Data624_HW9
Alexis Mekueko
11/30/2021
Chapter 8: Regression Trees and Rule-Based Models
Do problems 8.1, 8.2, 8.3, and 8.7 in Kuhn and Johnson. Please submit the Rpubs link along with the .rmd file.
Exercises
8.1. Recreate the simulated data from Exercise 7.2:
library(mlbench)## Warning: package 'mlbench' was built under R version 4.0.5set.seed(200)
simulated <- mlbench.friedman1(200, sd = 1)
simulated <- cbind(simulated$x, simulated$y)
simulated <- as.data.frame(simulated)
colnames(simulated)[ncol(simulated)] <- "y"- Fit a random forest model to all of the predictors, then estimate the variable importance scores:
library(randomForest)## Warning: package 'randomForest' was built under R version 4.0.5## randomForest 4.6-14## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:ggplot2':
##
## margin## The following object is masked from 'package:dplyr':
##
## combinelibrary(caret)
model1 <- randomForest(y ~ ., data = simulated,
importance = TRUE,
ntree = 1000)
rfImp1 <- varImp(model1, scale = FALSE)
rfImp1## Overall
## V1 8.732235404
## V2 6.415369387
## V3 0.763591825
## V4 7.615118809
## V5 2.023524577
## V6 0.165111172
## V7 -0.005961659
## V8 -0.166362581
## V9 -0.095292651
## V10 -0.074944788Did the random forest model significantly use the uninformative predictors (V6 – V10)? No, the random forest modest significant predictors are V1, V2, V4.
- Now add an additional predictor that is highly correlated with one of the informative predictors. For example:
simulated$duplicate1 <- simulated$V1 + rnorm(200) * .1
cor(simulated$duplicate1, simulated$V1)## [1] 0.9460206Fit another random forest model to these data.
model2 <- randomForest(y ~ ., data = simulated,
importance = TRUE,
ntree = 1000)
rfImp2 <- varImp(model2, scale = FALSE)
rfImp2## Overall
## V1 5.69119973
## V2 6.06896061
## V3 0.62970218
## V4 7.04752238
## V5 1.87238438
## V6 0.13569065
## V7 -0.01345645
## V8 -0.04370565
## V9 0.00840438
## V10 0.02894814
## duplicate1 4.28331581Did the importance score for V1 change? Yes, the importance score for V1 change. What happens when you add another predictor that is also highly correlated with V1? The addition of another predictor highly correlated with V1 had influence in the random forest model. V1 is no longer the most significant predictor. with the addition of predictor, duplicated1 , we see V4 is now the most significant predictor in the random forest model.
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 Stroblet al. (2007).
library(party)## Warning: package 'party' was built under R version 4.0.5## Loading required package: grid## Loading required package: mvtnorm## Loading required package: modeltools## Loading required package: stats4##
## Attaching package: 'modeltools'## The following object is masked from 'package:plyr':
##
## empty## The following object is masked from 'package:fabletools':
##
## refit## The following object is masked from 'package:BayesFactor':
##
## posterior## Loading required package: strucchange## Warning: package 'strucchange' was built under R version 4.0.5## Loading required package: sandwich## Warning: package 'sandwich' was built under R version 4.0.4##
## Attaching package: 'party'## The following object is masked from 'package:fabletools':
##
## response model3 <- cforest(y~ ., data = simulated)
rfImp3 <- varImp(model3, conditional = TRUE)
rfImp3## Overall
## V1 1.8986239733
## V2 4.8021626697
## V3 0.0229993405
## V4 6.0471706526
## V5 0.9850544288
## V6 -0.0119652434
## V7 -0.0104327775
## V8 -0.0104862941
## V9 0.0004516316
## V10 -0.0074652543
## duplicate1 1.9703660210Do these importances show the same pattern as the traditional random forest model? Yes, it is about the same with exception that the most significant predictor is V4 instead of V1. V6-V10 still falling at the bottom.
- Repeat this process with different tree models, such as boosted trees and Cubist. Does the same pattern occur?
