth_1 %>%
arrange(desc(Overall))
top20A <-head(interaction_depth_1, 20)
top20A <- as.data.frame(top20A)
top20A['Predictors'] <- rownames(top20A)
colnames(top20A) <- c("Overall", "Predictors")
rownames(top20A) <- 1:nrow(top20A)
top20A <- top20A[, c("Predictors","Overall")]
top20A %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "orange") +
theme_minimal() +
coord_flip() +
labs(title="Interaction Depth = 1, learning rate= .1, bagging fraction=.1",
y="Importance", x="Predictors") +
scale_y_continuous()
interaction_depth_1A <- as.data.frame(varImp(gbmTune1A, numTrees = 100))
interaction_depth_1A <- interaction_depth_1A %>%
arrange(desc(Overall))
top20A <-head(interaction_depth_1A, 20)
top20A <- as.data.frame(top20A)
top20A['Predictors'] <- rownames(top20A)
colnames(top20A) <- c("Overall", "Predictors")
rownames(top20A) <- 1:nrow(top20A)
top20A <- top20A[, c("Predictors","Overall")]
top20A %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "orange") +
theme_minimal() +
coord_flip() +
labs(title="Interaction Depth = 1, learning rate = .9, bagging fraction = .9",
y="Importance", x="Predictors") +
scale_y_continuous()
Next, I set the interaction.depth = 10 with the learning rate and bagging fractions set to .9.
set.seed(100)
gbmTune2 <- gbm(solTrainY ~ ., data = solTrainXtrans,
distribution = "gaussian",
bag.fraction = 0.1,
n.trees = 100,
interaction.depth=10,
shrinkage = 0.1,
n.minobsinnode = 10)
gbmTune2A <- gbm(solTrainY ~ ., data = solTrainXtrans,
distribution = "gaussian",
bag.fraction = 0.9,
n.trees = 100,
interaction.depth=10,
shrinkage = 0.9,
n.minobsinnode = 10)
interaction_depth_2 <- as.data.frame(varImp(gbmTune2, numTrees = 100))
interaction_depth_2 <- interaction_depth_2 %>%
arrange(desc(Overall))
top20B <- head(interaction_depth_2, 20)
top20B <- as.data.frame(top20B)
top20B['Predictors'] <- rownames(top20B)
colnames(top20B) <- c("Overall", "Predictors")
rownames(top20B) <- 1:nrow(top20A)
top20B <- top20B[, c("Predictors","Overall")]
top20B %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "purple") +
theme_minimal() +
coord_flip() +
labs(title="Interaction Depth = 10, learning rate = .1, bagging fraction = .1",
y="Importance", x="Predictors") +
scale_y_continuous()
interaction_depth_2 <- as.data.frame(varImp(gbmTune2A, numTrees = 100))
interaction_depth_2 <- interaction_depth_2 %>%
arrange(desc(Overall))
top20B <- head(interaction_depth_2, 20)
top20B <- as.data.frame(top20B)
top20B['Predictors'] <- rownames(top20B)
colnames(top20B) <- c("Overall", "Predictors")
rownames(top20B) <- 1:nrow(top20A)
top20B <- top20B[, c("Predictors","Overall")]
top20B %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "purple") +
theme_minimal() +
coord_flip() +
labs(title="Interaction Depth = 10, learning rate = .9, bagging fraction = .9",
y="Importance", x="Predictors") +
scale_y_continuous()
8.7
The matrix processPredictors contains the 57 predictors (12 describing the input biological material and 45 describing the process predictors) for the 176 manufacturing runs. yield contains the percent yield for each run.
processPredictors <- ChemicalManufacturingProcess[2:ncol(ChemicalManufacturingProcess)]
print(paste0("The number of predictors is ", ncol(processPredictors), " and the number of observations is ", nrow(processPredictors)))## [1] "The number of predictors is 57 and the number of observations is 176"## Created from 152 samples and 57 variables
##
## Pre-processing:
## - bagged tree imputation (57)
## - ignored (0)processPredictors_imputed <- try(predict(processPredictors_imputed, processPredictors), silent = TRUE)
processPredictors_imputed## BiologicalMaterial01 BiologicalMaterial02 BiologicalMaterial03
## 1 6.25 49.58 56.97
## 2 8.01 60.97 67.48
## 3 8.01 60.97 67.48
## 4 8.01 60.97 67.48
## 5 7.47 63.33 72.25
## 6 6.12 58.36 65.31
## 7 7.48 64.47 72.41
## 8 6.94 63.60 72.06
## 9 6.94 63.60 72.06
## 10 6.94 63.60 72.06
## 11 7.17 61.23 70.01
## 12 7.17 61.23 70.01
## 13 7.17 61.23 70.01
## 14 7.63 60.51 69.24
## 15 6.23 62.93 69.74
## 16 7.13 60.30 68.18
## 17 7.85 58.22 66.95
## 18 7.64 59.44 67.22
## 19 7.51 59.74 67.28
## 20 7.51 59.74 67.28
## 21 7.51 59.74 67.28
## 22 7.08 61.83 70.69
## 23 6.58 58.38 67.17
## 24 6.27 56.23 64.98
## 25 8.17 63.66 73.44
## 26 6.60 55.74 66.25
## 27 6.90 54.26 60.99
## 28 6.86 55.66 63.43
## 29 6.67 63.44 76.94
## 30 6.53 61.68 77.15
## 31 6.89 61.54 76.07
## 32 7.13 61.39 74.10
## 33 6.84 61.46 73.91
## 34 5.17 61.17 76.39
## 35 7.01 61.30 72.71
## 36 6.30 57.04 70.03
## 37 5.32 59.14 71.05
## 38 5.32 59.14 71.05
## 39 5.32 59.14 71.05
## 40 5.71 57.68 69.37
## 41 6.60 58.80 71.17
## 42 6.76 55.42 69.80
## 43 6.76 55.42 69.80
## 44 6.76 55.42 69.80
## 45 6.77 58.76 72.74
## 46 6.95 60.31 73.97
## 47 6.95 60.31 73.97
## 48 6.95 60.31 73.97
## 49 7.97 64.75 74.10
## 50 6.94 57.02 69.51
## 51 6.94 57.02 69.51
## 52 6.94 57.02 69.51
## 53 7.56 61.62 72.17
## 54 6.87 57.33 71.52
## 55 6.87 57.33 71.52
## 56 6.87 57.33 71.52
## 57 6.65 55.61 68.93
## 58 6.65 55.61 68.93
## 59 6.65 55.61 68.93
## 60 6.72 57.24 71.27
## 61 6.57 55.93 69.48
## 62 6.16 54.67 66.95
## 63 6.16 54.67 66.95
## 64 6.16 54.67 66.95
## 65 6.37 52.67 64.34
## 66 6.37 52.67 64.34
## 67 6.37 52.67 64.34
## 68 6.31 54.42 66.13
## 69 6.27 53.51 66.52
## 70 6.27 53.51 66.52
## 71 6.27 53.51 66.52
## 72 6.58 52.50 63.29
## 73 6.45 53.18 64.98
## 74 6.39 58.85 73.45
## 75 6.39 58.85 73.45
## 76 6.39 58.85 73.45
## 77 6.35 56.93 70.87
## 78 6.17 53.80 65.53
## 79 6.97 58.18 71.85
## 80 6.97 58.18 71.85
## 81 6.97 58.18 71.85
## 82 8.81 63.99 78.25
## 83 6.80 57.21 70.34
## 84 6.80 57.21 70.34
## 85 6.80 57.21 70.34
## 86 6.30 51.96 64.07
## 87 6.30 51.96 64.07
## 88 6.30 51.96 64.07
## 89 6.45 55.09 69.18
## 90 6.45 55.09 69.18
## 91 6.45 55.09 69.18
## 92 6.28 54.33 68.30
## 93 7.33 56.87 70.17
## 94 7.22 57.32 71.02
## 95 6.19 53.59 66.40
## 96 5.98 54.10 66.50
## 97 5.98 54.10 66.50
## 98 5.98 54.10 66.50
## 99 5.85 51.75 64.02
## 100 5.85 51.75 64.02
## 101 5.85 51.75 64.02
## 102 6.01 51.83 63.80
## 103 5.89 51.28 64.04
## 104 5.90 51.44 63.61
## 105 5.90 51.44 63.61
## 106 5.90 51.44 63.61
## 107 5.79 53.96 66.53
## 108 5.79 53.96 66.53
## 109 5.79 53.96 66.53
## 110 5.94 51.27 63.54
## 111 6.40 58.73 71.51
## 112 6.40 58.73 71.51
## 113 6.40 58.73 71.51
## 114 6.10 56.36 69.52
## 115 5.78 53.70 67.22
## 116 6.15 53.06 70.29
## 117 6.40 52.62 72.39
## 118 5.60 51.45 63.44
## 119 5.60 51.45 63.44
## 120 5.60 51.45 63.44
## 121 5.43 49.10 62.08
## 122 6.02 50.01 60.82
## 123 6.03 52.58 65.05
## 124 6.08 52.89 66.72
## 125 5.76 52.73 63.88
## 126 5.79 52.70 64.33
## 127 6.23 52.95 66.71
## 128 6.23 52.95 66.71
## 129 6.23 52.95 66.71
## 130 6.26 55.94 69.22
## 131 6.26 55.94 69.22
## 132 6.26 55.94 69.22
## 133 6.36 53.18 66.57
## 134 6.72 53.85 67.10
## 135 5.18 48.60 61.04
## 136 5.18 48.60 61.04
## 137 5.18 48.60 61.04
## 138 6.29 50.64 63.92
## 139 6.10 50.60 63.37
## 140 5.30 46.87 57.56
## 141 5.83 50.17 63.11
## 142 6.25 54.57 67.56
## 143 6.25 54.57 67.56
## 144 6.25 54.57 67.56
## 145 6.00 53.29 65.50
## 146 6.00 53.29 65.50
## 147 6.00 53.29 65.50
## 148 5.49 48.03 58.99
## 149 5.30 46.87 57.56
## 150 5.54 52.48 64.98
## 151 5.54 52.29 64.61
## 152 6.25 52.68 65.12
## 153 6.25 52.68 65.12
## 154 6.25 52.68 65.12
## 155 6.22 52.76 65.13
## 156 5.90 51.37 63.65
## 157 5.90 51.37 63.65
## 158 5.90 51.37 63.65
## 159 5.70 52.77 66.25
## 160 5.70 52.77 66.25
## 161 5.70 52.77 66.25
## 162 5.97 53.13 66.58
## 163 6.39 53.72 67.13
## 164 5.36 53.39 65.30
## 165 5.27 52.45 64.09
## 166 4.58 49.56 61.08
## 167 4.58 49.56 61.08
## 168 4.58 49.56 61.08
## 169 7.70 62.92 75.91
## 170 6.39 59.10 71.04
## 171 6.63 59.81 71.94
## 172 6.71 56.32 66.19
## 173 6.87 56.74 66.61
## 174 7.50 58.41 68.30
## 175 7.53 58.36 69.25
## 176 7.53 58.36 69.25
## BiologicalMaterial04 BiologicalMaterial05 BiologicalMaterial06
## 1 12.74 19.51 43.73
## 2 14.65 19.36 53.14
## 3 14.65 19.36 53.14
## 4 14.65 19.36 53.14
## 5 14.02 17.91 54.66
## 6 15.17 21.79 51.23
## 7 13.82 17.71 54.45
## 8 15.70 19.42 54.72
## 9 15.70 19.42 54.72
## 10 15.70 19.42 54.72
## 11 13.36 18.67 52.83
## 12 13.36 18.67 52.83
## 13 13.36 18.67 52.83
## 14 17.59 20.67 52.83
## 15 11.80 20.54 54.57
## 16 13.80 20.72 52.49
## 17 15.38 20.86 50.84
## 18 15.67 21.50 52.02
## 19 15.72 21.80 52.30
## 20 15.72 21.80 52.30
## 21 15.72 21.80 52.30
## 22 13.43 17.72 53.27
## 23 12.22 18.46 51.45
## 24 11.47 18.93 50.31
## 25 18.37 23.76 56.64
## 26 11.83 22.52 48.95
## 27 12.22 20.16 47.23
## 28 12.53 20.39 48.94
## 29 14.28 21.67 58.42
## 30 11.81 21.12 59.38
## 31 12.41 21.14 57.89
## 32 13.27 20.96 55.95
## 33 13.18 20.77 56.39
## 34 12.51 20.32 58.17
## 35 13.23 24.85 54.89
## 36 11.70 18.04 50.50
## 37 13.02 21.17 52.58
## 38 13.02 21.17 52.58
## 39 13.02 21.17 52.58
## 40 12.26 21.32 50.79
## 41 12.40 22.14 52.24
## 42 11.25 18.15 49.89
## 43 11.25 18.15 49.89
## 44 11.25 18.15 49.89
## 45 12.12 20.65 53.17
## 46 12.42 19.05 52.31
## 47 12.42 19.05 52.31
## 48 12.42 19.05 52.31
## 49 15.11 22.66 56.22
## 50 13.45 18.44 50.16
## 51 13.45 18.44 50.16
## 52 13.45 18.44 50.16
## 53 14.46 21.02 53.78
## 54 13.22 15.62 50.85
## 55 13.22 15.62 50.85
## 56 13.22 15.62 50.85
## 57 12.72 15.91 48.64
## 58 12.72 15.91 48.64
## 59 12.72 15.91 48.64
## 60 12.25 16.58 50.88
## 61 11.95 18.00 50.50
## 62 11.15 17.25 48.12
## 63 11.15 17.25 48.12
## 64 11.15 17.25 48.12
## 65 12.02 17.40 46.52
## 66 12.02 17.40 46.52
## 67 12.02 17.40 46.52
## 68 11.97 18.40 48.01
## 69 11.83 16.95 46.62
## 70 11.83 16.95 46.62
## 71 11.83 16.95 46.62
## 72 12.24 18.28 46.04
## 73 12.11 18.77 46.80
## 74 12.69 16.92 51.25
## 75 12.69 16.92 51.25
## 76 12.69 16.92 51.25
## 77 12.27 18.06 49.92
## 78 12.70 18.65 47.67
## 79 14.25 17.08 50.06
## 80 14.25 17.08 50.06
## 81 14.25 17.08 50.06
## 82 23.09 19.96 53.87
## 83 13.98 16.81 48.46
## 84 13.98 16.81 48.46
## 85 13.98 16.81 48.46
## 86 12.65 19.23 44.66
## 87 12.65 19.23 44.66
## 88 12.65 19.23 44.66
## 89 11.98 17.22 47.12
## 90 11.98 17.22 47.12
## 91 11.98 17.22 47.12
## 92 12.37 15.46 46.72
## 93 14.20 20.16 49.06
## 94 14.05 19.16 49.21
## 95 11.99 18.73 47.41
## 96 11.73 18.80 47.98
## 97 11.73 18.80 47.98
## 98 11.73 18.80 47.98
## 99 10.41 20.40 44.30
## 100 10.41 20.40 44.30
## 101 10.41 20.40 44.30
## 102 11.22 19.69 44.57
## 103 9.99 16.90 44.74
## 104 10.49 18.04 44.73
## 105 10.49 18.04 44.73
## 106 10.49 18.04 44.73
## 107 10.40 18.26 47.57
## 108 10.40 18.26 47.57
## 109 10.40 18.26 47.57
## 110 10.48 17.72 44.43
## 111 12.29 17.09 50.62
## 112 12.29 17.09 50.62
## 113 12.29 17.09 50.62
## 114 11.71 16.35 49.10
## 115 11.17 15.44 47.33
## 116 11.87 16.59 49.97
## 117 12.34 17.38 51.77
## 118 10.50 19.17 45.06
## 119 10.50 19.17 45.06
## 120 10.50 19.17 45.06
## 121 10.11 19.09 44.45
## 122 11.79 19.43 43.24
## 123 11.45 19.11 46.06
## 124 11.23 19.06 47.29
## 125 10.59 20.49 47.29
## 126 10.70 20.09 47.21
## 127 12.75 16.31 45.84
## 128 12.75 16.31 45.84
## 129 12.75 16.31 45.84
## 130 12.07 18.08 48.92
## 131 12.07 18.08 48.92
## 132 12.07 18.08 48.92
## 133 12.07 16.22 46.51
## 134 12.50 16.15 46.87
## 135 9.38 16.30 43.78
## 136 9.38 16.30 43.78
## 137 9.38 16.30 43.78
## 138 11.46 13.24 43.50
## 139 10.90 19.05 44.18
## 140 9.93 18.07 40.60
## 141 10.32 17.24 44.31
## 142 12.10 17.66 47.80
## 143 12.10 17.66 47.80
## 144 12.10 17.66 47.80
## 145 11.71 18.80 46.34
## 146 11.71 18.80 46.34
## 147 11.71 18.80 46.34
## 148 10.24 18.30 41.50
## 149 9.93 18.07 40.60
## 150 10.30 18.24 45.86
## 151 10.32 18.52 45.76
## 152 11.64 18.11 45.42
## 153 11.64 18.11 45.42
## 154 11.64 18.11 45.42
## 155 11.50 18.55 45.48
## 156 10.76 19.90 45.07
## 157 10.76 19.90 45.07
## 158 10.76 19.90 45.07
## 159 10.50 15.18 47.07
## 160 10.50 15.18 47.07
## 161 10.50 15.18 47.07
## 162 11.00 16.55 46.77
## 163 11.75 18.61 46.32
## 164 12.05 18.57 46.91
## 165 10.84 18.10 46.02
## 166 9.84 18.68 43.53
## 167 9.84 18.68 43.53
## 168 9.84 18.68 43.53
## 169 13.49 16.10 55.29
## 170 11.52 21.82 53.53
## 171 11.89 20.76 53.86
## 172 12.35 20.02 50.26
## 173 12.55 20.18 50.80
## 174 13.33 20.81 52.96
## 175 14.35 20.57 51.31
## 176 14.35 20.57 51.31
## BiologicalMaterial07 BiologicalMaterial08 BiologicalMaterial09
## 1 100.00 16.66 11.44
## 2 100.00 19.04 12.55
## 3 100.00 19.04 12.55
## 4 100.00 19.04 12.55
## 5 100.00 18.22 12.80
## 6 100.00 18.30 12.13
## 7 100.00 18.72 12.95
## 8 100.00 18.85 13.13
## 9 100.00 18.85 13.13
## 10 100.00 18.85 13.13
## 11 100.00 17.88 12.62
## 12 100.00 17.88 12.62
## 13 100.00 17.88 12.62
## 14 100.00 18.74 13.21
## 15 100.00 18.89 12.82
## 16 100.00 18.68 12.75
## 17 100.00 18.51 12.70
## 18 100.00 18.72 12.86
## 19 100.00 18.81 12.98
## 20 100.00 18.81 12.98
## 21 100.00 18.81 12.98
## 22 100.00 19.14 13.38
## 23 100.00 18.22 12.83
## 24 100.00 17.64 12.48
## 25 100.00 17.94 12.18
## 26 100.00 16.67 12.11
## 27 100.00 16.57 11.73
## 28 100.00 16.71 11.94
## 29 100.00 17.47 13.12
## 30 100.00 17.31 12.83
## 31 100.00 17.42 12.79
## 32 100.00 17.58 12.63
## 33 100.00 17.56 12.55
## 34 100.00 17.79 13.05
## 35 100.00 17.38 12.47
## 36 100.00 17.27 12.79
## 37 100.00 16.94 12.32
## 38 100.00 16.94 12.32
## 39 100.00 16.94 12.32
## 40 100.00 17.01 12.44
## 41 100.00 17.21 12.77
## 42 100.00 17.61 13.40
## 43 100.00 17.61 13.40
## 44 100.00 17.61 13.40
## 45 100.00 17.59 13.31
## 46 100.00 17.64 13.28
## 47 100.00 17.64 13.28
## 48 100.00 17.64 13.28
## 49 100.00 18.82 12.76
## 50 100.00 17.55 12.83
## 51 100.00 17.55 12.83
## 52 100.00 17.55 12.83
## 53 100.00 18.33 12.82
## 54 100.00 17.74 13.16
## 55 100.00 17.74 13.16
## 56 100.00 17.74 13.16
## 57 100.00 17.87 13.31
## 58 100.00 17.87 13.31
## 59 100.00 17.87 13.31
## 60 100.00 