Cubist Model
library(Cubist)## Warning: package 'Cubist' was built under R version 4.0.5model4 <- cubist(x = simulated[, -(ncol(simulated)-1)], y = simulated$y, committees = 100)
rfImp4 <- varImp(model4, conditional = TRUE)
rfImp4## Overall
## V3 43.5
## V1 52.5
## V2 59.5
## duplicate1 27.5
## V4 46.0
## V8 4.0
## V5 27.0
## V6 10.0
## V10 1.0
## V7 0.0
## V9 0.0summary(model4)##
## Call:
## cubist.default(x = simulated[, -(ncol(simulated) - 1)], y =
## simulated$y, committees = 100)
##
##
## Cubist [Release 2.07 GPL Edition] Tue Nov 30 18:47:01 2021
## ---------------------------------
##
## Target attribute `outcome'
##
## Read 200 cases (12 attributes) from undefined.data
##
## Model 1:
##
## Rule 1/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 1.936506]
##
## outcome = 0.269253 + 8.9 V4 + 7.1 V2 + 5.1 V5 + 4.8 V1 + 3.2 duplicate1
##
## Model 2:
##
## Rule 2/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 1.990785]
##
## outcome = 0.826137 + 9 V4 + 8.3 V1 + 7.3 V2 + 5.2 V5 - 3 V6
##
## Model 3:
##
## Rule 3/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.029922]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 2.658355 - 12.6 V3 + 11.6 duplicate1 + 10.2 V4 + 7.8 V2
## + 2.4 V6 + 1.5 V1 + 0.5 V5
##
## Rule 3/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 2.450924]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 2.108552 + 35 V2 + 10.4 V4 - 6 V3 + 1.3 duplicate1 + 0.8 V5
##
## Rule 3/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.814725]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -21.377814 + 25.2 V3 + 11.3 V4 + 11 V1 + 8.1 V2 + 7.1 V5
##
## Rule 3/4: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.682001]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 43.992161 - 34.9 V2 + 0.2 V4
##
## Model 4:
##
## Rule 4/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.058539]
##
## outcome = 0.1879 + 9.1 V4 + 7.9 V1 + 7 V5 + 7.2 V2 - 3.1 V6
##
## Model 5:
##
## Rule 5/1: [106 cases, mean 12.285650, range 3.55596 to 23.3956, est err 3.237101]
##
## if
## V2 <= 0.5403168
## then
## outcome = -7.104052 + 28.4 V2 + 12.9 duplicate1 + 7.9 V4 + 0.3 V5
##
## Rule 5/2: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.238507]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 3.509951 - 13.8 V3 + 12.8 duplicate1 + 9.9 V4 + 7.7 V2
## + 2.6 V6 + 0.4 V1
##
## Rule 5/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.820595]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -20.764964 + 25.3 V3 + 11.4 V1 + 11.2 V4 + 8.2 V2 + 5.3 V5
##
## Rule 5/4: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.651464]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 43.756229 - 34.5 V2 + 0.2 V4
##
## Model 6:
##
## Rule 6/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.317699]
##
## outcome = 1.218663 + 12.6 V1 + 10 V4 + 8.5 V5 - 5.4 duplicate1 + 4.1 V2
## - 2.6 V6
##
## Model 7:
##
## Rule 7/1: [14 cases, mean 11.101607, range 5.325261 to 17.15359, est err 3.645042]
##
## if
## V2 <= 0.9183624
## duplicate1 <= 0.07016665
## then
## outcome = -2.763226 + 43.1 duplicate1 + 12.8 V2 + 10.6 V4
##
## Rule 7/2: [12 cases, mean 14.461304, range 7.444598 to 19.79759, est err 3.295416]
##
## if
## V2 > 0.9183624
## then
## outcome = 5.665264 + 11.8 duplicate1 + 2.1 V2 + 1.5 V4
##
## Rule 7/3: [100 cases, mean 14.512158, range 3.55596 to 28.38167, est err 2.334867]
##
## if
## V3 > 0.4459752
## duplicate1 > 0.07016665
## then
## outcome = -14.769383 + 18.5 V3 + 13.7 V2 + 9.7 V4 + 7 duplicate1
## + 2.6 V5
##
## Rule 7/4: [83 cases, mean 15.070425, range 5.784235 to 23.57269, est err 3.290021]
##
## if
## V3 <= 0.4459752
## duplicate1 > 0.07016665
## then
## outcome = 6.19234 - 21.2 V3 + 14.9 duplicate1 + 13.1 V2 - 8.1 V1
## + 7.7 V4
##
## Model 8:
##
## Rule 8/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.479266]
##
## outcome = 0.203753 + 13 V1 + 10 V4 + 9.3 V5 - 5.7 duplicate1 + 2.7 V2
##
## Model 9:
##
## Rule 9/1: [17 cases, mean 10.657375, range 5.325261 to 17.15359, est err 4.792915]
##
## if
## duplicate1 <= 0.07016665
## then
## outcome = -2.702351 + 43.8 duplicate1 + 15.2 V2 + 10.1 V4
##
## Rule 9/2: [78 cases, mean 13.686872, range 3.55596 to 28.38167, est err 2.377873]
##
## if
## V2 <= 0.7803221
## V3 > 0.4459752
## duplicate1 > 0.07016665
## then
## outcome = -15.617722 + 20.1 V3 + 16.6 V2 + 10.1 V4 + 6.1 duplicate1
##
## Rule 9/3: [68 cases, mean 14.288445, range 5.784235 to 23.57269, est err 3.086318]
##
## if
## V2 <= 0.7803221
## V3 <= 0.4459752
## duplicate1 > 0.07016665
## then
## outcome = 4.558539 - 18.8 V3 + 16.2 V2 + 13.9 duplicate1 + 8.1 V4
## - 6.6 V1 - 0.2 V6
##
## Rule 9/4: [17 cases, mean 16.810188, range 7.444598 to 25.01616, est err 4.524103]
##
## if
## V1 <= 0.671787
## V2 > 0.7803221
## V3 > 0.6060145
## then
## outcome = 5.227253 + 36.2 V3 - 28.3 V2 + 15.8 duplicate1 + 6.3 V4
##
## Rule 9/5: [52 cases, mean 16.931290, range 8.442596 to 26.94567, est err 4.433290]
##
## if
## V1 > 0.671787
## then
## outcome = 29.735355 - 24.5 V1 + 7.4 V4 + 0.9 V2 + 0.7 duplicate1
## - 0.2 V6
##
## Rule 9/6: [16 cases, mean 17.710804, range 9.597466 to 22.05247, est err 4.757797]
##
## if
## V1 <= 0.671787
## V2 > 0.7803221
## V3 <= 0.6060145
## then
## outcome = 39.25704 - 27 V2 + 14.4 V1 - 11.7 V3 + 1.8 duplicate1
##
## Model 10:
##
## Rule 10/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.432866]
##
## outcome = -1.808888 + 13.8 V1 + 10.1 V4 + 9.8 V5 - 3.7 duplicate1
## + 3.4 V2
##
## Model 11:
##
## Rule 11/1: [110 cases, mean 14.087054, range 3.55596 to 28.38167, est err 2.779835]
##
## if
## V3 > 0.4459752
## then
## outcome = -12.561468 + 17.6 V3 + 14.5 V2 + 9.5 V4 + 5.4 duplicate1
##
## Rule 11/2: [90 cases, mean 14.818451, range 5.325261 to 23.57269, est err 3.266586]
##
## if
## V3 <= 0.4459752
## then
## outcome = 6.060055 - 18.2 V3 + 16.1 duplicate1 + 14 V2 - 10.5 V1 + 8 V4
## - 0.2 V6
##
## Rule 11/3: [41 cases, mean 17.110712, range 