18.18 13.60
## 61 100.00 17.92 13.23
## 62 100.83 17.97 13.12
## 63 100.83 17.97 13.12
## 64 100.83 17.97 13.12
## 65 100.00 17.38 12.48
## 66 100.00 17.38 12.48
## 67 100.00 17.38 12.48
## 68 100.00 17.81 12.75
## 69 100.00 17.76 13.31
## 70 100.00 17.76 13.31
## 71 100.00 17.76 13.31
## 72 100.00 17.67 12.47
## 73 100.00 17.58 12.69
## 74 100.00 17.92 13.50
## 75 100.00 17.92 13.50
## 76 100.00 17.92 13.50
## 77 100.00 17.76 13.29
## 78 100.00 16.82 12.11
## 79 100.00 18.02 13.51
## 80 100.00 18.02 13.51
## 81 100.00 18.02 13.51
## 82 100.00 18.84 14.08
## 83 100.00 17.91 13.34
## 84 100.00 17.91 13.34
## 85 100.00 17.91 13.34
## 86 100.00 17.16 12.71
## 87 100.00 17.16 12.71
## 88 100.00 17.16 12.71
## 89 100.00 17.74 13.47
## 90 100.00 17.74 13.47
## 91 100.00 17.74 13.47
## 92 100.00 17.41 13.28
## 93 100.00 18.01 13.34
## 94 100.00 18.02 13.43
## 95 100.00 17.04 12.58
## 96 100.00 17.35 12.75
## 97 100.00 17.35 12.75
## 98 100.00 17.35 12.75
## 99 100.00 16.96 12.68
## 100 100.00 16.96 12.68
## 101 100.00 16.96 12.68
## 102 100.00 17.09 12.57
## 103 100.00 16.79 13.04
## 104 100.00 17.18 12.95
## 105 100.00 17.18 12.95
## 106 100.00 17.18 12.95
## 107 100.00 17.24 12.99
## 108 100.00 17.24 12.99
## 109 100.00 17.24 12.99
## 110 100.00 17.13 13.00
## 111 100.00 17.44 13.10
## 112 100.00 17.44 13.10
## 113 100.00 17.44 13.10
## 114 100.00 17.15 12.99
## 115 100.00 16.76 12.81
## 116 100.00 16.78 12.63
## 117 100.00 16.80 12.51
## 118 100.00 16.83 12.53
## 119 100.00 16.83 12.53
## 120 100.00 16.83 12.53
## 121 100.00 16.54 12.21
## 122 100.00 17.54 12.61
## 123 100.00 17.23 12.84
## 124 100.00 17.03 12.96
## 125 100.00 17.70 12.48
## 126 100.00 17.54 12.55
## 127 100.00 16.70 12.75
## 128 100.00 16.70 12.75
## 129 100.00 16.70 12.75
## 130 100.00 17.56 13.14
## 131 100.00 17.56 13.14
## 132 100.00 17.56 13.14
## 133 100.00 17.19 12.97
## 134 100.00 17.61 13.15
## 135 100.00 15.88 12.16
## 136 100.00 15.88 12.16
## 137 100.00 15.88 12.16
## 138 100.00 16.58 12.88
## 139 100.00 17.37 13.10
## 140 100.00 16.34 12.12
## 141 100.00 16.86 12.88
## 142 100.00 17.32 12.89
## 143 100.00 17.32 12.89
## 144 100.00 17.32 12.89
## 145 100.00 17.32 12.75
## 146 100.00 17.32 12.75
## 147 100.00 17.32 12.75
## 148 100.00 16.61 12.34
## 149 100.00 16.34 12.12
## 150 100.00 17.07 12.90
## 151 100.00 17.05 12.82
## 152 100.00 17.51 13.01
## 153 100.00 17.51 13.01
## 154 100.00 17.51 13.01
## 155 100.00 17.57 13.08
## 156 100.00 17.06 12.78
## 157 100.00 17.06 12.78
## 158 100.00 17.06 12.78
## 159 100.00 16.67 12.84
## 160 100.00 16.67 12.84
## 161 100.00 16.67 12.84
## 162 100.00 16.97 13.00
## 163 100.00 17.44 13.25
## 164 100.00 16.42 12.32
## 165 100.00 16.35 12.22
## 166 100.00 16.16 12.14
## 167 100.00 16.16 12.14
## 168 100.00 16.16 12.14
## 169 100.00 18.28 13.83
## 170 100.00 17.93 12.92
## 171 100.00 17.99 13.09
## 172 100.00 17.54 12.50
## 173 100.00 17.48 12.41
## 174 100.00 17.23 12.04
## 175 100.00 17.87 12.77
## 176 100.00 17.87 12.77
## BiologicalMaterial10 BiologicalMaterial11 BiologicalMaterial12
## 1 3.46 138.09 18.83
## 2 3.46 153.67 21.05
## 3 3.46 153.67 21.05
## 4 3.46 153.67 21.05
## 5 3.05 147.61 21.05
## 6 3.78 151.88 20.76
## 7 3.04 147.11 20.75
## 8 3.85 154.20 21.45
## 9 3.85 154.20 21.45
## 10 3.85 154.20 21.45
## 11 2.90 143.28 20.21
## 12 2.90 143.28 20.21
## 13 2.90 143.28 20.21
## 14 4.94 158.42 21.77
## 15 2.30 152.83 22.18
## 16 3.25 152.82 21.35
## 17 4.01 152.82 20.70
## 18 4.16 156.51 21.47
## 19 4.24 158.36 21.82
## 20 4.24 158.36 21.82
## 21 4.24 158.36 21.82
## 22 3.02 153.10 21.90
## 23 2.69 148.49 21.23
## 24 2.49 145.61 20.81
## 25 4.15 151.54 20.27
## 26 2.75 140.84 19.07
## 27 3.06 139.52 18.62
## 28 3.07 142.45 19.12
## 29 3.10 158.66 21.88
## 30 2.14 154.56 22.18
## 31 2.35 153.00 21.58
## 32 2.61 151.00 20.80
## 33 2.53 151.48 20.99
## 34 2.50 157.45 22.21
## 35 2.76 149.46 20.42
## 36 2.41 145.62 20.18
## 37 2.46 144.80 20.03
## 38 2.46 144.80 20.03
## 39 2.46 144.80 20.03
## 40 2.46 143.94 19.78
## 41 2.58 148.28 20.33
## 42 2.57 151.50 20.88
## 43 2.57 151.50 20.88
## 44 2.57 151.50 20.88
## 45 2.61 154.06 21.31
## 46 2.75 151.21 20.75
## 47 2.75 151.21 20.75
## 48 2.75 151.21 20.75
## 49 3.18 157.34 21.33
## 50 3.09 149.60 20.25
## 51 3.09 149.60 20.25
## 52 3.09 149.60 20.25
## 53 3.18 154.71 20.95
## 54 2.91 148.45 20.44
## 55 2.91 148.45 20.44
## 56 2.91 148.45 20.44
## 57 2.98 146.08 20.33
## 58 2.98 146.08 20.33
## 59 2.98 146.08 20.33
## 60 2.75 151.23 21.30
## 61 2.63 151.67 21.29
## 62 2.48 149.03 20.88
## 63 2.48 149.03 20.88
## 64 2.48 149.03 20.88
## 65 2.75 144.50 19.82
## 66 2.75 144.50 19.82
## 67 2.75 144.50 19.82
## 68 2.76 147.17 20.41
## 69 2.87 143.65 20.35
## 70 2.87 143.65 20.35
## 71 2.87 143.65 20.35
## 72 2.85 144.40 19.85
## 73 2.79 145.90 19.96
## 74 2.62 151.25 20.89
## 75 2.62 151.25 20.89
## 76 2.62 151.25 20.89
## 77 2.61 150.06 20.65
## 78 2.58 142.66 19.64
## 79 3.37 148.92 20.33
## 80 3.37 148.92 20.33
## 81 3.37 148.92 20.33
## 82 6.87 158.73 20.57
## 83 3.37 146.67 19.95
## 84 3.37 146.67 19.95
## 85 3.37 146.67 19.95
## 86 3.15 142.11 19.13
## 87 3.15 142.11 19.13
## 88 3.15 142.11 19.13
## 89 2.86 148.00 20.04
## 90 2.86 148.00 20.04
## 91 2.86 148.00 20.04
## 92 2.96 143.47 19.85
## 93 3.62 147.63 19.77
## 94 3.52 148.07 19.87
## 95 2.45 146.20 19.83
## 96 2.51 147.95 20.25
## 97 2.51 147.95 20.25
## 98 2.51 147.95 20.25
## 99 2.34 143.33 19.63
## 100 2.34 143.33 19.63
## 101 2.34 143.33 19.63
## 102 2.55 143.07 19.47
## 103 2.33 142.66 19.67
## 104 2.46 143.84 19.85
## 105 2.46 143.84 19.85
## 106 2.46 143.84 19.85
## 107 2.16 146.64 20.57
## 108 2.16 146.64 20.57
## 109 2.16 146.64 20.57
## 110 2.52 143.19 19.69
## 111 2.58 147.66 20.25
## 112 2.58 147.66 20.25
## 113 2.58 147.66 20.25
## 114 2.44 146.29 20.16
## 115 2.30 144.34 19.95
## 116 2.31 144.75 19.94
## 117 2.32 145.03 19.93
## 118 2.27 142.90 19.64
## 119 2.27 142.90 19.64
## 120 2.27 142.90 19.64
## 121 2.11 141.49 19.46
## 122 3.08 142.33 19.17
## 123 2.67 145.08 19.74
## 124 2.49 147.33 20.04
## 125 2.23 150.39 20.62
## 126 2.27 149.52 20.48
## 127 2.98 140.93 19.10
## 128 2.98 140.93 19.10
## 129 2.98 140.93 19.10
## 130 2.60 148.53 20.45
## 131 2.60 148.53 20.45
## 132 2.60 148.53 20.45
## 133 2.80 144.38 19.51
## 134 3.02 145.80 19.56
## 135 1.87 138.14 19.20
## 136 1.87 138.14 19.20
## 137 1.87 138.14 19.20
## 138 2.90 136.35 18.35
## 139 2.67 146.66 19.73
## 140 2.43 135.81 18.57
## 141 2.38 143.75 19.59
## 142 2.73 145.57 19.76
## 143 2.73 145.57 19.76
## 144 2.73 145.57 19.76
## 145 2.63 145.37 19.75
## 146 2.63 145.37 19.75
## 147 2.63 145.37 19.75
## 148 2.55 137.49 18.77
## 149 2.43 135.81 18.57
## 150 2.18 145.88 20.08
## 151 2.19 145.59 20.02
## 152 2.88 145.07 19.56
## 153 2.88 145.07 19.56
## 154 2.88 145.07 19.56
## 155 2.88 145.10 19.64
## 156 2.46 144.98 19.73
## 157 2.46 144.98 19.73
## 158 2.46 144.98 19.73
## 159 2.17 144.39 19.93
## 160 2.17 144.39 19.93
## 161 2.17 144.39 19.93
## 162 2.40 145.03 19.88
## 163 2.75 145.96 19.80
## 164 2.31 144.29 19.71
## 165 1.77 143.59 19.66
## 166 1.99 139.64 18.80
## 167 1.99 139.64 18.80
## 168 1.99 139.64 18.80
## 169 3.20 149.91 21.23
## 170 2.38 155.77 20.76
## 171 2.53 154.68 20.85
## 172 2.82 143.45 20.32
## 173 2.82 143.10 20.24
## 174 2.83 141.72 19.92
## 175 3.55 145.56 20.04
## 176 3.55 145.56 20.04
## ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03
## 1 10.9909 12.79439 1.508846
## 2 0.0000 0.00000 1.527970
## 3 0.0000 0.00000 1.530834
## 4 0.0000 0.00000 1.530834
## 5 10.7000 0.00000 1.531619
## 6 12.0000 0.00000 1.530527
## 7 11.5000 0.00000 1.560000
## 8 12.0000 0.00000 1.550000
## 9 12.0000 0.00000 1.560000
## 10 12.0000 0.00000 1.550000
## 11 10.3000 0.00000 1.550000
## 12 10.3000 0.00000 1.550000
## 13 10.3000 0.00000 1.550000
## 14 11.1000 0.00000 1.590000
## 15 11.3000 0.00000 1.546671
## 16 11.1000 0.00000 1.541506
## 17 11.1000 0.00000 1.546286
## 18 12.4000 0.00000 1.558276
## 19 12.7000 0.00000 1.561032
## 20 12.7000 0.00000 1.556032
## 21 12.7000 0.00000 1.560000
## 22 10.9000 0.00000 1.543572
## 23 11.1000 0.00000 1.548480
## 24 11.3000 0.00000 1.540136
## 25 9.0000 0.00000 1.540000
## 26 11.6000 0.00000 1.520000
## 27 9.2000 0.00000 1.530000
## 28 9.2000 0.00000 1.540000
## 29 9.2000 0.00000 1.520000
## 30 10.4000 0.00000 1.520000
## 31 10.3000 0.00000 1.540000
## 32 11.2000 0.00000 1.530000
## 33 11.6000 0.00000 1.520000
## 34 10.6000 0.00000 1.520000
## 35 11.6000 0.00000 1.530000
## 36 12.5000 0.00000 1.530000
## 37 11.9000 19.70000 1.530000
## 38 11.9000 19.90000 1.520000
## 39 11.9000 19.30000 1.540000
## 40 11.0000 19.50000 1.520000
## 41 11.3000 19.30000 1.520000
## 42 10.8000 22.50000 1.480000
## 43 10.8000 20.50000 1.530000
## 44 10.8000 21.50000 1.550000
## 45 11.4000 20.50000 1.560000
## 46 12.2000 20.50000 1.500000
## 47 12.2000 20.50000 1.500000
## 48 12.2000 20.00000 1.560000
## 49 11.7000 18.00000 1.520000
## 50 10.4000 19.00000 1.520000
## 51 10.4000 18.00000 1.530000
## 52 10.4000 19.50000 1.540000
## 53 11.1000 19.50000 1.540000
## 54 9.7000 19.50000 1.540000
## 55 9.7000 19.50000 1.540000
## 56 9.7000 19.50000 1.520000
## 57 10.7000 19.50000 1.500000
## 58 10.7000 19.50000 1.520000
## 59 10.7000 18.00000 1.580000
## 60 9.3000 20.00000 1.570000
## 61 8.7000 19.00000 1.600000
## 62 9.1000 20.00000 1.510000
## 63 9.1000 19.50000 1.510000
## 64 9.1000 19.50000 1.490000
## 65 11.0000 20.00000 1.500000
## 66 11.0000 19.50000 1.510000
## 67 11.0000 19.50000 1.500000
## 68 12.0000 19.50000 1.480000
## 69 10.0000 20.00000 1.490000
## 70 10.2000 19.00000 1.480000
## 71 10.2000 19.00000 1.480000
## 72 9.5000 19.00000 1.470000
## 73 10.9000 19.50000 1.510000
## 74 11.3000 21.50000 1.550000
## 75 11.3000 22.20000 1.540000
## 76 11.3000 22.00000 1.540000
## 77 11.5000 22.50000 1.550000
## 78 11.4000 21.50000 1.550000
## 79 11.0000 21.50000 1.550000
## 80 11.0000 22.00000 1.520000
## 81 11.0000 22.00000 1.530000
## 82 12.7000 22.00000 1.550000
## 83 11.2000 20.50000 1.550000
## 84 11.2000 21.00000 1.550000
## 85 11.2000 22.00000 1.540000
## 86 11.6000 21.00000 1.550000
## 87 11.6000 21.50000 1.550000
## 88 11.6000 21.50000 1.550000
## 89 10.8000 21.50000 1.540000
## 90 10.8000 21.50000 1.550000
## 91 10.8000 21.70000 1.550000
## 92 12.4000 22.00000 1.540000
## 93 9.9000 21.50000 1.540000
## 94 10.0000 21.50000 1.550000
## 95 9.1000 21.50000 1.530000
## 96 10.6000 22.00000 1.530000
## 97 10.6000 22.00000 1.540000
## 98 10.6000 20.90000 1.550000
## 99 11.5000 22.00000 1.540000
## 100 11.5000 21.00000 1.550000
## 101 11.5000 21.50000 1.530000
## 102 11.8000 21.90000 1.540000
## 103 12.3000 21.70000 1.550000
## 104 11.8000 21.60000 1.550000
## 105 11.8000 21.80000 1.550000
## 106 11.8000 20.80000 1.550000
## 107 9.8000 22.00000 1.540000
## 108 9.8000 21.90000 1.500000
## 109 9.8000 22.40000 1.480000
## 110 11.7000 22.00000 1.520000
## 111 11.4000 20.50000 1.570000
## 112 11.4000 22.20000 1.540000
## 113 11.4000 22.30000 1.530000
## 114 11.7000 22.00000 1.510000
## 115 12.0000 21.20000 1.550000
## 116 12.3000 21.10000 1.540000
## 117 12.5000 21.00000 1.550000
## 118 11.4000 21.00000 1.550000
## 119 11.4000 20.90000 1.540000
## 120 11.4000 21.10000 1.550000
## 121 12.0000 21.20000 1.550000
## 122 12.3000 21.50000 1.550000
## 123 11.3000 21.20000 1.550000
## 124 11.2000 20.80000 1.550000
## 125 12.1000 20.90000 1.540000
## 126 11.9000 21.20000 1.550000
## 127 11.4000 21.30000 1.540000
## 128 11.4000 21.30000 1.550000
## 129 11.4000 21.40000 1.540000
## 130 12.2000 21.50000 1.550000
## 131 12.2000 21.40000 1.550000
## 132 12.2000 21.50000 1.540000
## 133 10.8000 21.20000 1.550000
## 134 10.9000 21.40937 1.550000
## 135 11.3000 21.40000 1.540000
## 136 11.3000 21.30000 1.550000
## 137 11.3000 21.30000 1.550000
## 138 12.2000 21.60000 1.550000
## 139 10.0000 21.40937 1.550000
## 140 13.1000 21.30000 1.550000
## 141 10.2000 21.20000 1.540000
## 142 12.4000 21.20000 1.550000
## 143 12.4000 21.40000 1.540000
## 144 12.4000 21.40000 1.550000
## 145 12.7000 21.40000 1.550000
## 146 12.7000 21.60000 1.540000
## 147 12.7000 21.60000 1.550000
## 148 13.0000 21.40000 1.540000
## 149 13.3000 21.40000 1.540000
## 150 13.4000 21.40000 1.540000
## 151 13.3000 21.10000 1.540000
## 152 12.7000 21.50000 1.600000
## 153 12.7000 21.70000 1.590000
## 154 12.7000 21.30000 1.600000
## 155 12.7000 21.20000 1.600000
## 156 12.4000 21.30000 1.540000
## 157 12.4000 21.00000 1.550000
## 158 12.4000 21.20000 1.550000
## 159 12.1000 21.40000 1.550000
## 160 12.1000 21.30000 1.550000
## 161 12.1000 21.50000 1.540000
## 162 12.1000 21.10000 1.540000
## 163 12.4000 21.00000 1.550000
## 164 11.5000 21.20000 1.550000
## 165 11.4000 21.20000 1.550000
## 166 11.6000 21.20000 1.550000
## 167 11.6000 21.20000 1.550000
## 168 11.6000 20.00000 1.550000
## 169 11.3000 20.80000 1.550000
## 170 12.5000 19.90000 1.550000
## 171 14.1000 20.00000 1.540000
## 172 12.8000 21.50000 1.540000
## 173 12.8000 21.50000 1.560000
## 174 13.0000 20.40000 1.550000
## 175 14.1000 21.60000 1.550000
## 176 14.1000 20.80000 1.550000
## ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06
## 1 927.0047 998.8306 205.8232
## 2 917.0000 1032.2000 210.0000
## 3 912.0000 1003.6000 207.1000
## 4 911.0000 1014.6000 213.3000
## 5 918.0000 1027.5000 205.7000
## 6 924.0000 1016.8000 208.9000
## 7 933.0000 988.9000 210.0000
## 8 929.0000 1010.9000 211.7000
## 9 928.0000 1003.5000 208.7000
## 10 938.0000 1003.8000 209.8000
## 11 932.0000 983.1000 209.4000
## 12 930.0000 992.0000 209.4000
## 13 934.0000 1004.1000 207.8000
## 14 934.0000 1036.8000 209.1000
## 15 930.0000 1120.7000 207.8000
## 16 928.0000 1073.6000 207.1000
## 17 928.0000 1027.5000 205.9000
## 18 930.0000 