7.444598 to 25.01616, est err 6.489881]
##
## if
## V2 > 0.7803221
## then
## outcome = 8.034255 + 2.3 V2 + 1.6 V4 + 1.4 duplicate1 - 0.6 V6
##
## Rule 11/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 2.897774]
##
## if
## V1 <= 0.7421085
## V2 > 0.7803221
## then
## outcome = 40.756111 - 31.7 V2 + 11.1 V1 + 1 V4 + 0.9 duplicate1 - 0.4 V6
##
## Model 12:
##
## Rule 12/1: [164 cases, mean 13.949840, range 3.55596 to 28.38167, est err 2.349439]
##
## if
## V1 <= 0.7514832
## then
## outcome = -4.684432 + 15.1 V1 + 11.1 V4 + 9.8 V5 + 5.1 V2
##
## Rule 12/2: [36 cases, mean 16.540636, range 8.442596 to 23.57269, est err 2.349583]
##
## if
## V1 > 0.7514832
## then
## outcome = 0.145388 + 10.2 V4 + 7.4 V5 + 7 V1 + 2.9 V2
##
## Model 13:
##
## Rule 13/1: [110 cases, mean 14.087054, range 3.55596 to 28.38167, est err 2.850824]
##
## if
## V3 > 0.4459752
## then
## outcome = -11.696705 + 18.1 V3 + 14 V2 + 8.9 V4 + 3.9 V1
##
## Rule 13/2: [90 cases, mean 14.818451, range 5.325261 to 23.57269, est err 3.362806]
##
## if
## V3 <= 0.4459752
## then
## outcome = 6.742455 - 20.9 V3 + 12.8 duplicate1 + 13.4 V2 + 8.3 V4
## - 6.6 V1
##
## Rule 13/3: [41 cases, mean 17.110712, range 7.444598 to 25.01616, est err 2.771123]
##
## if
## V2 > 0.7803221
## then
## outcome = 44.851998 - 33.1 V2 + 1.5 V4 + 1.2 duplicate1
##
## Model 14:
##
## Rule 14/1: [164 cases, mean 13.949840, range 3.55596 to 28.38167, est err 2.508220]
##
## if
## V1 <= 0.7514832
## then
## outcome = -4.057296 + 15.4 V1 + 11 V4 + 10.1 V5 + 3.1 V2 - 0.4 V6
## + 0.2 V3
##
## Rule 14/2: [36 cases, mean 16.540636, range 8.442596 to 23.57269, est err 2.458088]
##
## if
## V1 > 0.7514832
## then
## outcome = -1.343076 + 10.7 V4 + 8.6 V1 + 8.4 V5 - 2.1 V6 + 1.9 V2
## + 1.2 V3
##
## Model 15:
##
## Rule 15/1: [85 cases, mean 13.413920, range 3.55596 to 28.38167, est err 2.607504]
##
## if
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -11.744776 + 17.3 V3 + 15.7 V2 + 8.7 V4 + 3.7 V1
## + 0.2 duplicate1
##
## Rule 15/2: [74 cases, mean 14.074516, range 5.325261 to 23.57269, est err 3.106939]
##
## if
## V2 <= 0.7803221
## V3 <= 0.4459752
## then
## outcome = 6.285717 - 21.4 V3 + 15.1 V2 + 8.2 V4 + 6.9 duplicate1
##
## Rule 15/3: [41 cases, mean 17.110712, range 7.444598 to 25.01616, est err 2.792759]
##
## if
## V2 > 0.7803221
## then
## outcome = 43.111191 - 30.3 V2 + 1.6 V4 + 1.3 duplicate1
##
## Model 16:
##
## Rule 16/1: [164 cases, mean 13.949840, range 3.55596 to 28.38167, est err 2.496711]
##
## if
## V1 <= 0.7514832
## then
## outcome = -4.747534 + 14.9 V1 + 11.7 V4 + 9.9 V5 + 3.6 V2
## + 0.5 duplicate1 + 0.2 V3
##
## Rule 16/2: [36 cases, mean 16.540636, range 8.442596 to 23.57269, est err 2.689233]
##
## if
## V1 > 0.7514832
## then
## outcome = -2.046392 + 10.8 V4 + 7.5 V5 + 4.3 V1 + 3.1 duplicate1
## + 2.1 V2 + 1.4 V3
##
## Model 17:
##
## Rule 17/1: [85 cases, mean 13.413920, range 3.55596 to 28.38167, est err 2.580971]
##
## if
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -11.940892 + 18.3 V3 + 15.5 V2 + 8.3 V4 + 4 duplicate1
##
## Rule 17/2: [74 cases, mean 14.074516, range 5.325261 to 23.57269, est err 3.121916]
##
## if
## V2 <= 0.7803221
## V3 <= 0.4459752
## then
## outcome = 6.54601 - 21.9 V3 + 14.6 V2 + 7.7 duplicate1 + 7.9 V4
##
## Rule 17/3: [41 cases, mean 17.110712, range 7.444598 to 25.01616, est err 2.776035]
##
## if
## V2 > 0.7803221
## then
## outcome = 43.613615 - 31 V2 + 1.4 duplicate1 + 1.4 V4
##
## Model 18:
##
## Rule 18/1: [164 cases, mean 13.949840, range 3.55596 to 28.38167, est err 2.499548]
##
## if
## V1 <= 0.7514832
## then
## outcome = -5.392214 + 15.7 V1 + 12.2 V4 + 9.7 V5 + 4.4 V2
##
## Rule 18/2: [36 cases, mean 16.540636, range 8.442596 to 23.57269, est err 2.627912]
##
## if
## V1 > 0.7514832
## then
## outcome = -1.4426 + 11.2 V4 + 7.6 V5 + 7.1 V1 + 2.6 V2
##
## Model 19:
##
## Rule 19/1: [84 cases, mean 13.374577, range 3.55596 to 28.38167, est err 2.586975]
##
## if
## V2 <= 0.770291
## V3 > 0.4459752
## then
## outcome = -11.572484 + 18.8 V3 + 15 V2 + 7.7 V4 + 4 duplicate1
##
## Rule 19/2: [73 cases, mean 13.980781, range 5.325261 to 23.57269, est err 3.218686]
##
## if
## V2 <= 0.770291
## V3 <= 0.4459752
## then
## outcome = 6.635832 - 20.7 V3 + 14.2 V2 + 13.1 duplicate1 + 7.7 V4
## - 6.1 V1
##
## Rule 19/3: [43 cases, mean 17.190119, range 7.444598 to 25.01616, est err 2.792291]
##
## if
## V2 > 0.770291
## then
## outcome = 44.540363 - 31.6 V2 + 0.9 duplicate1 + 0.9 V4
##
## Model 20:
##
## Rule 20/1: [164 cases, mean 13.949840, range 3.55596 to 28.38167, est err 2.555268]
##
## if
## V1 <= 0.7514832
## then
## outcome = -5.959895 + 16 V1 + 12.6 V4 + 9.7 V5 + 4.8 V2
##
## Rule 20/2: [36 cases, mean 16.540636, range 8.442596 to 23.57269, est err 3.267745]
##
## if
## V1 > 0.7514832
## then
## outcome = 6.763101 + 10.5 V5 + 10.6 V4 - 3.4 V6 + 0.4 V1
##
## Model 21:
##
## Rule 21/1: [83 cases, mean 13.300468, range 3.55596 to 28.38167, est err 2.682181]
##
## if
## V2 <= 0.7609186
## V3 > 0.4459752
## then
## outcome = -12.155207 + 18.4 V3 + 14.6 V2 + 7.7 V4 + 4.3 V1 + 2.1 V8
##
## Rule 21/2: [72 cases, mean 13.967180, range 5.325261 to 23.57269, est err 3.008975]
##
## if
## V2 <= 0.7609186
## V3 <= 0.4459752
## then
## outcome = 5.846918 - 19.7 V3 + 15.8 V2 + 7.7 V4 + 6.9 duplicate1
##
## Rule 21/3: [27 cases, mean 16.795534, range 7.444598 to 22.05247, est err 3.537932]
##
## if
## V2 > 0.7609186
## V3 <= 0.654213
## then
## outcome = 39.512719 - 23.2 V2 - 14.3 V3 + 4.4 duplicate1
##
## Rule 21/4: [18 cases, mean 17.787848, range 13.07191 to 25.01616, est err 3.917614]
##
## if
## V2 > 0.7609186
## V3 > 0.654213
## then
## outcome = 15.537456 + 22.4 V3 - 18.8 V2 + 5.5 V4
##
## Model 22:
##
## Rule 22/1: [73 cases, mean 12.206748, range 3.55596 to 22.29367, est err 2.490807]
##
## if
## V4 <= 0.3455864
## then
## outcome = -3.892424 + 13.6 V4 + 10.7 V5 + 9.4 V1 + 4.2 V2
## + 1.3 duplicate1 - 1.2 