1021.4000 208.4000
## 19 929.0000 1092.2000 207.5000
## 20 929.0000 1175.3000 204.1000
## 21 925.0000 1102.8000 206.6000
## 22 936.0000 1024.4000 218.7000
## 23 937.0000 997.7000 209.6000
## 24 940.0000 1031.3000 215.1000
## 25 934.0000 1007.3000 209.4000
## 26 930.0000 950.7000 203.6000
## 27 926.0000 955.8000 203.0000
## 28 922.0000 975.8000 203.6000
## 29 924.0000 986.9000 206.4000
## 30 921.0000 1001.1000 205.5000
## 31 928.0000 1006.7000 206.2000
## 32 926.0000 1024.0000 208.2000
## 33 923.0000 1041.2000 207.3000
## 34 928.0000 999.5000 209.4000
## 35 925.0000 1010.3000 209.1000
## 36 930.0000 1002.4000 207.5000
## 37 926.0000 1019.6000 206.4000
## 38 924.0000 1008.6000 208.7000
## 39 926.0000 1014.3000 208.7000
## 40 924.0000 1027.0000 206.6000
## 41 925.0000 1015.0000 205.9000
## 42 936.0000 954.7000 211.2000
## 43 923.0000 954.0000 210.0000
## 44 930.0000 969.3000 208.7000
## 45 928.0000 980.3000 208.2000
## 46 926.0000 986.4000 208.7000
## 47 925.0000 977.8000 227.4000
## 48 927.0000 1006.4000 210.7000
## 49 921.0000 1002.4000 209.8000
## 50 923.0000 971.2000 207.8000
## 51 918.0000 977.6000 204.8000
## 52 926.0000 989.2000 206.4000
## 53 929.0000 989.6000 205.5000
## 54 923.0000 1003.8000 206.8000
## 55 925.0000 984.2000 205.2000
## 56 924.0000 992.5000 207.3000
## 57 924.0000 987.0000 206.2000
## 58 926.0000 991.5000 211.4000
## 59 920.0000 1003.2000 207.8000
## 60 928.0000 983.2000 208.0000
## 61 921.0000 980.8000 206.2000
## 62 925.0000 982.3000 205.9000
## 63 923.0000 983.4000 206.2000
## 64 928.0000 1004.5000 206.8000
## 65 927.0000 1016.1000 210.3000
## 66 922.0000 999.7000 213.3000
## 67 923.0000 1013.9000 209.6000
## 68 923.0000 994.0000 206.8000
## 69 929.0000 960.0000 210.7000
## 70 921.0000 961.3000 205.0000
## 71 921.0000 969.7000 207.8000
## 72 923.0000 989.7000 205.7000
## 73 923.0000 996.4000 206.2000
## 74 935.0000 976.4000 204.8000
## 75 933.0000 971.6000 208.0000
## 76 933.0000 974.0000 205.9000
## 77 932.0000 978.0000 209.4000
## 78 932.0000 980.2000 205.7000
## 79 937.0000 993.4000 205.5000
## 80 931.0000 990.5000 207.1000
## 81 935.0000 982.9000 206.6000
## 82 934.0000 1000.7000 205.5000
## 83 934.0000 1000.8000 205.2000
## 84 939.0000 1171.2000 206.4000
## 85 936.0000 979.2000 208.7000
## 86 932.0000 994.5000 207.8000
## 87 937.0000 989.2000 205.2000
## 88 939.0000 983.7000 206.4000
## 89 937.0000 960.4000 204.8000
## 90 935.0000 954.8000 205.1658
## 91 938.0000 975.8000 205.2000
## 92 941.0000 1009.1000 206.4000
## 93 933.0000 992.6000 205.9000
## 94 937.0000 1003.7000 205.0000
## 95 931.0000 1006.1000 206.8000
## 96 934.0000 1001.0000 204.8000
## 97 937.0000 994.9000 205.0000
## 98 933.0000 1001.3000 205.2000
## 99 934.0000 1004.3000 205.0000
## 100 934.0000 1008.1000 204.6000
## 101 937.0000 1004.8000 206.6000
## 102 937.0000 992.8000 204.6000
## 103 936.0000 974.0000 206.4000
## 104 937.0000 987.7000 206.6000
## 105 936.0000 987.9000 205.5000
## 106 933.0000 986.6000 205.5000
## 107 932.0000 992.3000 208.4000
## 108 934.0000 987.9000 208.9000
## 109 937.0000 994.3000 211.4000
## 110 940.0000 980.3000 205.2000
## 111 929.0000 976.0000 204.8000
## 112 937.0000 994.1000 208.9000
## 113 936.0000 983.2000 213.7000
## 114 935.0000 981.6000 204.3000
## 115 942.0000 992.0000 204.1000
## 116 934.0000 980.0000 206.4000
## 117 938.0000 997.8000 205.7000
## 118 934.0000 991.9000 205.0000
## 119 934.0000 986.1000 204.1000
## 120 935.0000 923.0000 204.8000
## 121 935.0000 1003.2000 206.8000
## 122 939.0000 995.2000 205.7000
## 123 936.0000 991.8000 208.2000
## 124 935.0000 994.7000 207.3000
## 125 934.0000 996.9000 207.3000
## 126 935.0000 996.5000 209.1000
## 127 939.0000 987.3000 211.4000
## 128 939.0000 981.9000 205.7000
## 129 941.0000 990.0000 207.1000
## 130 939.0000 1004.4000 206.4000
## 131 936.0000 990.8000 208.2000
## 132 939.0000 999.2000 206.4000
## 133 940.0000 998.9000 208.9000
## 134 934.0000 1000.1000 208.7000
## 135 936.0000 1001.2000 206.2000
## 136 936.0000 1011.9000 207.5000
## 137 936.0000 998.6000 206.2000
## 138 940.0000 1002.1000 207.5000
## 139 935.0000 986.1000 205.2000
## 140 936.0000 983.6000 207.5000
## 141 934.0000 989.8000 206.8000
## 142 935.0000 1008.1000 206.6000
## 143 934.0000 1000.6000 207.3000
## 144 939.0000 1011.6000 206.8000
## 145 937.0000 1005.1000 208.9000
## 146 938.0000 1014.4000 206.4000
## 147 941.0000 1012.5000 206.6000
## 148 939.0000 998.5000 209.8000
## 149 940.0000 1012.2000 209.4000
## 150 939.0000 1007.6000 208.9000
## 151 936.0000 1022.3000 206.4000
## 152 946.0000 1005.0000 210.5000
## 153 939.0000 998.0000 205.5000
## 154 934.0000 997.1000 206.2000
## 155 936.0000 1006.1000 207.3000
## 156 935.0000 990.5000 205.7000
## 157 934.0000 1002.4000 206.2000
## 158 940.0000 984.3000 204.3000
## 159 938.0000 1005.3000 207.1000
## 160 936.0000 1003.8000 206.2000
## 161 934.0000 1009.5000 205.7000
## 162 938.0000 1015.1000 207.5000
## 163 936.0000 1020.8000 206.6000
## 164 939.0000 1014.5000 206.6000
## 165 933.0000 1029.0000 205.9000
## 166 933.0000 1008.0000 205.5000
## 167 934.0000 999.9000 208.2000
## 168 928.0000 1003.2000 206.6000
## 169 934.0000 1014.6000 208.7000
## 170 933.0000 1005.1000 205.2000
## 171 936.0000 1029.7000 206.8000
## 172 935.0000 1027.0000 206.2000
## 173 933.0000 1032.0000 206.6000
## 174 930.0000 1040.0000 208.7000
## 175 935.0000 1044.8000 208.0000
## 176 932.0000 1053.8000 207.5000
## ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess09
## 1 177.4114 177.9193 43.00
## 2 177.0000 178.0000 46.57
## 3 178.0000 178.0000 45.07
## 4 177.0000 177.0000 44.92
## 5 178.0000 178.0000 44.96
## 6 178.0000 178.0000 45.32
## 7 177.0000 178.0000 49.36
## 8 178.0000 178.0000 48.68
## 9 177.0000 177.0000 47.20
## 10 177.0000 177.0000 47.11
## 11 177.0000 177.0000 46.24
## 12 178.0000 178.0000 46.10
## 13 177.0000 177.0000 47.53
## 14 178.0000 178.0000 45.28
## 15 177.0000 177.0000 46.44
## 16 177.0000 177.0000 45.40
## 17 177.0000 177.0000 45.54
## 18 177.0000 177.0000 45.73
## 19 178.0000 178.0000 44.46
## 20 177.0000 177.0000 45.02
## 21 178.0000 178.0000 45.22
## 22 178.0000 178.0000 47.04
## 23 177.0000 177.0000 46.43
## 24 177.0000 177.0000 47.09
## 25 178.0000 178.0000 47.28
## 26 178.0000 178.0000 38.89
## 27 177.0000 178.0000 39.02
## 28 178.0000 178.0000 40.46
## 29 177.0000 177.0000 42.67
## 30 178.0000 178.0000 44.95
## 31 177.0000 177.0000 46.27
## 32 178.0000 178.0000 47.08
## 33 177.0000 177.0000 48.77
## 34 178.0000 178.0000 45.78
## 35 177.0000 177.0000 44.77
## 36 177.0000 177.0000 46.65
## 37 178.0000 178.0000 46.17
## 38 177.0000 177.0000 46.38
## 39 178.0000 178.0000 45.92
## 40 177.0000 177.0000 46.77
## 41 178.0000 178.0000 46.69
## 42 177.0000 177.0000 45.95
## 43 178.0000 177.0000 46.66
## 44 177.0000 178.0000 47.33
## 45 178.0000 178.0000 46.78
## 46 177.0000 177.0000 46.48
## 47 178.0000 178.0000 46.03
## 48 177.0000 177.0000 48.11
## 49 177.0000 178.0000 47.45
## 50 178.0000 178.0000 44.65
## 51 177.0000 177.0000 46.47
## 52 178.0000 178.0000 47.33
## 53 177.0000 177.0000 46.34
## 54 178.0000 177.0000 48.84
## 55 177.0000 178.0000 46.32
## 56 178.0000 178.0000 47.03
## 57 177.0000 177.0000 45.66
## 58 178.0000 178.0000 47.09
## 59 177.0000 177.0000 49.04
## 60 177.0000 178.0000 46.30
## 61 178.0000 178.0000 46.37
## 62 177.0000 177.0000 46.32
## 63 178.0000 178.0000 46.02
## 64 177.0000 177.0000 48.17
## 65 178.0000 177.0000 47.44
## 66 177.0000 178.0000 47.30
## 67 178.0000 178.0000 48.11
## 68 178.0000 178.0000 46.00
## 69 177.0000 177.0000 45.05
## 70 178.0000 177.0000 43.83
## 71 177.0000 178.0000 43.86
## 72 177.0000 177.0000 47.40
## 73 178.0000 178.0000 47.52
## 74 177.0000 177.0000 45.88
## 75 178.0000 177.0000 45.52
## 76 177.0000 178.0000 45.11
## 77 178.0000 178.0000 45.57
## 78 177.0000 177.0000 44.92
## 79 177.0000 177.0000 46.11
## 80 178.0000 177.0000 46.12
## 81 177.0000 178.0000 44.55
## 82 178.0000 178.0000 45.10
## 83 178.0000 178.0000 44.99
## 84 177.0000 178.0000 45.64
## 85 178.0000 178.0000 44.62
## 86 177.0000 177.0000 45.45
## 87 178.0000 178.0000 45.52
## 88 177.0000 177.0000 46.10
## 89 177.0000 178.0000 43.52
## 90 178.0000 178.0000 43.52
## 91 177.0000 177.0000 44.11
## 92 178.0000 178.0000 46.33
## 93 177.0000 177.0000 45.69
## 94 178.0000 178.0000 44.22
## 95 178.0000 177.0000 45.49
## 96 177.0000 177.0000 44.09
## 97 178.0000 178.0000 44.56
## 98 177.0000 177.0000 45.14
## 99 177.0000 178.0000 43.73
## 100 178.0000 177.0000 44.35
## 101 177.0000 177.0000 44.13
## 102 178.0000 178.0000 43.49
## 103 177.0000 177.0000 42.66
## 104 178.0000 178.0000 43.58
## 105 177.0000 177.0000 44.70
## 106 178.0000 178.0000 44.23
## 107 177.0000 177.0000 45.61
## 108 178.0000 178.0000 45.99
## 109 177.0000 177.0000 46.01
## 110 178.0000 178.0000 43.75
## 111 178.0000 177.0000 43.75
## 112 177.0000 177.0000 44.64
## 113 178.0000 178.0000 43.84
## 114 177.0000 177.0000 43.37
## 115 177.0000 177.0000 44.94
## 116 178.0000 178.0000 43.12
## 117 177.0000 177.0000 45.23
## 118 178.0000 177.0000 44.10
## 119 177.0000 178.0000 43.92
## 120 178.0000 178.0000 43.26
## 121 177.0000 177.0000 45.63
## 122 178.0000 178.0000 46.51
## 123 177.0000 178.0000 45.85
## 124 178.0000 178.0000 46.95
## 125 177.0000 178.0000 47.21
## 126 178.0000 178.0000 46.23
## 127 177.0000 178.0000 45.71
## 128 178.0000 178.0000 44.99
## 129 177.0000 178.0000 45.62
## 130 178.0000 178.0000 46.67
## 131 177.0000 177.0000 45.23
## 132 178.0000 178.0000 45.73
## 133 178.0000 178.0000 46.36
## 134 177.0000 178.0000 47.06
## 135 178.0000 177.0000 46.95
## 136 177.0000 177.0000 47.47
## 137 178.0000 178.0000 46.06
## 138 178.0000 178.0000 46.58
## 139 177.0000 178.0000 46.06
## 140 178.0000 178.0000 45.30
## 141 177.0000 178.0000 46.53
## 142 178.0000 178.0000 46.12
## 143 177.0000 178.0000 46.39
## 144 178.0000 178.0000 46.50
## 145 177.0000 178.0000 44.78
## 146 178.0000 178.0000 44.52
## 147 177.0000 177.0000 46.46
## 148 177.0000 178.0000 45.23
## 149 178.0000 178.0000 46.74
## 150 177.0000 177.0000 45.54
## 151 178.0000 178.0000 46.26
## 152 178.0000 178.0000 45.76
## 153 177.0000 177.0000 44.90
## 154 178.0000 178.0000 45.30
## 155 177.0000 177.0000 45.28
## 156 177.0000 177.0000 44.38
## 157 178.0000 178.0000 44.25
## 158 177.0000 177.0000 44.38
## 159 178.0000 178.0000 44.86
## 160 177.0000 177.0000 44.09
## 161 178.0000 178.0000 44.62
## 162 178.0000 178.0000 45.51
## 163 177.0000 177.0000 46.22
## 164 177.0000 177.0000 45.87
## 165 178.0000 177.0000 47.70
## 166 177.0000 178.0000 45.51
## 167 178.0000 178.0000 45.13
## 168 177.0000 177.0000 45.73
## 169 177.0000 177.0000 46.04
## 170 178.0000 177.0000 45.31
## 171 177.0000 178.0000 44.77
## 172 178.0000 177.0000 46.78
## 173 177.0000 178.0000 46.51
## 174 178.0000 177.0000 48.05
## 175 177.0000 177.0000 48.11
## 176 178.0000 178.0000 48.13
## ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12
## 1 8.636328 10.025683 262.5544
## 2 9.164042 10.025683 0.0000
## 3 9.138575 9.551027 0.0000
## 4 8.738187 9.551027 0.0000
## 5 8.468328 8.957722 0.0000
## 6 8.636328 10.115706 0.0000
## 7 11.600000 11.500000 0.0000
## 8 10.200000 11.300000 0.0000
## 9 9.700000 11.100000 0.0000
## 10 10.100000 10.200000 0.0000
## 11 9.000000 9.500000 0.0000
## 12 8.800000 9.700000 0.0000
## 13 9.300000 10.400000 0.0000
## 14 9.600000 9.800000 0.0000
## 15 9.400000 10.200000 0.0000
## 16 9.600000 10.200000 0.0000
## 17 9.000000 10.000000 0.0000
## 18 9.500000 10.600000 0.0000
## 19 8.900000 9.800000 0.0000
## 20 8.900000 9.900000 0.0000
## 21 9.000000 10.000000 0.0000
## 22 9.773592 9.146609 0.0000
## 23 10.635233 8.900656 0.0000
## 24 9.069647 9.551027 0.0000
## 25 11.100000 9.000000 0.0000
## 26 9.200000 7.600000 0.0000
## 27 8.400000 7.500000 0.0000
## 28 7.800000 7.500000 0.0000
## 29 7.500000 7.700000 0.0000
## 30 9.400000 9.000000 0.0000
## 31 9.000000 9.100000 0.0000
## 32 10.700000 9.500000 0.0000
## 33 10.100000 10.500000 0.0000
## 34 9.800000 9.700000 0.0000
## 35 9.400000 9.300000 0.0000
## 36 9.700000 10.000000 4549.0000
## 37 9.400000 10.200000 4549.0000
## 38 9.700000 10.000000 4549.0000
## 39 9.500000 10.000000 4549.0000
## 40 10.200000 9.800000 4549.0000
## 41 9.800000 10.000000 4549.0000
## 42 11.100000 10.500000 4549.0000
## 43 8.100000 8.900000 4549.0000
## 44 9.300000 9.300000 4549.0000
## 45 9.000000 8.800000 4549.0000
## 46 8.500000 9.200000 4549.0000
## 47 9.400000 9.100000 4549.0000
## 48 8.900000 9.900000 4549.0000
## 49 9.500000 9.600000 4549.0000
## 50 8.900000 9.100000 4549.0000
## 51 8.900000 9.400000 4549.0000
## 52 8.700000 11.000000 4549.0000
## 53 9.000000 9.500000 4549.0000
## 54 8.700000 10.800000 4549.0000
## 55 8.400000 8.600000 4549.0000
## 56 8.200000 9.400000 4549.0000
## 57 10.300000 9.400000 4549.0000
## 58 10.300000 9.800000 4549.0000
## 59 11.100000 10.200000 4549.0000
## 60 9.400000 9.100000 4549.0000
## 61 9.600000 9.100000 4549.0000
## 62 10.400000 9.000000 4549.0000
## 63 10.200000 8.700000 4549.0000
## 64 9.600000 10.200000 4549.0000
## 65 11.200000 9.900000 4549.0000
## 66 10.900000 10.100000 4549.0000
## 67 11.000000 10.400000 4549.0000
## 68 9.700000 9.600000 4549.0000
## 69 9.400000 9.000000 0.0000
## 70 8.900000 8.400000 0.0000
## 71 8.400000 8.300000 0.0000
## 72 9.700000 9.500000 0.0000
## 73 10.200000 9.900000 0.0000
## 74 8.500000 9.100000 0.0000
## 75 8.200000 8.700000 0.0000
## 76 8.700000 8.600000 0.0000
## 77 9.800000 9.300000 0.0000
## 78 8.700000 9.100000 0.0000
## 79 9.300000 9.400000 0.0000
## 80 8.400000 9.300000 0.0000
## 81 8.200000 8.400000 0.0000
## 82 8.600000 8.800000 0.0000
## 83 9.100000 8.500000 0.0000
## 84 8.900000 9.100000 0.0000
## 85 8.600000 8.400000 0.0000
## 86 9.400000 9.400000 0.0000
## 87 9.300000 9.500000 0.0000
## 88 9.400000 9.600000 0.0000
## 89 8.100000 8.300000 0.0000
## 90 8.400000 8.300000 0.0000
## 91 8.400000 8.300000 0.0000
## 92 8.700000 9.200000 0.0000
## 93 8.400000 9.100000 0.0000
## 94 8.600000 8.900000 0.0000
## 95 9.100000 8.900000 0.0000
## 96 8.800000 8.700000 0.0000
## 97 9.300000 9.000000 0.0000
## 98 9.100000 9.035977 0.0000
## 99 11.400000 8.700000 0.0000
## 100 8.700000 9.200000 0.0000
## 101 8.900000 9.300000 0.0000
## 102 8.800000 9.000000 0.0000
## 103 8.900000 8.700000 0.0000
## 104 8.700000 9.100000 0.0000
## 105 9.300000 9.100000 0.0000
## 106 8.700000 9.000000 0.0000
## 107 9.000000 8.900000 0.0000
## 108 9.400000 9.300000 0.0000
## 109 9.000000 8.900000 0.0000
## 110 9.600000 9.400000 0.0000
## 111 9.500000 7.900000 0.0000
## 112 7.800000 8.700000 0.0000
## 113 8.100000 8.700000 0.0000
## 114 7.800000 8.100000 0.0000
## 115 9.100000 9.000000 0.0000
## 116 8.300000 8.300000 0.0000
## 117 8.500000 9.100000 0.0000
## 118 8.800000 9.200000 0.0000
## 119 9.000000 9.100000 0.0000
## 120 8.700000 8.600000 0.0000
## 121 9.000000 9.600000 0.0000
## 122 9.800000 10.100000 0.0000
## 123 8.800000 9.700000 0.0000
## 124 8.900000 9.800000 0.0000
## 125 10.000000 10.200000 0.0000
## 126 9.300000 10.000000 0.0000
## 127 8.100000 9.100000 0.0000
## 128 8.300000 8.800000 0.0000
## 129 8.200000 9.400000 0.0000
## 130 9.100000 10.100000 0.0000
## 131 8.900000 8.200000 0.0000
## 132 7.900000 8.800000 0.0000
## 133 8.200000 9.200000 0.0000
## 134 8.700000 9.400000 0.0000
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## 99 2.000000 2.000000 14.00000