V6
##
## Rule 22/2: [155 cases, mean 13.756007, range 3.55596 to 28.38167, est err 2.557655]
##
## if
## V1 <= 0.691673
## then
## outcome = -5.610602 + 15.4 V1 + 13.5 V4 + 9.4 V5 + 3.8 V2
## + 0.6 duplicate1
##
## Rule 22/3: [30 cases, mean 17.781307, range 8.789037 to 23.57269, est err 3.180271]
##
## if
## V1 > 0.691673
## V4 > 0.3455864
## then
## outcome = 4.858768 + 12.2 V4 + 9.5 V5
##
## Model 23:
##
## Rule 23/1: [85 cases, mean 13.413920, range 3.55596 to 28.38167, est err 2.578686]
##
## if
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -11.38938 + 18.3 V3 + 14.9 V2 + 7.3 V4 + 5.1 V1
##
## Rule 23/2: [74 cases, mean 14.074516, range 5.325261 to 23.57269, est err 3.224154]
##
## if
## V2 <= 0.7803221
## V3 <= 0.4459752
## then
## outcome = 6.375911 - 19.6 V3 + 15.4 V2 + 11.6 duplicate1 + 7 V4 - 5.8 V1
##
## Rule 23/3: [41 cases, mean 17.110712, range 7.444598 to 25.01616, est err 2.801205]
##
## if
## V2 > 0.7803221
## then
## outcome = 44.540851 - 31.7 V2 + 1 duplicate1 + 1 V4
##
## Model 24:
##
## Rule 24/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.607872]
##
## outcome = -3.604589 + 12.2 V4 + 10.6 V5 + 10.2 V1 + 3.4 V2
##
## Model 25:
##
## Rule 25/1: [85 cases, mean 13.413920, range 3.55596 to 28.38167, est err 2.505665]
##
## if
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -10.609523 + 17.3 V3 + 14.3 V2 + 7.3 V4 + 4.9 V1
## + 0.2 duplicate1
##
## Rule 25/2: [90 cases, mean 14.818451, range 5.325261 to 23.57269, est err 3.308547]
##
## if
## V3 <= 0.4459752
## then
## outcome = 7.472565 - 18.5 V3 + 13.9 V2 + 12.7 duplicate1 - 7.4 V1
## + 5.9 V4 - 0.2 V6
##
## Rule 25/3: [6 cases, mean 15.537283, range 13.07191 to 18.82835, est err 8.892220]
##
## if
## V1 > 0.7421085
## V2 > 0.7803221
## then
## outcome = 34.230604 - 21.3 V1 - 5.4 V2 + 0.5 V10
##
## Rule 25/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 3.332184]
##
## if
## V1 <= 0.7421085
## V2 > 0.7803221
## then
## outcome = 48.896153 - 38 V2 + 12.2 V1 - 3.6 V8 + 0.5 V10
##
## Model 26:
##
## Rule 26/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.685134]
##
## outcome = -3.423234 + 12.4 V4 + 10.9 V5 + 10 V1 + 2.7 V2
##
## Model 27:
##
## Rule 27/1: [85 cases, mean 13.413920, range 3.55596 to 28.38167, est err 2.536677]
##
## if
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -10.99119 + 17.3 V3 + 14.9 V2 + 7.1 V4 + 5.2 V1
## + 0.2 duplicate1
##
## Rule 27/2: [90 cases, mean 14.818451, range 5.325261 to 23.57269, est err 3.393640]
##
## if
## V3 <= 0.4459752
## then
## outcome = 7.077329 - 18.6 V3 + 14.6 V2 + 12.8 duplicate1 - 7.2 V1
## + 5.7 V4 - 0.2 V6
##
## Rule 27/3: [6 cases, mean 15.537283, range 13.07191 to 18.82835, est err 8.033576]
##
## if
## V1 > 0.7421085
## V2 > 0.7803221
## then
## outcome = 34.916417 - 21.8 V1 - 5.2 V2 + 0.5 V10
##
## Rule 27/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 3.549303]
##
## if
## V1 <= 0.7421085
## V2 > 0.7803221
## then
## outcome = 48.458363 - 37.4 V2 + 12.6 V1 - 3.6 V8 + 0.5 V10
##
## Model 28:
##
## Rule 28/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.719511]
##
## outcome = -2.945268 + 12.6 V4 + 10.9 V5 + 9.7 V1 + 2 V2
##
## Model 29:
##
## Rule 29/1: [85 cases, mean 13.413920, range 3.55596 to 28.38167, est err 2.600552]
##
## if
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -11.469155 + 17.3 V3 + 15.6 V2 + 6.9 V4 + 5.5 V1
## + 0.2 duplicate1
##
## Rule 29/2: [90 cases, mean 14.818451, range 5.325261 to 23.57269, est err 3.467560]
##
## if
## V3 <= 0.4459752
## then
## outcome = 6.655974 - 18.6 V3 + 15.3 V2 + 12.8 duplicate1 - 7 V1 + 5.5 V4
## - 0.2 V6
##
## Rule 29/3: [6 cases, mean 15.537283, range 13.07191 to 18.82835, est err 7.424666]
##
## if
## V1 > 0.7421085
## V2 > 0.7803221
## then
## outcome = 34.5494 - 22.8 V1 - 3 V2
##
## Rule 29/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 3.142060]
##
## if
## V1 <= 0.7421085
## V2 > 0.7803221
## then
## outcome = 50.014197 - 42.1 V2 + 13 duplicate1
##
## Model 30:
##
## Rule 30/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.908942]
##
## outcome = -2.082856 + 12.8 V4 + 11.2 V5 + 9.4 V1
##
## Model 31:
##
## Rule 31/1: [85 cases, mean 13.413920, range 3.55596 to 28.38167, est err 2.800211]
##
## if
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -12.378588 + 17.3 V3 + 17.6 V2 + 6.7 V4 + 5.8 V1
## + 0.2 duplicate1
##
## Rule 31/2: [90 cases, mean 14.818451, range 5.325261 to 23.57269, est err 3.782642]
##
## if
## V3 <= 0.4459752
## then
## outcome = 5.824701 - 18.8 V3 + 17.3 V2 + 12.8 duplicate1 - 6.7 V1
## + 5.3 V4 - 0.2 V6
##
## Rule 31/3: [6 cases, mean 15.537283, range 13.07191 to 18.82835, est err 6.777534]
##
## if
## V1 > 0.7421085
## V2 > 0.7803221
## then
## outcome = 36.361461 - 23 V1 - 4.2 V2 + 0.4 V10
##
## Rule 31/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 4.226573]
##
## if
## V1 <= 0.7421085
## V2 > 0.7803221
## then
## outcome = 46.563353 - 34.6 V2 + 13.4 V1 - 3.6 V8 + 0.4 V10
##
## Model 32:
##
## Rule 32/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.899177]
##
## outcome = -1.906038 + 12.9 V4 + 10.9 V5 + 9 V1
##
## Model 33:
##
## Rule 33/1: [85 cases, mean 13.413920, range 3.55596 to 28.38167, est err 2.786879]
##
## if
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -12.448892 + 17.3 V3 + 17.6 V2 + 6.6 V4 + 6.1 V1
## + 0.2 duplicate1
##
## Rule 33/2: [90 cases, mean 14.818451, range 5.325261 to 23.57269, est err 3.760767]
##
## if
## V3 <= 0.4459752
## then
## outcome = 5.616744 - 18.6 V3 + 17.3 V2 + 12.8 duplicate1 - 6.3 V1
## + 5.2 V4 - 0.2 V6
##
## Rule 33/3: [37 cases, mean 16.557484, range 8.442596 to 23.57269, est err 5.526962]
##
## if
## V1 > 0.7421085
## then
## outcome = 35.81146 - 22.5 V1 - 3.8 V2 + 0.4 V10
##
## Rule 33/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 4.721152]
##
## if
## V1 <= 0.7421085
## V2 > 0.7803221
## then
## outcome = 41.891639 - 29.3 V2 + 16.1 V1 - 11.4 V3 + 0.3 duplicate1
## + 0.2 V4
##
## Model 34:
##
## Rule 34/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.969827]
##
## outcome = -2.36173 + 13.7 V4 + 11.1 V5 + 10 V1
##
## Model 35:
##
## Rule 35/1: [79 cases, mean 13.052387, range 3.55596 to 28.38167, est err 2.877875]
##
## if
## V1 <= 0.8392937
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -15.056667 + 19.1 V3 + 19.6 V2 + 7.8 V1 + 6.1 V4