## 100 3.000000 3.000000 15.00000
## 101 4.000000 4.000000 16.00000
## 102 5.000000 5.000000 17.00000
## 103 6.000000 6.000000 18.00000
## 104 7.000000 1.000000 1.00000
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## 110 1.000000 1.000000 7.00000
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## 144 1.000000 1.000000 7.00000
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## 149 7.000000 4.000000 13.00000
## 150 8.000000 5.000000 14.00000
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## 152 1.000000 1.000000 16.00000
## 153 2.000000 2.000000 17.00000
## 154 3.000000 3.000000 18.00000
## 155 4.000000 4.000000 19.00000
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## 158 9.000000 5.000000 5.00000
## 159 10.000000 1.000000 6.00000
## 160 11.000000 2.000000 7.00000
## 161 12.000000 3.000000 8.00000
## 162 2.000000 1.000000 10.00000
## 163 9.000000 5.000000 17.00000
## 164 1.000000 1.000000 19.00000
## 165 2.000000 2.000000 20.00000
## 166 3.000000 3.000000 21.00000
## 167 4.000000 4.000000 22.00000
## 168 5.000000 5.000000 23.00000
## 169 7.000000 1.000000 1.00000
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## 171 9.000000 3.000000 3.00000
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## 173 0.000000 0.000000 0.00000
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## ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27
## 1 4873.000 6074.000 4685.000
## 2 4869.000 6107.000 4630.000
## 3 4897.000 6116.000 4637.000
## 4 4892.000 6111.000 4630.000
## 5 4930.000 6151.000 4684.000
## 6 4871.000 6128.000 4687.000
## 7 4795.000 6057.000 4572.000
## 8 4806.000 6059.000 4586.000
## 9 4842.000 6103.000 4609.000
## 10 4893.000 6135.000 4650.000
## 11 4925.000 6161.000 4687.000
## 12 4924.000 6161.000 4692.000
## 13 4888.000 6129.000 4653.000
## 14 4911.000 6124.000 4684.000
## 15 4874.000 6125.000 4659.000
## 16 4848.000 6095.000 4630.000
## 17 4860.000 6100.000 4659.000
## 18 4815.000 6055.000 4631.000
## 19 4876.000 6109.000 4696.000
## 20 4850.000 6094.000 4665.000
## 21 4879.000 6117.000 4696.000
## 22 4918.000 6152.000 4618.000
## 23 4906.000 6134.000 4626.000
## 24 4875.000 6095.000 4606.000
## 25 4907.000 6150.000 4631.000
## 26 4990.000 6160.000 4693.000
## 27 4966.000 6112.000 4660.000
## 28 4961.000 6112.000 4649.000
## 29 4966.000 6137.000 4641.000
## 30 4863.000 6039.000 4564.000
## 31 4872.000 6060.000 4583.000
## 32 4842.000 6057.000 4574.000
## 33 4820.000 6042.000 4563.000
## 34 4829.000 6020.000 4590.000
## 35 4854.000 6061.000 4654.000
## 36 4818.000 6041.000 4537.000
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## 38 4820.000 6006.000 4552.000
## 39 4820.000 6013.000 4554.000
## 40 4847.000 6053.000 4607.000
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## 44 4869.000 6061.000 4603.000
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## 47 4864.000 6056.000 4556.000
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## 51 4846.000 6032.000 4521.000
## 52 4721.000 5901.000 4416.000
## 53 4861.000 6071.000 4550.000
## 54 4747.000 5929.000 4423.000
## 55 4890.000 6069.000 4552.000
## 56 4847.000 6021.000 4518.000
## 57 4853.000 6033.000 4545.000
## 58 4820.000 6016.000 4524.000
## 59 4811.000 6016.000 4519.000
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## 61 4867.000 6041.000 4554.000
## 62 4877.000 6051.000 4587.000
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## 65 4835.000 6074.000 4592.000
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## 67 4819.000 6065.000 4575.000
## 68 4857.000 6065.000 4613.000
## 69 4877.000 6036.000 4569.000
## 70 4901.000 6063.000 4588.000
## 71 4916.000 6075.000 4595.000
## 72 4876.000 6106.000 4609.000
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## 74 4849.000 6041.000 4557.000
## 75 4883.000 6045.000 4583.000
## 76 4890.000 6058.000 4587.000
## 77 4859.000 6058.000 4581.000
## 78 4876.000 6087.000 4601.000
## 79 4835.000 6015.000 4537.000
## 80 4834.000 6015.000 4526.000
## 81 4898.000 6073.000 4573.000
## 82 4878.000 6049.000 4546.000
## 83 4881.000 6060.000 4576.000
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## 85 4907.000 6087.000 4602.000
## 86 4867.000 6082.000 4642.000
## 87 4844.000 6067.000 4632.000
## 88 4838.000 6053.000 4622.000
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## 90 4897.000 6047.000 4572.000
## 91 4885.000 6042.000 4546.000
## 92 4846.000 6019.000 4572.000
## 93 4870.000 6054.000 4595.000
## 94 4887.000 6056.000 4575.000
## 95 4872.000 6054.000 4566.000
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## 100 4855.000 6046.000 4644.000
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## 103 4886.000 6051.000 4594.000
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## 105 4841.000 6010.000 4583.000
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## 108 0.000 0.000 0.000
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## 111 4912.000 6080.000 4572.000
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## 126 4820.000 6050.000 4606.000
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## 139 4822.000 6018.000 4606.000
## 140 4806.000 6000.000 4612.000
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## 142 4829.000 6026.000 4572.000
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## 150 4841.000 6023.000 4581.000
## 151 4781.000 5983.000 4551.000
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## 155 4844.000 6025.000 4594.000
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## 157 4839.000 6015.000 4594.000
## 158 4862.000 6060.000 4609.000
## 159 4852.000 6009.000 4556.000
## 160 4906.000 6040.000 4586.000
## 161 4906.000 6047.000 4585.000
## 162 4846.000 6015.000 4541.000
## 163 4855.000 6055.000 4581.000
## 164 4809.000 5990.000 4536.000
## 165 4790.000 5993.000 4541.000
## 166 4815.000 5991.000 4597.000
## 167 4837.000 6024.000 4608.000
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## 169 4903.000 6034.000 4606.000
## 170 4872.000 6058.000 4629.000
## 171 4832.000 6013.000 4585.000
## 172 4857.701 6050.775 4599.108
## 173 4856.330 6047.751 4588.018
## 174 4856.330 6043.161 4579.733
## 175 4856.330 6050.775 4588.018
## 176 4856.330 6051.906 4589.596
## ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30
## 1 10.700000 21.00000 9.900000
## 2 11.200000 21.40000 9.900000
## 3 11.100000 21.30000 9.400000
## 4 11.100000 21.30000 9.400000
## 5 11.300000 21.60000 9.000000
## 6 11.400000 21.70000 10.100000
## 7 11.200000 21.20000 11.200000
## 8 11.100000 21.20000 10.900000
## 9 11.300000 21.50000 10.500000
## 10 11.400000 21.70000 9.800000
## 11 11.500000 21.90000 9.400000
## 12 11.500000 22.00000 9.400000
## 13 11.400000 21.70000 9.900000
## 14 11.100000 21.50000 9.400000
## 15 11.300000 21.60000 9.900000
## 16 11.100000 21.20000 10.300000
## 17 11.100000 21.30000 10.000000
## 18 10.800000 20.90000 10.600000
## 19 11.100000 21.40000 9.800000
## 20 11.000000 21.20000 10.100000
## 21 11.100000 21.50000 9.900000
## 22 11.400000 21.10000 8.800000
## 23 11.200000 21.00000 8.900000
## 24 11.200000 20.90000 9.500000
## 25 11.500000 21.30000 9.200000
## 26 11.000000 21.00000 7.500000
## 27 10.700000 20.60000 7.600000
## 28 10.700000 20.50000 7.600000
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## 30 10.600000 20.10000 9.000000
## 31 10.700000 20.40000 9.100000
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## 174 8.613903 19.83353 9.779629
## 175 6.153698 19.95070 9.651628
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## ManufacturingProcess31 ManufacturingProcess32 ManufacturingProcess33
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## 2 68.70000 169 66.00000
## 3 69.30000 173 66.00000
## 4 69.30000 171 68.00000
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## 138 71.50000 153 64.00000
## 139 70.60000 152 60.00000
## 140 70.40000 151 59.00000
## 141 71.30000 152 60.00000
## 142 70.70000 156 61.00000
## 143 70.80000 156 61.00000
## 144 70.70000 156 64.00000
## 145 70.70000 153 62.00000
## 146 70.70000 152 63.00000
## 147 70.70000 153 61.00000
## 148 70.30000 149 59.00000
## 149 69.80000 143 56.00000
## 150 70.90000 151 60.00000
## 151 70.40000 148 59.00000
## 152 70.60000 154 63.00000
## 153 71.00000 155 63.00000
## 154 70.90000 154 61.00000
## 155 70.90000 152 61.00000
## 156 71.00000 152 65.00000
## 157 71.00000 154 64.00000
## 158 70.80000 156 63.00000
## 159 71.80000 156 64.00000
## 160 72.30000 158 65.00000
## 161 72.20000 158 63.00000
## 162 71.40000 158 64.00000
## 163 71.00000 158 65.00000
## 164 70.90000 155 61.00000
## 165 70.40000 149 59.00000
## 166 70.70000 151 61.00000
## 167 70.80000 151 60.00000
## 168 70.50000 150 60.00000
## 169 72.50000 158 66.00000
## 170 71.00000 160 66.00000
## 171 71.00000 160 63.00000
## 172 70.69354 156 62.38444
## 173 70.64208 158 63.94486
## 174 70.64208 167 66.62356
## 175 70.64208 156 63.10210
## 176 70.64208 160 63.94486
## ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36
## 1 2.400000 486.0000 0.01900000
## 2 2.600000 508.0000 0.01900000
## 3 2.600000 509.0000 0.01800000
## 4 2.500000 496.0000 0.01800000
## 5 2.500000 468.0000 0.01700000
## 6 2.500000 490.0000 0.01800000
## 7 2.500000 475.0000 0.01900000
## 8 2.500000 478.0000 0.01900000
## 9 2.500000 491.0000 0.01900000
## 10 2.500000 488.0000 0.01900000
## 11 2.500000 493.0000 0.01900000
## 12 2.500000 498.0000 0.01800000
## 13 2.400000 490.0000 0.01800000
## 14 2.400000 490.0000 0.01900000
## 15 2.500000 490.0000 0.01900000
## 16 2.500000 493.0000 0.01900000
## 17 2.500000 495.0000 0.01900000
## 18 2.500000 497.0000 0.02000000
## 19 2.400000 514.0000 0.02100000
## 20 2.500000 490.0000 0.02000000
## 21 2.500000 495.0000 0.02000000
## 22 2.400000 479.0000 0.01800000
## 23 2.400000 492.0000 0.01900000
## 24 2.500000 468.0000 0.01800000
## 25 2.500000 505.0000 0.01900000
## 26 2.500000 500.0000 0.01900000
## 27 2.400000 492.0000 0.01900000
## 28 2.500000 522.0000 0.02100000
## 29 2.500000 499.0000 0.02000000
## 30 2.500000 504.0000 0.02000000
## 31 2.500000 486.0000 0.01900000
## 32 2.500000 486.0000 0.01900000
## 33 2.500000 476.0000 0.01800000
## 34 2.500000 496.0000 0.02000000
## 35 2.500000 507.0000 0.02000000
## 36 2.400000 481.0000 0.02000000
## 37 2.600000 495.0000 0.01900000
## 38 2.500000 484.0000 0.01800000
## 39 2.400000 506.0000 0.01900000
## 40 2.500000 488.0000 0.01900000
## 41 2.500000 493.0000 0.01900000
## 42 2.600000 509.0000 0.02000000
## 43 2.500000 498.0000 0.01900000
## 44 2.500000 501.0000 0.02000000
## 45 2.500000 490.0000 0.01900000
## 46 2.500000 490.0000 0.01900000
## 47 2.600000 492.0000 0.01800000
## 48 2.400000 493.0000 0.01900000
## 49 2.400000 490.0000 0.01800000
## 50 2.500000 490.0000 0.01800000
## 51 2.500000 504.0000 0.01900000
## 52 2.500000 496.0000 0.01900000
## 53 2.500000 495.0000 0.01900000
## 54 2.500000 501.0000 0.02000000
## 55 2.500000 483.0000 0.01800000
## 56 2.400000 509.0000 0.02000000
## 57 2.500000 463.0000 0.01900000
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## 60 2.500000 499.0000 0.01900000
## 61 2.500000 513.0000 0.02000000
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## 63 2.500000 502.0000 0.02000000
## 64 2.500000 492.0000 0.02100000
## 65 2.600000 492.0000 0.01900000
## 66 2.600000 498.0000 0.01900000
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## 68 2.500000 494.0000 0.01900000
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## 71 2.600000 484.0000 0.01900000
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## 73 2.600000 500.0000 0.02000000
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## 79 2.500000 494.0000 0.02000000
## 80 2.500000 517.0000 0.02100000
## 81 2.400000 495.0000 0.01900000
## 82 2.600000 507.0000 0.01900000
## 83 2.500000 492.0000 0.01900000
## 84 2.500000 506.0000 0.01900000
## 85 2.400000 493.0000 0.01900000
## 86 2.500000 499.0000 0.01900000
## 87 2.500000 513.0000 0.02000000
## 88 2.500000 498.0000 0.02000000
## 89 2.500000 486.0000 0.01900000
## 90 2.500000 493.0000 0.02000000
## 91 2.500000 478.0000 0.01900000
## 92 2.500000 522.0000 0.02100000
## 93 2.500000 492.0000 0.02000000
## 94 2.500000 491.0000 0.01900000
## 95 2.500000 490.0000 0.01900000
## 96 2.500000 482.0000 0.01900000
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## 99 2.400000 490.0000 0.02000000
## 100 2.500000 491.0000 0.02000000
## 101 2.500000 486.0000 0.02000000
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## 103 2.500000 498.0000 0.02000000
## 104 2.500000 496.0000 0.02000000
## 105 2.500000 481.0000 0.01900000
## 106 2.500000 493.0000 0.02000000
## 107 2.500000 495.0000 0.02000000
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## 109 2.500000 491.0000 0.02000000
## 110 2.500000 510.0000 0.02100000
## 111 2.500000 494.0000 0.01900000
## 112 2.500000 488.0000 0.01900000
## 113 2.500000 497.0000 0.01900000
## 114 2.500000 500.0000 0.01900000
## 115 2.500000 492.0000 0.01900000
## 116 2.500000 501.0000 0.01900000
## 117 2.500000 495.0000 0.01900000
## 118 2.500000 500.0000 0.02000000
## 119 2.600000 501.0000 0.02000000
## 120 2.600000 497.0000 0.02000000
## 121 2.600000 486.0000 0.02000000
## 122 2.600000 499.0000 0.02100000
## 123 2.500000 489.0000 0.01900000
## 124 2.600000 481.0000 0.01900000
## 125 2.500000 498.0000 0.02100000
## 126 2.500000 505.0000 0.02000000
## 127 2.500000 507.0000 0.02000000
## 128 2.400000 502.0000 0.02000000
## 129 2.500000 500.0000 0.01900000
## 130 2.500000 516.0000 0.02000000
## 131 2.500000 490.0000 0.01900000
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## 133 2.500000 499.0000 0.02000000
## 134 2.500000 495.0000 0.02000000
## 135 2.400000 502.0000 0.02100000
## 136 2.500000 500.0000 0.02100000
## 137 2.500000 495.0000 0.02000000
## 138 2.400000 502.0000 0.02100000
## 139 2.600000 497.0000 0.02000000
## 140 2.600000 509.0000 0.02100000
## 141 2.500000 494.0000 0.02000000
## 142 2.500000 497.0000 0.02000000
## 143 2.500000 509.0000 0.02000000
## 144 2.400000 493.0000 0.02000000
## 145 2.500000 485.0000 0.02000000
## 146 2.400000 517.0000 0.02100000
## 147 2.500000 472.0000 0.01900000
## 148 2.500000 490.0000 0.02100000
## 149 2.500000 496.0000 0.02200000
## 150 2.500000 470.0000 0.01900000
## 151 2.500000 507.0000 0.02100000
## 152 2.500000 500.0000 0.02000000
## 153 2.400000 493.0000 0.02000000
## 154 2.500000 501.0000 0.02000000
## 155 2.500000 470.0000 0.01900000
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## 159 2.500000 502.0000 0.02000000
## 160 2.400000 481.0000 0.01900000
## 161 2.500000 506.0000 0.02000000
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## 163 2.400000 482.0000 0.01900000
## 164 2.500000 488.0000 0.02000000
## 165 2.500000 512.0000 0.02100000
## 166 2.500000 511.0000 0.02100000
## 167 2.500000 507.0000 0.02100000
## 168 2.500000 518.0000 0.02200000
## 169 2.400000 475.0000 0.01900000
## 170 2.400000 496.0000 0.01900000
## 171 2.500000 496.0000 0.01900000
## 172 2.479683 498.3441 0.02000228
## 173 2.492512 486.4670 0.01917610
## 174 2.474715 493.4833 0.01838520
## 175 2.486006 498.3441 0.02004514
## 176 2.473177 489.8636 0.01898716
## ManufacturingProcess37 ManufacturingProcess38 ManufacturingProcess39
## 1 0.5 3 7.2
## 2 2.0 2 7.2
## 3 0.7 2 7.2
## 4 1.2 2 7.2
## 5 0.2 2 7.3
## 6 0.4 2 7.2
## 7 0.8 2 7.3
## 8 1.0 2 7.3
## 9 1.2 3 7.4
## 10 1.8 3 7.1
## 11 1.5 2 7.0
## 12 0.3 3 7.0
## 13 1.1 3 7.1
## 14 0.6 3 7.4
## 15 1.6 3 7.2
## 16 1.2 3 7.3
## 17 1.3 3 7.4
## 18 1.1 3 7.4
## 19 0.7 3 7.3
## 20 1.2 2 7.3
## 21 0.9 3 7.3
## 22 0.9 2 7.4
## 23 1.5 3 7.4
## 24 1.3 2 7.2
## 25 1.0 2 7.2
## 26 0.9 3 6.9
## 27 0.9 3 7.1
## 28 0.9 3 7.4
## 29 1.9 3 7.3
## 30 0.7 3 6.8
## 31 1.6 2 7.1
## 32 0.7 2 7.1
## 33 1.6 2 7.2
## 34 1.1 2 7.5
## 35 1.7 3 7.3
## 36 1.0 2 7.4
## 37 0.9 3 7.1
## 38 1.7 2 7.1
## 39 0.0 2 7.1
## 40 0.0 2 7.2
## 41 0.0 2 7.2
## 42 1.1 3 7.4
## 43 0.9 3 7.3
## 44 1.0 3 7.1
## 45 0.3 2 7.1
## 46 1.2 3 7.0
## 47 0.7 3 7.4
## 48 1.8 3 6.7
## 49 0.6 3 7.3
## 50 0.8 3 7.3
## 51 1.3 3 7.1
## 52 0.4 3 7.1
## 53 1.9 3 7.4
## 54 1.4 3 7.3
## 55 0.9 3 7.2
## 56 0.6 3 7.3
## 57 1.1 2 7.3
## 58 0.5 3 7.3
## 59 1.4 3 7.1
## 60 0.8 3 7.0
## 61 0.7 3 7.1
## 62 1.3 2 7.1
## 63 0.5 3 7.1
## 64 1.1 2 7.1
## 65 1.0 2 7.0
## 66 1.0 3 6.9
## 67 0.5 3 6.8
## 68 0.4 3 7.0
## 69 1.1 3 7.3
## 70 0.9 3 7.1
## 71 0.7 3 7.0
## 72 1.3 3 7.1
## 73 0.6 2 7.0
## 74 1.1 3 7.4
## 75 1.9 2 7.1
## 76 0.7 2 7.0
## 77 0.8 3 7.1
## 78 1.7 3 7.0
## 79 1.0 3 7.1
## 80 1.2 3 7.1
## 81 0.3 2 7.1
## 82 0.2 3 7.1
## 83 0.3 3 7.1
## 84 0.9 2 7.2
## 85 0.9 2 7.1
## 86 1.4 3 7.2
## 87 0.9 2 7.1
## 88 1.2 2 7.2
## 89 0.8 2 7.2
## 90 1.2 2 7.2
## 91 1.0 2 7.2
## 92 0.8 3 7.2
## 93 1.1 2 7.2
## 94 0.9 2 7.2
## 95 1.0 2 7.2
## 96 1.0 2 7.2
## 97 0.7 2 7.2
## 98 0.9 2 7.3
## 99 0.8 3 7.2
## 100 1.3 2 7.2
## 101 1.6 2 7.2
## 102 0.8 3 7.2
## 103 1.3 3 7.2
## 104 0.7 3 7.3
## 105 1.0 2 6.9
## 106 0.5 3 7.1
## 107 1.4 3 7.0
## 108 0.7 3 7.0
## 109 1.5 2 7.1
## 110 0.6 3 7.3
## 111 0.7 2 7.0
## 112 0.7 3 7.0
## 113 0.9 2 7.0
## 114 0.7 3 7.1
## 115 1.3 3 7.1
## 116 0.4 3 7.2
## 117 1.0 3 6.9
## 118 0.9 3 7.0
## 119 0.7 2 7.1
## 120 0.5 3 6.9
## 121 1.1 3 6.9
## 122 0.5 2 7.0
## 123 0.9 2 7.1
## 124 0.7 2 7.1
## 125 1.1 3 7.1
## 126 0.7 3 7.0
## 127 1.0 3 7.2
## 128 0.7 2 7.2
## 129 0.4 2 7.0
## 130 0.8 3 7.0
## 131 1.0 2 7.2
## 132 0.4 3 7.2
## 133 0.6 2 7.2
## 134 1.3 2 7.3
## 135 1.1 3 7.2
## 136 1.1 2 7.2
## 137 1.1 3 7.3
## 138 1.1 3 7.3
## 139 1.1 3 7.2
## 140 1.3 3 7.3
## 141 1.0 3 7.2
## 142 1.0 3 7.2
## 143 1.0 3 7.2
## 144 1.1 2 7.3
## 145 1.8 2 7.3
## 146 1.0 3 7.3
## 147 2.0 2 7.1
## 148 0.7 2 7.2
## 149 1.0 3 7.1
## 150 1.3 2 7.2
## 151 0.6 3 7.2
## 152 0.8 3 7.4
## 153 1.8 2 7.3
## 154 0.7 3 7.3
## 155 1.7 2 7.3
## 156 1.5 3 7.3
## 157 0.4 3 7.3
## 158 1.7 3 7.3
## 159 0.9 3 7.3
## 160 1.3 2 7.2
## 161 0.9 3 7.3
## 162 0.5 3 7.4
## 163 1.6 3 7.3
## 164 1.0 3 7.3
## 165 1.8 3 7.3
## 166 1.1 3 7.2
## 167 1.9 3 7.3
## 168 1.6 3 7.3
## 169 1.6 3 0.0
## 170 1.4 3 0.0
## 171 0.6 3 0.0
## 172 2.3 0 0.0
## 173 1.0 0 0.0
## 174 1.3 0 0.0
## 175 2.3 0 0.0
## 176 0.9 0 0.0
## ManufacturingProcess40 ManufacturingProcess41 ManufacturingProcess42
## 1 0.0 0.0004980465 11.6
## 2 0.1 0.1500000000 11.1
## 3 0.0 0.0000000000 12.0
## 4 0.0 0.0000000000 10.6
## 5 0.0 0.0000000000 11.0
## 6 0.0 0.0000000000 11.5
## 7 0.0 0.0000000000 11.7
## 8 0.0 0.0000000000 11.4
## 9 0.0 0.0000000000 11.4
## 10 0.0 0.0000000000 11.3
## 11 0.0 0.0000000000 11.0
## 12 0.0 0.0000000000 11.2
## 13 0.0 0.0000000000 11.1
## 14 0.0 0.0000000000 11.7
## 15 0.0 0.0000000000 11.6
## 16 0.1 0.2000000000 11.6
## 17 0.0 0.0000000000 11.5
## 18 0.0 0.0000000000 11.7
## 19 0.0 0.0000000000 11.6
## 20 0.0 0.0000000000 11.4
## 21 0.1 0.2000000000 11.4
## 22 0.0 0.0000000000 11.9
## 23 0.0 0.0000000000 11.6
## 24 0.0 0.0000000000 11.4
## 25 0.0 0.0000000000 11.5
## 26 0.0 0.0000000000 11.8
## 27 0.0 0.0000000000 11.7
## 28 0.0 0.0000000000 11.6
## 29 0.1 0.2000000000 11.7
## 30 0.0 0.0000000000 11.6
## 31 0.0 0.0000000000 11.7
## 32 0.0 0.0000000000 11.6
## 33 0.1 0.1000000000 11.6
## 34 0.1 0.1000000000 11.6
## 35 0.0 0.0000000000 11.7
## 36 0.1 0.2000000000 11.0
## 37 0.0 0.0000000000 11.2
## 38 0.0 0.0000000000 11.1
## 39 0.1 0.2000000000 11.0
## 40 0.0 0.0000000000 11.4
## 41 0.0 0.0000000000 10.9
## 42 0.0 0.0000000000 11.4
## 43 0.1 0.1000000000 11.4
## 44 0.0 0.0000000000 11.0
## 45 0.0 0.0000000000 10.5
## 46 0.0 0.0000000000 10.7
## 47 0.0 0.0000000000 11.1
## 48 0.1 0.1000000000 11.6
## 49 0.0 0.0000000000 11.6
## 50 0.0 0.0000000000 11.6
## 51 0.0 0.0000000000 11.4
## 52 0.1 0.2000000000 11.4
## 53 0.0 0.0000000000 11.4
## 54 0.0 0.0000000000 11.6
## 55 0.0 0.0000000000 11.2
## 56 0.0 0.0000000000 11.0
## 57 0.1 0.2000000000 11.0
## 58 0.0 0.0000000000 11.3
## 59 0.0 0.0000000000 11.8
## 60 0.0 0.0000000000 11.5
## 61 0.1 0.1000000000 11.6
## 62 0.0 0.0000000000 11.7
## 63 0.0 0.0000000000 11.6
## 64 0.0 0.0000000000 11.5
## 65 0.0 0.0000000000 11.6
## 66 0.0 0.0000000000 11.7
## 67 0.0 0.0000000000 11.7
## 68 0.0 0.0000000000 11.2
## 69 0.0 0.0000000000 11.9
## 70 0.1 0.1000000000 11.9
## 71 0.0 0.0000000000 11.5
## 72 0.0 0.0000000000 11.7
## 73 0.0 0.0000000000 11.5
## 74 0.1 0.1000000000 11.7
## 75 0.0 0.0000000000 11.8
## 76 0.0 0.0000000000 11.6
## 77 0.0 0.0000000000 11.6
## 78 0.0 0.0000000000 11.4
## 79 0.0 0.0000000000 11.4
## 80 0.0 0.0000000000 11.3
## 81 0.0 0.0000000000 11.3
## 82 0.0 0.0000000000 11.6
## 83 0.0 0.0000000000 11.5
## 84 0.0 0.0000000000 11.5
## 85 0.0 0.0000000000 11.6
## 86 0.0 0.0000000000 11.5
## 87 0.1 0.1000000000 11.7
## 88 0.0 0.0000000000 11.7
## 89 0.0 0.0000000000 11.5
## 90 0.0 0.0000000000 11.3
## 91 0.1 0.1000000000 11.6
## 92 0.0 0.0000000000 11.6
## 93 0.0 0.0000000000 11.5
## 94 0.0 0.0000000000 11.9
## 95 0.1 0.1000000000 11.8
## 96 0.0 0.0000000000 11.6
## 97 0.0 0.0000000000 11.6
## 98 0.0 0.0000000000 11.5
## 99 0.1 0.1000000000 11.7
## 100 0.0 0.0000000000 11.5
## 101 0.0 0.0000000000 11.5
## 102 0.0 0.0000000000 11.6
## 103 0.0 0.0000000000 11.4
## 104 0.1 0.1000000000 11.8
## 105 0.0 0.0000000000 11.7
## 106 0.0 0.0000000000 11.9
## 107 0.0 0.0000000000 11.7
## 108 0.0 0.0000000000 11.6
## 109 0.0 0.1000000000 11.7
## 110 0.0 0.0000000000 11.5
## 111 0.0 0.0000000000 11.6
## 112 0.0 0.0000000000 11.3
## 113 0.1 0.1000000000 11.3
## 114 0.0 0.0000000000 11.4
## 115 0.0 0.0000000000 11.8
## 116 0.0 0.0000000000 11.8
## 117 0.0 0.0000000000 11.8
## 118 0.1 0.1000000000 11.7
## 119 0.0 0.0000000000 11.6
## 120 0.0 0.0000000000 11.9
## 121 0.0 0.0000000000 11.6
## 122 0.0 0.0000000000 11.8
## 123 0.1 0.2000000000 11.5
## 124 0.0 0.0000000000 11.6
## 125 0.0 0.0000000000 11.5
## 126 0.0 0.0000000000 11.5
## 127 0.0 0.0000000000 11.4
## 128 0.1 0.1000000000 11.4
## 129 0.0 0.0000000000 11.7
## 130 0.0 0.0000000000 11.4
## 131 0.0 0.0000000000 11.4
## 132 0.0 0.0000000000 11.6
## 133 0.0 0.0000000000 11.9
## 134 0.0 0.0000000000 11.8
## 135 0.0 0.0000000000 11.8
## 136 0.0 0.0000000000 11.7
## 137 0.1 0.1000000000 11.7
## 138 0.0 0.0000000000 11.8
## 139 0.0 0.0000000000 11.7
## 140 0.0 0.0000000000 11.8
## 141 0.1 0.1000000000 11.7
## 142 0.0 0.0000000000 11.7
## 143 0.0 0.0000000000 11.7
## 144 0.0 0.0000000000 11.8
## 145 0.1 0.1000000000 11.5
## 146 0.0 0.0000000000 11.8
## 147 0.0 0.0000000000 11.7
## 148 0.0 0.0000000000 11.9
## 149 0.1 0.1000000000 11.9
## 150 0.0 0.0000000000 12.0
## 151 0.0 0.0000000000 11.7
## 152 0.0 0.0000000000 11.6
## 153 0.0 0.0000000000 11.3
## 154 0.1 0.1000000000 10.7
## 155 0.0 0.0000000000 11.3
## 156 0.0 0.0000000000 11.0
## 157 0.1 0.2000000000 10.9
## 158 0.0 0.0000000000 12.0
## 159 0.0 0.0000000000 12.1
## 160 0.0 0.0000000000 12.1
## 161 0.0 0.0000000000 12.0
## 162 0.0 0.0000000000 11.7
## 163 0.0 0.0000000000 11.5
## 164 0.1 0.1000000000 11.8
## 165 0.0 0.0000000000 11.6
## 166 0.0 0.0000000000 11.4
## 167 0.0 0.0000000000 11.4
## 168 0.0 0.0000000000 11.3
## 169 0.0 0.0000000000 11.8
## 170 0.0 0.0000000000 11.6
## 171 0.0 0.0000000000 11.7
## 172 0.0 0.0000000000 0.0
## 173 0.0 0.0000000000 0.0
## 174 0.0 0.0000000000 0.0
## 175 0.0 0.0000000000 0.0
## 176 0.0 0.0000000000 0.0
## ManufacturingProcess43 ManufacturingProcess44 ManufacturingProcess45
## 1 3.0 1.8 2.4
## 2 0.9 1.9 2.2
## 3 1.0 1.8 2.3
## 4 1.1 1.8 2.1
## 5 1.1 1.7 2.1
## 6 2.2 1.8 2.0
## 7 0.7 2.0 2.2
## 8 0.8 2.0 2.2
## 9 0.9 1.9 2.1
## 10 0.8 1.9 2.4
## 11 1.0 1.9 1.8
## 12 0.8 2.0 1.8
## 13 0.8 1.9 2.4
## 14 0.6 1.7 1.9
## 15 0.8 1.9 2.0
## 16 1.0 1.9 2.5
## 17 1.1 1.9 2.3
## 18 1.7 1.8 2.2
## 19 1.8 1.7 2.3
## 20 1.5 1.5 2.0
## 21 2.0 1.6 2.0
## 22 0.8 1.9 2.1
## 23 0.8 1.9 2.4
## 24 1.1 2.0 1.8
## 25 0.7 1.7 2.4
## 26 0.8 1.7 2.2
## 27 0.7 1.7 2.0
## 28 1.3 1.7 2.2
## 29 0.8 1.7 2.2
## 30 0.5 1.9 2.2
## 31 0.6 2.0 2.4
## 32 0.6 2.0 2.1
## 33 0.7 1.9 2.4
## 34 0.5 1.8 2.3
## 35 0.6 1.9 2.6
## 36 0.9 2.0 2.1
## 37 1.1 1.9 2.4
## 38 1.2 1.8 2.4
## 39 1.5 1.8 2.4
## 40 1.0 1.9 2.3
## 41 1.0 1.9 2.2
## 42 0.7 1.8 2.4
## 43 0.7 2.0 2.4
## 44 0.7 1.8 2.4
## 45 0.9 1.8 2.1
## 46 0.7 1.8 2.3
## 47 1.1 1.8 2.1
## 48 1.4 1.8 2.4
## 49 1.3 1.8 2.1
## 50 0.9 1.8 2.0
## 51 2.5 1.8 2.1
## 52 1.0 1.8 2.2
## 53 1.1 2.0 2.3
## 54 1.2 1.9 2.2
## 55 0.9 1.9 2.1
## 56 0.9 2.1 2.2
## 57 1.0 1.9 2.2
## 58 0.0 2.0 2.2
## 59 11.0 1.9 2.3
## 60 0.7 1.8 2.3
## 61 0.9 1.8 2.2
## 62 0.8 1.8 2.1
## 63 0.8 1.8 2.0
## 64 0.7 1.9 2.3
## 65 0.9 2.0 2.3
## 66 1.4 1.9 1.8
## 67 1.4 1.9 1.8
## 68 1.2 1.9 1.8
## 69 1.2 1.8 2.5
## 70 1.7 1.8 2.3
## 71 1.7 1.9 2.2
## 72 1.2 1.8 1.9
## 73 1.2 1.8 1.8
## 74 0.8 2.0 2.3
## 75 0.8 2.0 2.1
## 76 1.3 1.9 2.4
## 77 0.6 2.0 2.3
## 78 1.3 1.9 2.2
## 79 0.8 2.0 2.5
## 80 0.9 2.1 2.2
## 81 1.0 1.9 2.1
## 82 1.2 1.9 2.2
## 83 1.6 1.9 2.4
## 84 1.5 1.9 2.4
## 85 1.6 2.0 2.4
## 86 1.0 1.9 2.4
## 87 1.1 1.8 2.1
## 88 1.1 1.9 2.3
## 89 1.1 1.9 2.3
## 90 0.8 1.9 2.1
## 91 0.9 1.9 2.5
## 92 1.1 1.8 2.2
## 93 0.9 1.8 2.0
## 94 0.9 1.9 2.5
## 95 0.8 1.9 2.3
## 96 0.8 1.9 2.2
## 97 0.9 2.0 2.1
## 98 0.9 1.9 2.1
## 99 1.1 1.9 2.2
## 100 0.9 1.9 2.3
## 101 0.8 1.9 2.3
## 102 1.1 1.8 2.3
## 103 1.0 1.8 2.4
## 104 0.6 1.9 2.1
## 105 0.8 1.9 2.0
## 106 0.8 1.9 2.3
## 107 0.8 1.9 1.9
## 108 0.8 1.9 2.4
## 109 0.8 1.9 1.9
## 110 0.9 1.8 2.4
## 111 1.7 1.8 2.2
## 112 1.2 1.9 2.3
## 113 0.9 1.8 2.3
## 114 1.1 1.8 2.3
## 115 0.5 1.9 2.3
## 116 0.6 1.9 2.2
## 117 0.7 1.9 2.2
## 118 0.8 1.9 2.0
## 119 0.8 1.7 2.4
## 120 0.5 1.9 2.2
## 121 0.5 1.7 1.9
## 122 0.5 1.8 2.1
## 123 0.5 1.9 2.2
## 124 0.7 1.8 2.2
## 125 0.6 1.9 2.2
## 126 0.7 1.9 2.1
## 127 0.6 1.9 2.2
## 128 0.7 1.9 2.0
## 129 0.5 2.0 2.2
## 130 0.5 1.9 2.3
## 131 0.4 1.9 2.2
## 132 0.6 1.8 2.1
## 133 0.4 2.0 2.3
## 134 0.4 1.9 2.2
## 135 0.4 1.9 2.4
## 136 0.5 1.8 2.4
## 137 0.5 1.9 2.4
## 138 0.5 1.8 2.1
## 139 0.7 1.9 2.3
## 140 0.4 1.8 2.4
## 141 0.5 1.8 2.3
## 142 0.6 1.8 2.3
## 143 0.5 1.8 2.3
## 144 0.5 1.9 2.3
## 145 0.5 1.9 2.2
## 146 0.5 1.9 1.8
## 147 0.5 1.8 1.9
## 148 0.6 1.8 2.1
## 149 0.4 1.7 1.8
## 150 0.5 1.8 1.9
## 151 0.6 1.7 2.3
## 152 0.7 1.9 1.9
## 153 0.5 1.9 2.1
## 154 0.7 1.8 2.1
## 155 0.5 1.8 1.8
## 156 0.4 1.9 2.3
## 157 0.5 1.9 2.3
## 158 0.5 1.8 2.3
## 159 0.3 1.8 2.3
## 160 0.7 1.8 2.1
## 161 0.3 1.8 2.3
## 162 0.3 1.9 1.8
## 163 0.6 1.8 2.2
## 164 0.4 1.8 2.4
## 165 0.4 1.8 2.3
## 166 0.8 1.7 2.2
## 167 0.7 1.8 2.4
## 168 0.5 1.7 2.1
## 169 0.2 1.8 2.2
## 170 0.3 1.8 2.5
## 171 0.5 1.8 2.2
## 172 0.6 0.0 0.0
## 173 0.6 0.0 0.0
## 174 0.6 0.0 0.0
## 175 0.5 0.0 0.0
## 176 0.6 0.0 0.0missingData <- as.data.frame(colSums(is.na(processPredictors_imputed)))
colnames(missingData) <- c("NAs")
missingData <- cbind(Predictors = rownames(missingData), missingData)
rownames(missingData) <- 1:nrow(missingData)
missingData <- missingData[missingData$NAs != 0,]
head(missingData)## [1] Predictors NAs
## <0 rows> (or 0-length row.names)- Pre-Process the Data - Remove nearZeroVar predictors:
## [1] "BiologicalMaterial07"## [1] 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
## [20] 100- Pre-Process the Data - Check and remove Multi-Colinearity. We can remove these variables for multi-colinearity:
## [1] "BiologicalMaterial02" "BiologicalMaterial04" "BiologicalMaterial12"
## [4] "ManufacturingProcess29" "ManufacturingProcess42" "ManufacturingProcess27"
## [7] "ManufacturingProcess25" "ManufacturingProcess31" "ManufacturingProcess18"
## [10] "ManufacturingProcess40"removePredictors <- findCorrelation(cor(processPredictors_imputed), 0.90, names = TRUE)
removePredictors## [1] "BiologicalMaterial02" "BiologicalMaterial04" "BiologicalMaterial12"
## [4] "ManufacturingProcess29" "ManufacturingProcess42" "ManufacturingProcess27"
## [7] "ManufacturingProcess25" "ManufacturingProcess31" "ManufacturingProcess18"
## [10] "ManufacturingProcess40"## [1] "BiologicalMaterial01" "BiologicalMaterial03" "BiologicalMaterial05"
## [4] "BiologicalMaterial06" "BiologicalMaterial08" "BiologicalMaterial09"
## [7] "BiologicalMaterial10" "BiologicalMaterial11" "ManufacturingProcess01"
## [10] "ManufacturingProcess02" "ManufacturingProcess03" "ManufacturingProcess04"
## [13] "ManufacturingProcess05" "ManufacturingProcess06" "ManufacturingProcess07"
## [16] "ManufacturingProcess08" "ManufacturingProcess09" "ManufacturingProcess10"
## [19] "ManufacturingProcess11" "ManufacturingProcess12" "ManufacturingProcess13"
## [22] "ManufacturingProcess14" "ManufacturingProcess15" "ManufacturingProcess16"
## [25] "ManufacturingProcess17" "ManufacturingProcess19" "ManufacturingProcess20"
## [28] "ManufacturingProcess21" "ManufacturingProcess22" "ManufacturingProcess23"
## [31] "ManufacturingProcess24" "ManufacturingProcess26" "ManufacturingProcess28"
## [34] "ManufacturingProcess30" "ManufacturingProcess32" "ManufacturingProcess33"
## [37] "ManufacturingProcess34" "ManufacturingProcess35" "ManufacturingProcess36"
## [40] "ManufacturingProcess37" "ManufacturingProcess38" "ManufacturingProcess39"
## [43] "ManufacturingProcess41" "ManufacturingProcess43" "ManufacturingProcess44"
## [46] "ManufacturingProcess45"chemmfgproc <- cbind(ChemicalManufacturingProcess$Yield, processPredictors_imputed)
names(chemmfgproc)[names(chemmfgproc) == "ChemicalManufacturingProcess$Yield"] <- "Yield"
head(chemmfgproc )## Yield BiologicalMaterial01 BiologicalMaterial03 BiologicalMaterial05
## 1 38.00 6.25 56.97 19.51
## 2 42.44 8.01 67.48 19.36
## 3 42.03 8.01 67.48 19.36
## 4 41.42 8.01 67.48 19.36
## 5 42.49 7.47 72.25 17.91
## 6 43.57 6.12 65.31 21.79
## BiologicalMaterial06 BiologicalMaterial08 BiologicalMaterial09
## 1 43.73 16.66 11.44
## 2 53.14 19.04 12.55
## 3 53.14 19.04 12.55
## 4 53.14 19.04 12.55
## 5 54.66 18.22 12.80
## 6 51.23 18.30 12.13
## BiologicalMaterial10 BiologicalMaterial11 ManufacturingProcess01
## 1 3.46 138.09 10.9909
## 2 3.46 153.67 0.0000
## 3 3.46 153.67 0.0000
## 4 3.46 153.67 0.0000
## 5 3.05 147.61 10.7000
## 6 3.78 151.88 12.0000
## ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04
## 1 12.79439 1.508846 927.0047
## 2 0.00000 1.527970 917.0000
## 3 0.00000 1.530834 912.0000
## 4 0.00000 1.530834 911.0000
## 5 0.00000 1.531619 918.0000
## 6 0.00000 1.530527 924.0000
## ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07
## 1 998.8306 205.8232 177.4114
## 2 1032.2000 210.0000 177.0000
## 3 1003.6000 207.1000 178.0000
## 4 1014.6000 213.3000 177.0000
## 5 1027.5000 205.7000 178.0000
## 6 1016.8000 208.9000 178.0000
## ManufacturingProcess08 ManufacturingProcess09 ManufacturingProcess10
## 1 177.9193 43.00 8.636328
## 2 178.0000 46.57 9.164042
## 3 178.0000 45.07 9.138575
## 4 177.0000 44.92 8.738187
## 5 178.0000 44.96 8.468328
## 6 178.0000 45.32 8.636328
## ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess13
## 1 10.025683 262.5544 35.5
## 2 10.025683 0.0000 34.0
## 3 9.551027 0.0000 34.8
## 4 9.551027 0.0000 34.8
## 5 8.957722 0.0000 34.6
## 6 10.115706 0.0000 34.0
## ManufacturingProcess14 ManufacturingProcess15 ManufacturingProcess16
## 1 4898 6108 4682
## 2 4869 6095 4617
## 3 4878 6087 4617
## 4 4897 6102 4635
## 5 4992 6233 4733
## 6 4985 6222 4786
## ManufacturingProcess17 ManufacturingProcess19 ManufacturingProcess20
## 1 35.5 6049 4665
## 2 34.0 6097 4621
## 3 34.8 6078 4621
## 4 34.8 6073 4611
## 5 33.9 6102 4659
## 6 33.4 6115 4696
## ManufacturingProcess21 ManufacturingProcess22 ManufacturingProcess23
## 1 0.0 4.249653 3.502078
## 2 0.0 3.000000 0.000000
## 3 0.0 4.000000 1.000000
## 4 0.0 5.000000 2.000000
## 5 -0.7 8.000000 4.000000
## 6 -0.6 9.000000 1.000000
## ManufacturingProcess24 ManufacturingProcess26 ManufacturingProcess28
## 1 14.92497 6074 10.7
## 2 3.00000 6107 11.2
## 3 4.00000 6116 11.1
## 4 5.00000 6111 11.1
## 5 18.00000 6151 11.3
## 6 1.00000 6128 11.4
## ManufacturingProcess30 ManufacturingProcess32 ManufacturingProcess33
## 1 9.9 156 66
## 2 9.9 169 66
## 3 9.4 173 66
## 4 9.4 171 68
## 5 9.0 171 70
## 6 10.1 173 70
## ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36
## 1 2.4 486 0.019
## 2 2.6 508 0.019
## 3 2.6 509 0.018
## 4 2.5 496 0.018
## 5 2.5 468 0.017
## 6 2.5 490 0.018
## ManufacturingProcess37 ManufacturingProcess38 ManufacturingProcess39
## 1 0.5 3 7.2
## 2 2.0 2 7.2
## 3 0.7 2 7.2
## 4 1.2 2 7.2
## 5 0.2 2 7.3
## 6 0.4 2 7.2
## ManufacturingProcess41 ManufacturingProcess43 ManufacturingProcess44
## 1 0.0004980465 3.0 1.8
## 2 0.1500000000 0.9 1.9
## 3 0.0000000000 1.0 1.8
## 4 0.0000000000 1.1 1.8
## 5 0.0000000000 1.1 1.7
## 6 0.0000000000 2.2 1.8
## ManufacturingProcess45
## 1 2.4
## 2 2.2
## 3 2.3
## 4 2.1
## 5 2.1
## 6 2.05. Split the data into Training and Test Set
chemmfgproc_train <- initial_split(chemmfgproc, prop = 0.8, strata = "Yield")
train_chemmfgproc <- training(chemmfgproc_train)
test_chemmfgproc <- testing(chemmfgproc_train)
print (paste0("The number of observations in the training set is ", nrow(train_chemmfgproc)))## [1] "The number of observations in the training set is 144"## [1] "The number of observations in the test set is 32"trainingData_x <- as.data.frame(train_chemmfgproc[2:47])
trainingData_y <- as.data.frame(train_chemmfgproc$Yield)
colnames(trainingData_y) <- c("y")
testData_x <- as.data.frame(test_chemmfgproc[2:47])
testData_y <- as.data.frame(test_chemmfgproc$Yield)
colnames(testData_y) <- c("y")set.seed(100)
rpartModel <- train(x = trainingData_x,
y = trainingData_y$y,
method = "rpart",
tuneLength = 30,
trControl = controlObject
)## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, :
## There were missing values in resampled performance measures.set.seed(100)
ctreeModel <- train(x = trainingData_x,
y = trainingData_y$y,
method = "ctree",
tuneLength = 10,
trControl = controlObject
)
set.seed(100)
gbmGrid <- expand.grid(interaction.depth = seq(1, 7, by = 2),
n.trees = c(seq(100, 1000, by = 50)),
shrinkage = c(0.01, .1),
n.minobsinnode = c(5, 10, 15))
set.seed(100)
gbmTune <- train(x = trainingData_x, y = trainingData_y$y,
method = "gbm",
tuneGrid = gbmGrid,
verbose = FALSE,
trControl = controlObject
)
set.seed(100)
cubistGrid <- expand.grid(committees = c(1, 5, 10, 50, 75, 100),
neighbors = c(0, 1, 3, 5, 7, 9))
cubistTuned <- train( x= trainingData_x[, colnames(trainingData_x)],
y = trainingData_y$y,
method = "cubist",
tuneGrid = cubistGrid,
trControl = controlObject
)(a)
Which tree-based regression model gives the optimal resampling and test set performance?
The Cubist model gave the optimal re-sampling and test set performance.
resamples <- resamples(list(CART=rpartModel,
"Cond Inf Tree"=ctreeModel,
"Boosted Tree" =gbmTune,
Cubist=cubistTuned))
summary(resamples)##
## Call:
## summary.resamples(object = resamples)
##
## Models: CART, Cond Inf Tree, Boosted Tree, Cubist
## Number of resamples: 50
##
## MAE
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## CART 0.6987644 0.9964704 1.1287515 1.1467891 1.2718839 1.698406 0
## Cond Inf Tree 0.7578358 0.9667242 1.1023619 1.1224321 1.2734039 1.682129 0
## Boosted Tree 0.4670047 0.7177877 0.8417164 0.8269844 0.9142986 1.303525 0
## Cubist 0.3458477 0.6451495 0.7399143 0.7557013 0.8541947 1.204599 0
##
## RMSE
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## CART 0.8430900 1.2524573 1.4269716 1.4250825 1.630184 1.995059 0
## Cond Inf Tree 0.8826277 1.2430463 1.3678897 1.4175017 1.578764 2.011548 0
## Boosted Tree 0.5520562 0.8938217 1.0532100 1.0592244 1.193044 1.612538 0
## Cubist 0.4809586 0.8460765 0.9210511 0.9575843 1.129748 1.483914 0
##
## Rsquared
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## CART 0.15018131 0.3393391 0.5039208 0.4732591 0.6088581 0.8517376 0
## Cond Inf Tree 0.08185229 0.3681705 0.5000381 0.4808266 0.6127432 0.8278142 0
## Boosted Tree 0.38510523 0.6235827 0.7083037 0.6941189 0.7891789 0.8832076 0
## Cubist 0.42039116 0.6555111 0.7754456 0.7447688 0.8339765 0.9330651 0rpartPredictions <- predict(rpartModel, testData_x)
ctreePredictions <- predict(ctreeModel, testData_x)
gbmPredictions <- predict(gbmTune, testData_x)
cubistPredictions <- predict(cubistTuned, testData_x)rPart:
## RMSE Rsquared MAE
## 1.4523969 0.3269829 1.1986451cTree:
## RMSE Rsquared MAE
## 1.5256196 0.2967076 1.2501367gbm:
## RMSE Rsquared MAE
## 0.9946852 0.6566986 0.7967199Cubist:
## RMSE Rsquared MAE
## 0.8411718 0.7569305 0.6850943(b)
Which predictors are most important in the optimal tree-based regression model?
Optimal Tree Based Regression top ten most important predictors are:
ManufacturingProcess32 ManufacturingProcess17 BiologicalMaterial06 ManufacturingProcess09
ManufacturingProcess04
ManufacturingProcess28
ManufacturingProcess13
ManufacturingProcess33
ManufacturingProcess39
BiologicalMaterial03
Do either the biological or process variables dominate the list?
Of the top 20, 14 are Manufacturing processes and only 6 are biological.
How do the top 10 important predictors compare to the top 10 predictors from the optimal linear and nonlinear models?
For both the Linear and Non-Linear models, there is one more biological process in the top ten. There are six predictors among the top ten that they all have in common:
ManufacturingProcess13
ManufacturingProcess32
BiologicalMaterial06 ManufacturingProcess17
ManufacturingProcess09
BiologicalMaterial03
Optimal Linear top ten most important predictors are:
ManufacturingProcess32
ManufacturingProcess09
ManufacturingProcess13
ManufacturingProcess17
ManufacturingProcess36
BiologicalMaterial06
BiologicalMaterial08
ManufacturingProcess06
ManufacturingProcess33
BiologicalMaterial03
Optimal Non-Linear top ten most important predictors are:
ManufacturingProcess13
ManufacturingProcess32
BiologicalMaterial06 ManufacturingProcess17
ManufacturingProcess09
BiologicalMaterial03 ManufacturingProcess06
ManufacturingProcess36 BiologicalMaterial11 ManufacturingProcess11
cubistTuned1 <- varImp(cubistTuned)
cubistTuned1<- cubistTuned1$importance %>%
arrange(desc(Overall))
cubistTuned1 <- head(cubistTuned1,20)cubistTuned1_df <- as.data.frame(cubistTuned1)
cubistTuned1_df['Predictors'] <- rownames(cubistTuned1)
colnames(cubistTuned1_df) <- c("Overall", "Predictors")
rownames(cubistTuned1_df) <- 1:nrow(cubistTuned1_df)cubistTuned1_df %>%
arrange(Overall)%>%
mutate(name = factor(Predictors, levels=c(Predictors))) %>%
ggplot(aes(x=name, y=Overall)) +
geom_segment(aes(xend = Predictors, yend = 0)) +
geom_point(size = 4, color = "red") +
theme_minimal() +
coord_flip() +
labs(title="cubist Predictor Variable Importance",
y="cubist Importance", x="Predictors") +
scale_y_continuous()
(c)
Plot the optimal single tree with the distribution of yield in the terminal nodes. Does this view of the data provide additional knowledge about the biological or process predictors and their relationship with yield?
The view confirms that ManufacturingProcess32 is the optimal split in the data and carries the most importance to the Yield.
---
title: "DATA624 Spring 2021 HW9 - Regression Trees and Rule-Based Models"
author: "John K. Hancock"
date: "5/2/2021"
output:
  html_document:
    code_download: yes
    code_folding: show
    highlight: pygments
    number_sections: no
    theme: cerulean
    toc: yes
    toc_float: yes
  pdf_document:
    toc: yes
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

```{r, include=FALSE, warning=FALSE}

library(tidyverse)
library(ggplot2)
library(ggcorrplot)
library(caret)
library(elasticnet)
library(lars)
library(pls)
library(naniar)
library(heatmaply)
library(VIM)
library(ICSNP)
library(rsample)
library(glmnet)
library("mice")
library("e1071")
library(RANN)
library(earth)
library(kernlab)
library(nnet)

library(Cubist)
library(gbm)
library(ipred)
library(party)
library(partykit)
library(randomForest)
library(rpart)
library(RWeka)

```

# 8.1

##Recreate the simulated data from Exercise 7.2

```{r}
 library(mlbench)
 set.seed(200)
 simulated <- mlbench.friedman1(200, sd = 1)
 simulated <- cbind(simulated$x, simulated$y)
 simulated <- as.data.frame(simulated)
 colnames(simulated)[ncol(simulated)] <- "y"
 head(simulated)
```

##(a)

<i>Fit a random forest model to all of the predictors, then estimate the variable importance scores
Did the random forest model significantly use the uninformative predictors (V6 - V10)?</i>

No.  Looking at the top ten predictors, V6-V10 are in the bottom half of the top ten predictors. 

```{r}
model1 <- randomForest(y ~ ., data = simulated, importance = TRUE, ntree = 1000)
rfImp1 <- varImp(model1, scale = FALSE)
rfImp1 <- rfImp1 %>% 
            arrange(desc(Overall))
rfImp1
```
 
```{r}
rfImp1_df <- as.data.frame(rfImp1)
rfImp1_df['Predictors']  <- rownames(rfImp1_df)
colnames(rfImp1_df) <- c("Overall", "Predictors")
rfImp1_df <- rfImp1_df[, c("Predictors", "Overall") ]
rownames(rfImp1_df) <- 1:nrow(rfImp1_df)
rfImp1_df
```


 


```{r}
rfImp1_df %>% 
            arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "darkgoldenrod4") + 
            theme_minimal() + 
            coord_flip() +
            labs(title="randomForest Predictor Variable Importance",
               y="randomForest Importance", x="Predictors") +
            scale_y_continuous()
```

## (b)

<i>Now add an additional predictor that is highly correlated with one of the informative predictors. For example:</i>

Below another the variable "predictor" is created and correlated to existing predictor, "V1". 

```{r}
set.seed(100)
simulated$predictor <- simulated$V1 + rnorm(200) * .1
cor(simulated$predictor, simulated$V1)

```


```{r}
model <- randomForest(y ~ ., data = simulated, importance = TRUE, ntree = 1000)
rfImp1 <- varImp(model, scale = FALSE)
rfImp1 <- rfImp1 %>% 
            arrange(desc(Overall))
rfImp1
```

<i>Fit another random forest model to these data. Did the importance score for V1 change? What happens when you add another predictor that is   also highly correlated with V1? </i>

The importance score for V1 declined from the most importamt to the 2nd most important. Adding another highly correlated predictor with V1 dropped its importance. 

## (c)

Use the cforest function in the party package to fit a random forest model using conditional inference trees. The party package function varimp can calculate predictor importance. The conditional argument of that function toggles between the traditional importance measure and the modified version described in Strobl et al. (2007). Do these importances show the same pattern as the traditional random forest model?

Yes. They do show the same patterns. 


```{r}
model2 <- cforest(y ~ ., data = simulated)

```

```{r}
rfImp2 <- as.data.frame(  varimp(model2, conditional = TRUE))
rfImp2['Predictors']  <- rownames(rfImp2)
colnames(rfImp2) <- c("Overall", "Predictors")
rownames(rfImp2) <- 1:nrow(rfImp2)
rfImp2 <- rfImp2 %>% 
            arrange(desc(Overall))

```



```{r}
rfImp2 %>% 
   arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "green") + 
            theme_gray() + 
            coord_flip() +
            labs(title="cForest Predictor Variable Importance",
               y="cForest Importance", x="Predictors") +
            scale_y_continuous()
```


## (d)

Repeat this process with different tree models, such as boosted trees and Cubist. Does the same pattern occur?

<b><u>Boosted Trees</u></b>

```{r}
 library(mlbench)
 set.seed(200)
 simulated2 <- mlbench.friedman1(200, sd = 1)
 simulated2 <- cbind(simulated2$x, simulated2$y)
 simulated2 <- as.data.frame(simulated2)
 colnames(simulated2)[ncol(simulated2)] <- "y"
```


```{r}
gbmGrid <- expand.grid(interaction.depth = seq(1, 7, by = 2),
                        n.trees = seq(100, 1000, by = 50),
                        shrinkage = c(0.01, 0.1),
                        n.minobsinnode = 5)
```


```{r}
set.seed(100)
gbmTune <- train(simulated2[1:10], simulated2$y,
                  method = "gbm",
                  tuneGrid = gbmGrid,
                  verbose = FALSE)
```


```{r}
gbmTune1 <- varImp(gbmTune)
gbmTune1$importance %>% 
  arrange(desc(Overall))

```


```{r}
gbmTune1_df <- as.data.frame(gbmTune1$importance)
gbmTune1_df['Predictors']  <- rownames(gbmTune1_df)
colnames(gbmTune1_df) <- c("Overall", "Predictors")
rownames(gbmTune1_df) <- 1:nrow(gbmTune1_df)
gbmTune1_df
```



```{r}
gbmTune1_df %>% 
   arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "steelblue") + 
            theme_gray() + 
            coord_flip() +
            labs(title="boosted Predictor Variable Importance",
               y="boosted Importance", x="Predictors") +
            scale_y_continuous()
```

<i>Now add an additional predictor that is highly correlated with one of the informative predictors as was done in Part A:</i>



```{r}
set.seed(100)
simulated2$duplicate <- simulated2$V1 + rnorm(200) * .1
cor(simulated2$duplicate, simulated2$V1)

```

```{r}
col_order <- colnames(simulated2)
col_order <- c("V1","V2","V3","V4","V5","V6","V7","V8","V9","V10", "duplicate", "y")
simulated2 <- simulated2[, col_order]
simulated2
```



```{r}
set.seed(100)
gbmTune <- train(simulated2[1:11], simulated2$y,
                  method = "gbm",
                  tuneGrid = gbmGrid,
                  verbose = FALSE)
```


```{r}
gbmTune1 <- varImp(gbmTune)
gbmTune1$importance %>% 
  arrange(desc(Overall))

```


```{r}
gbmTune1_df <- as.data.frame(gbmTune1$importance)
gbmTune1_df['Predictors']  <- rownames(gbmTune1_df)
colnames(gbmTune1_df) <- c("Overall", "Predictors")
rownames(gbmTune1_df) <- 1:nrow(gbmTune1_df)

```



```{r}
gbmTune1_df %>% 
    arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "orange") + 
            theme_gray() + 
            coord_flip() +
            labs(title="boosted Predictor Variable Importance",
               y="boosted Importance", x="Predictors") +
            scale_y_continuous()
```

<b><u>Cubist</u></b>


```{r}
 library(mlbench)
 set.seed(200)
 simulated3 <- mlbench.friedman1(200, sd = 1)
 simulated3 <- cbind(simulated3$x, simulated3$y)
 simulated3 <- as.data.frame(simulated3)
 colnames(simulated3)[ncol(simulated3)] <- "y"
```

```{r}
set.seed(100)
colnamesx <- c("V1","V2","V3","V4","V5","V6","V7","V8","V9","V10")
cubistTuned <- train(simulated3[, colnamesx], simulated3$y, method = "cubist")

```


```{r}
cubistTuned1 <- varImp(cubistTuned)
cubistTuned1$importance %>% 
  arrange(desc(Overall))

```




```{r}
cubistTuned1_df <- as.data.frame(cubistTuned1$importance)
cubistTuned1_df['Predictors']  <- rownames(cubistTuned1_df)
colnames(cubistTuned1_df) <- c("Overall", "Predictors")
rownames(cubistTuned1_df) <- 1:nrow(cubistTuned1_df)
cubistTuned1_df
```



```{r}
cubistTuned1_df %>% 
    arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "seashell") + 
            theme_dark() + 
            coord_flip() +
            labs(title="cubist Predictor Variable Importance",
               y="cubist Importance", x="Predictors") +
            scale_y_continuous()
```

<i>Now add an additional predictor that is highly correlated with one of the informative predictors as was done in Part A:</i>

```{r}
set.seed(100)
simulated3$corr_pred <- simulated3$V1 + rnorm(200) * .1
cor(simulated3$corr_pred, simulated3$V1)

```

```{r}
col_order <- colnames(simulated3)
col_order <- c("V1","V2","V3","V4","V5","V6","V7","V8","V9","V10", "corr_pred", "y")
simulated3 <- simulated3[, col_order]
simulated3
```


```{r}
set.seed(100)
colnamesx <- c("V1","V2","V3","V4","V5","V6","V7","V8","V9","V10", "corr_pred")
cubistTuned <- train(simulated3[, colnamesx], simulated3$y, method = "cubist")

```

```{r}
simulated3[, colnamesx]
```





```{r}
cubistTuned1 <- varImp(cubistTuned)
cubistTuned1$importance %>% 
  arrange(desc(Overall))

```




```{r}
cubistTuned1_df <- as.data.frame(cubistTuned1$importance)
cubistTuned1_df['Predictors']  <- rownames(cubistTuned1_df)
colnames(cubistTuned1_df) <- c("Overall", "Predictors")
rownames(cubistTuned1_df) <- 1:nrow(cubistTuned1_df)
cubistTuned1_df
```




```{r}
cubistTuned1_df %>% 
  arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "gold") + 
            theme_minimal() + 
            coord_flip() +
            labs(title="cubist Predictor Variable Importance",
               y="cubist Importance", x="Predictors") +
            scale_y_continuous()
```


# 8.2. 

<i>Use a simulation to show tree bias with different granularities.</i>

After creating a simulated dataset using 8 samples and a dependent variable that is the summation of all of the variables except for gran5. After appling the tree models, cforest and boost, I found that the variables with the most granularity, gran1 and gran2, were the most important to the model. 


```{r}
set.seed(100)
gran1 <- c(sample(1:100, 100, replace=TRUE))
gran2 <- c(sample(1:90, 100, replace=TRUE))
gran3 <- c(sample(1:80, 100, replace=TRUE))
gran4 <- c(sample(1:70, 100, replace=TRUE))
gran5 <- c(sample(1:30, 100, replace=TRUE))
gran6 <- c(sample(1:15, 100, replace=TRUE))
gran7 <- c(sample(1:8, 100, replace=TRUE))
gran8 <- c(sample(1:3, 100, replace=TRUE))
y <- gran1 + gran2 + gran3 + gran4 + gran6 + gran7 + gran8 + rnorm(100)*.1

custom_simulation <- as.data.frame(cbind(gran1, gran2, gran3, gran4, gran5, gran6, gran7, gran8, y))

head(custom_simulation)

```

<b><u>cforest</u></b>

```{r}
custom_model <- cforest(y ~ ., data = custom_simulation)

```

```{r}
custImp <- as.data.frame(  varimp(custom_model, conditional = TRUE))
custImp ['Predictors']  <- rownames(custImp)
colnames(custImp ) <- c("Overall", "Predictors")
rownames(custImp ) <- 1:nrow(custImp)
custImp  <- custImp  %>% 
            arrange(desc(Overall))

```


```{r}
custImp %>% 
    arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "black") + 
            theme_minimal() + 
            coord_flip() +
            labs(title="cforest Predictor Variable Importance",
               y="cforest Importance", x="Predictors") +
            scale_y_continuous()
```



<b><u>Boosted Trees</u></b>


```{r}
gbmGrid <- expand.grid(interaction.depth = seq(1, 7, by = 2),
                        n.trees = seq(100, 1000, by = 50),
                        shrinkage = c(0.01, 0.1),
                        n.minobsinnode = 5)
```


```{r}
set.seed(100)
gbmTune <- train(custom_simulation[1:8], custom_simulation$y,
                  method = "gbm",
                  tuneGrid = gbmGrid,
                  verbose = FALSE)
```


```{r}
gbmTune1 <- varImp(gbmTune)
gbmTune1$importance %>% 
  arrange(desc(Overall))

```


```{r}
gbmTune1_df <- as.data.frame(gbmTune1$importance)
gbmTune1_df['Predictors']  <- rownames(gbmTune1_df)
colnames(gbmTune1_df) <- c("Overall", "Predictors")
rownames(gbmTune1_df) <- 1:nrow(gbmTune1_df)
```



```{r}
gbmTune1_df %>% 
    arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "purple") + 
            theme_minimal() + 
            coord_flip() +
            labs(title="boostPredictor Variable Importance",
               y="boost Importance", x="Predictors") +
            scale_y_continuous()
```


# 8.3. 

<i>In stochastic gradient boosting the bagging fraction and learning rate will govern the construction of the trees as they are guided by the gradient. Although the optimal values of these parameters should be obtained through the tuning process, it is helpful to understand how the magnitudes of these parameters affect magnitudes of variable importance. Figure 8.24 provides the variable importance plots for boosting using two extreme values for the bagging fraction (0.1 and 0.9) and the learning rate (0.1 and 0.9) for the solubility data. The left-hand plot has both parameters set to 0.1, and the right-hand plot has both set to 0.9:</i>


![Fig. 8.24](ComparisonOfBaggingFractionLearningRate.png){width=100% height=100%}

## (a)

<i>Why does the model on the right focus its importance on just the first few of predictors, whereas the model on the left spreads importance across
more predictors? </i>

First, let's define what a boosting algorithm does. Gradient boosting works by creating a combination of weak learners into an ensemble which is used to make predictions. Specifically:

"Given a loss function (e.g., squared error for regression) and a weak learner (e.g., regression trees), the algorithm seeks to find an additive model that minimizes the loss function. The algorithm is typically initialized with the best guess of the response (e.g., the mean of the response in regression). The gradient (e.g., residual) is calculated, and a model is then fit to the residuals to minimize the loss function. The current model is added to the previous model, and the procedure continues for a user-specified number of iteration"

<b><u>Max Kuhn, Kjell Johnson, <i>Applied Predictive Modeling</i>, New York, NY:Springer Science+Business Media LLC New York, 2013, p. 204</b></u>

Second, Trees-because they have the flexibility to be weak learners by restricting their depth, and they can be created easily and added together-are suitable for the additive modeling process. In boosting, Trees are dependent on past trees and unequally contribute to the model.  

Third, the learner in gradient boosting is susceptible to over fitting since the learner is using the greedy strategy of choosing the optimal weak learner at each stage. To address this, the learner is constrained by regularization, or shrinkage, where a fraction of the current predicted value is added to the previous iteration's predicted value. This fraction is known as the <b>learning rate</b> which is another parameter to tune in the model. The learning rate is set between 0 and 1.

Fourth, Stochastic Gradient Boosting involves fitting a base learner on a subsample of the training set drawn at random without replacement. This fraction is known as the bagging fraction.The suggested fraction is set to 0.5. 

Given these four points, the reasons why the right hand diagram places more importance on the first few predictors is that the model is over fitting the data. The parameters, learning rate and bagging fraction, which are both set close to one at .9. In this instance the learning rate will not be constrained and the model is using the greedy strategy when choosing the optimal weak learner. Also, given the bagging fraction at .9, the model is using practically the entire training set instead of a subsample.

## (b) 

<i>Which model do you think would be more predictive of other samples?</i>

Since the right hand model overfits on training data, the left hand model would be more predicitive when generalizing to unseen data.

## (c)

<i>How would increasing interaction depth affect the slope of predictor importancefor either model in Fig. 8.24?</i>

The interaction depth parameter is the number of splits it has to perform on a tree (starting from a single node).

I re-created the output using interaction.depth = 1 with the learning rate and bagging fractions set to .1 and then set at .9.  Then I increased the interaction.depth=10 with the learning rate and bagging fractions set to .1 and then set at .9

The model with the interaction.depth = 1 with higher learning rate and bagging fractions over fit the data.  When I increased the interaction.depth = 10,  the model with the lower learning rate and bagging fractions had more predictive power because they did not over fit.

```{r}
library(AppliedPredictiveModeling)

data(solubility)
set.seed(100)
gbmTune1 <- gbm(solTrainY ~ ., data = solTrainXtrans,
                   distribution = "gaussian", 
                   bag.fraction = 0.1, 
                   n.trees = 100,
                   interaction.depth=1,
                   shrinkage = 0.1,
                   n.minobsinnode = 10)

gbmTune1A <- gbm(solTrainY ~ ., data = solTrainXtrans,
                   distribution = "gaussian", 
                   bag.fraction = 0.9, 
                   n.trees = 100,
                   interaction.depth=1,
                   shrinkage = 0.9,
                   n.minobsinnode = 10)


```


```{r}

interaction_depth_1 <- as.data.frame(varImp(gbmTune1, numTrees = 100))

interaction_depth_1 <- interaction_depth_1 %>% 
                        arrange(desc(Overall))

top20A <-head(interaction_depth_1, 20)

top20A <- as.data.frame(top20A)
top20A['Predictors']  <- rownames(top20A)
colnames(top20A) <- c("Overall", "Predictors")
rownames(top20A) <- 1:nrow(top20A)
top20A <- top20A[, c("Predictors","Overall")]

top20A %>% 
   arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "orange") + 
            theme_minimal() + 
            coord_flip() +
            labs(title="Interaction Depth = 1, learning rate= .1, bagging fraction=.1",
               y="Importance", x="Predictors") +
            scale_y_continuous()




```


```{r}

interaction_depth_1A <- as.data.frame(varImp(gbmTune1A, numTrees = 100))

interaction_depth_1A <- interaction_depth_1A %>% 
                        arrange(desc(Overall))

top20A <-head(interaction_depth_1A, 20)

top20A <- as.data.frame(top20A)
top20A['Predictors']  <- rownames(top20A)
colnames(top20A) <- c("Overall", "Predictors")
rownames(top20A) <- 1:nrow(top20A)
top20A <- top20A[, c("Predictors","Overall")]

top20A %>% 
   arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "orange") + 
            theme_minimal() + 
            coord_flip() +
            labs(title="Interaction Depth = 1, learning rate = .9, bagging fraction = .9",
               y="Importance", x="Predictors") +
            scale_y_continuous()




```




Next,  I set the interaction.depth = 10 with the learning rate and bagging fractions set to .9.

```{r}
set.seed(100)
gbmTune2 <- gbm(solTrainY ~ ., data = solTrainXtrans,
                   distribution = "gaussian", 
                   bag.fraction = 0.1, 
                   n.trees = 100,
                   interaction.depth=10,
                   shrinkage = 0.1,
                   n.minobsinnode = 10)


gbmTune2A <- gbm(solTrainY ~ ., data = solTrainXtrans,
                   distribution = "gaussian", 
                   bag.fraction = 0.9, 
                   n.trees = 100,
                   interaction.depth=10,
                   shrinkage = 0.9,
                   n.minobsinnode = 10)

interaction_depth_2 <- as.data.frame(varImp(gbmTune2, numTrees = 100))

interaction_depth_2 <- interaction_depth_2 %>% 
                        arrange(desc(Overall))

top20B <- head(interaction_depth_2, 20)

top20B <- as.data.frame(top20B)
top20B['Predictors']  <- rownames(top20B)
colnames(top20B) <- c("Overall", "Predictors")
rownames(top20B) <- 1:nrow(top20A)
top20B <- top20B[, c("Predictors","Overall")]

top20B %>% 
   arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "purple") + 
            theme_minimal() + 
            coord_flip() +
            labs(title="Interaction Depth = 10, learning rate = .1, bagging fraction = .1",
               y="Importance", x="Predictors") +
            scale_y_continuous()



```


```{r}
interaction_depth_2 <- as.data.frame(varImp(gbmTune2A, numTrees = 100))

interaction_depth_2 <- interaction_depth_2 %>% 
                        arrange(desc(Overall))

top20B <- head(interaction_depth_2, 20)

top20B <- as.data.frame(top20B)
top20B['Predictors']  <- rownames(top20B)
colnames(top20B) <- c("Overall", "Predictors")
rownames(top20B) <- 1:nrow(top20A)
top20B <- top20B[, c("Predictors","Overall")]

top20B %>% 
   arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "purple") + 
            theme_minimal() + 
            coord_flip() +
            labs(title="Interaction Depth = 10, learning rate = .9, bagging fraction = .9",
               y="Importance", x="Predictors") +
            scale_y_continuous()


```

# 8.7


```{r message=FALSE}
library(AppliedPredictiveModeling)
data(ChemicalManufacturingProcess)
```

The matrix processPredictors contains the 57 predictors (12 describing the input biological material and 45 describing the process predictors) for the 176 manufacturing runs. yield contains the percent yield for each run.

```{r}
processPredictors <-  ChemicalManufacturingProcess[2:ncol(ChemicalManufacturingProcess)]
print(paste0("The number of predictors is ", ncol(processPredictors), " and the number of observations is ", nrow(processPredictors)))
```

```{r}
(processPredictors_imputed <- preProcess(processPredictors, method=c('bagImpute')))
```
```{r}
processPredictors_imputed <- try(predict(processPredictors_imputed, processPredictors), silent = TRUE)
processPredictors_imputed
```


```{r}
missingData <- as.data.frame(colSums(is.na(processPredictors_imputed)))
colnames(missingData) <- c("NAs") 
missingData <- cbind(Predictors = rownames(missingData), missingData)
rownames(missingData) <- 1:nrow(missingData)
missingData <- missingData[missingData$NAs != 0,]
head(missingData)
```
1. Pre-Process the Data - Remove nearZeroVar predictors:

```{r}
caret::nearZeroVar(processPredictors_imputed, names = TRUE)
```

```{r}
processPredictors_imputed$BiologicalMaterial07[1:20]
```


```{r}
 processPredictors_imputed <- subset ( processPredictors_imputed, select = -BiologicalMaterial07)
```

2. Pre-Process the Data - Check and remove Multi-Colinearity. We can remove these variables for multi-colinearity:

```{r}
tooHigh <- findCorrelation(cor(processPredictors_imputed), cutoff = .9, names = TRUE)
tooHigh
```


```{r}
removePredictors <- findCorrelation(cor(processPredictors_imputed), 0.90, names = TRUE)
removePredictors

```

```{r}
processPredictors_imputed[ ,c(removePredictors)] <- list(NULL)
colnames(processPredictors_imputed)
```


```{r}
chemmfgproc <- cbind(ChemicalManufacturingProcess$Yield, processPredictors_imputed)
names(chemmfgproc)[names(chemmfgproc) == "ChemicalManufacturingProcess$Yield"] <- "Yield"
head(chemmfgproc )
```

<i>5. Split the data into Training and Test Set</i>

```{r}
chemmfgproc_train <- initial_split(chemmfgproc, prop = 0.8, strata = "Yield")
train_chemmfgproc  <- training(chemmfgproc_train)
test_chemmfgproc  <- testing(chemmfgproc_train)
print (paste0("The number of observations in the training set is ", nrow(train_chemmfgproc)))
print (paste0("The number of observations in the test set is ", nrow(test_chemmfgproc)))
```



```{r}
trainingData_x <- as.data.frame(train_chemmfgproc[2:47])
trainingData_y <- as.data.frame(train_chemmfgproc$Yield)
colnames(trainingData_y) <- c("y")

testData_x <- as.data.frame(test_chemmfgproc[2:47])
testData_y <- as.data.frame(test_chemmfgproc$Yield)
colnames(testData_y) <- c("y")

```



```{r}
controlObject <- trainControl(method = "repeatedcv", 
                              repeats = 5,
                              number = 10)

```




```{r}
set.seed(100)
rpartModel <- train(x = trainingData_x,
                    y = trainingData_y$y,
                    method = "rpart",
                    tuneLength = 30,
                    trControl = controlObject
                    )
                    
set.seed(100)
ctreeModel <- train(x = trainingData_x,
                    y = trainingData_y$y,
                    method = "ctree",
                    tuneLength = 10,
                    trControl = controlObject
                    )

set.seed(100)
gbmGrid <- expand.grid(interaction.depth = seq(1, 7, by = 2),
                        n.trees = c(seq(100, 1000, by = 50)),
                        shrinkage = c(0.01, .1),
                        n.minobsinnode = c(5, 10, 15))

set.seed(100)
gbmTune <- train(x = trainingData_x, y = trainingData_y$y,
                  method = "gbm",
                  tuneGrid = gbmGrid,
                  verbose = FALSE,
                  trControl = controlObject
                 )

set.seed(100)
cubistGrid <- expand.grid(committees = c(1, 5, 10, 50, 75, 100),
                          neighbors = c(0, 1, 3, 5, 7, 9))


cubistTuned <- train(  x= trainingData_x[, colnames(trainingData_x)],
                       y = trainingData_y$y, 
                       method = "cubist", 
                       tuneGrid = cubistGrid,
                       trControl = controlObject
                      )
  



```


## (a)
<i> Which tree-based regression model gives the optimal resampling and test set performance? </i>

The Cubist model gave the optimal re-sampling and test set performance. 

```{r}
resamples <- resamples(list(CART=rpartModel,
                            "Cond Inf Tree"=ctreeModel,
                            "Boosted Tree" =gbmTune,
                            Cubist=cubistTuned))
summary(resamples)
```

```{r}
rpartPredictions <- predict(rpartModel, testData_x)
ctreePredictions <- predict(ctreeModel, testData_x)
gbmPredictions <- predict(gbmTune, testData_x)
cubistPredictions <- predict(cubistTuned, testData_x)
```

rPart:
```{r}
postResample(pred=rpartPredictions, obs=testData_y$y)
```

cTree:
```{r}
postResample(pred=ctreePredictions, obs=testData_y$y)
```

gbm:
```{r}
postResample(pred=gbmPredictions, obs=testData_y$y)
```

Cubist:

```{r}
postResample(pred=cubistPredictions, obs=testData_y$y)
```

## (b)

<i>Which predictors are most important in the optimal tree-based regression model?</i>

Optimal Tree Based Regression top ten most important predictors are:

ManufacturingProcess32
ManufacturingProcess17
BiologicalMaterial06
ManufacturingProcess09			
ManufacturingProcess04		
ManufacturingProcess28		
ManufacturingProcess13	
ManufacturingProcess33	
ManufacturingProcess39	
BiologicalMaterial03


<i>Do either the biological or process variables dominate the list?</I>

Of the top 20, 14 are Manufacturing processes and only 6 are biological.

<i>How do the top 10 important predictors compare to the top 10 predictors from the optimal linear and nonlinear models?</i>

For both the Linear and Non-Linear models, there is one more biological process in the top ten. There are six predictors among the top ten that they all have in common:

ManufacturingProcess13	
ManufacturingProcess32	
BiologicalMaterial06
ManufacturingProcess17	
ManufacturingProcess09	
BiologicalMaterial03






<b>Optimal Linear top ten most important predictors are:</b>

ManufacturingProcess32				
ManufacturingProcess09				
ManufacturingProcess13			
ManufacturingProcess17			
ManufacturingProcess36			
BiologicalMaterial06			
BiologicalMaterial08				
ManufacturingProcess06			
ManufacturingProcess33		
BiologicalMaterial03


<b>Optimal Non-Linear top ten most important predictors are:</b>

ManufacturingProcess13		
ManufacturingProcess32		
BiologicalMaterial06
ManufacturingProcess17	
ManufacturingProcess09		
BiologicalMaterial03
ManufacturingProcess06	
ManufacturingProcess36
BiologicalMaterial11
ManufacturingProcess11

```{r}
cubistTuned1 <- varImp(cubistTuned)
cubistTuned1<- cubistTuned1$importance %>% 
  arrange(desc(Overall)) 
cubistTuned1 <-   head(cubistTuned1,20)
```

```{r}
cubistTuned1_df <- as.data.frame(cubistTuned1)
cubistTuned1_df['Predictors']  <- rownames(cubistTuned1)
colnames(cubistTuned1_df) <- c("Overall", "Predictors")
rownames(cubistTuned1_df) <- 1:nrow(cubistTuned1_df)
```

```{r}
cubistTuned1_df %>% 
            arrange(Overall)%>% 
            mutate(name = factor(Predictors, levels=c(Predictors))) %>% 
            ggplot(aes(x=name, y=Overall)) +
            geom_segment(aes(xend = Predictors, yend = 0)) +
            geom_point(size = 4, color = "red") + 
            theme_minimal() + 
            coord_flip() +
            labs(title="cubist Predictor Variable Importance",
               y="cubist Importance", x="Predictors") +
            scale_y_continuous()
```


## (c)

<i>Plot the optimal single tree with the distribution of yield in the terminal nodes. Does this view of the data provide additional knowledge about the biological or process predictors and their relationship with yield?</i>

The view confirms that ManufacturingProcess32 is the optimal split in the data and carries the most importance to the Yield. 


```{r}
plot(as.party(rpartModel$finalModel))
```