##
## Rule 35/2: [90 cases, mean 14.818451, range 5.325261 to 23.57269, est err 3.754915]
##
## if
## V3 <= 0.4459752
## then
## outcome = 6.083732 - 18.7 V3 + 17.3 V2 + 12.8 duplicate1 - 7.3 V1
## + 4.4 V4 - 0.2 V6
##
## Rule 35/3: [6 cases, mean 15.537283, range 13.07191 to 18.82835, est err 7.184443]
##
## if
## V1 > 0.7421085
## V2 > 0.7803221
## then
## outcome = 35.981478 - 25.1 V1 - 1.8 V2
##
## Rule 35/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 4.840041]
##
## if
## V1 <= 0.7421085
## V2 > 0.7803221
## then
## outcome = 50.644825 - 39.5 V2 + 13.7 duplicate1 - 10.3 V3
##
## Rule 35/5: [7 cases, mean 17.445217, range 11.29407 to 21.87062, est err 4.098043]
##
## if
## V1 > 0.8392937
## V3 > 0.4459752
## then
## outcome = -10.454608 + 15.5 V2 + 13.6 V3 + 4.9 V4 + 4.1 V1
## + 0.7 duplicate1
##
## Model 36:
##
## Rule 36/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.934388]
##
## outcome = -1.826579 + 13.7 V4 + 10.8 V5 + 9.1 V1
##
## Model 37:
##
## Rule 37/1: [79 cases, mean 13.052387, range 3.55596 to 28.38167, est err 2.823941]
##
## if
## V1 <= 0.8392937
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -15.554826 + 19.1 V3 + 19.7 V2 + 8.7 V1 + 6.1 V4
## + 0.2 duplicate1
##
## Rule 37/2: [90 cases, mean 14.818451, range 5.325261 to 23.57269, est err 3.712238]
##
## if
## V3 <= 0.4459752
## then
## outcome = 5.545833 - 18.6 V3 + 17.3 V2 + 12.8 duplicate1 - 6.4 V1
## + 4.4 V4 - 0.2 V6
##
## Rule 37/3: [6 cases, mean 15.537283, range 13.07191 to 18.82835, est err 6.794468]
##
## if
## V1 > 0.7421085
## V2 > 0.7803221
## then
## outcome = 35.359563 - 24 V1 - 1.7 V2
##
## Rule 37/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 4.738714]
##
## if
## V1 <= 0.7421085
## V2 > 0.7803221
## then
## outcome = 51.161893 - 41.1 V2 + 14.4 duplicate1 - 9.5 V3 + 0.5 V10
##
## Rule 37/5: [7 cases, mean 17.445217, range 11.29407 to 21.87062, est err 4.121232]
##
## if
## V1 > 0.8392937
## V3 > 0.4459752
## then
## outcome = -10.699577 + 15.6 V2 + 13.3 V3 + 5 V4 + 4.6 V1 + 1 duplicate1
##
## Model 38:
##
## Rule 38/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.936890]
##
## outcome = -1.306362 + 13.7 V4 + 10.7 V5 + 8.2 V1
##
## Model 39:
##
## Rule 39/1: [79 cases, mean 13.052387, range 3.55596 to 28.38167, est err 2.863247]
##
## if
## V1 <= 0.8392937
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -16.574085 + 19.6 V3 + 19.8 V2 + 9.8 V1 + 6.2 V4
##
## Rule 39/2: [74 cases, mean 14.074516, range 5.325261 to 23.57269, est err 3.363985]
##
## if
## V2 <= 0.7803221
## V3 <= 0.4459752
## then
## outcome = 5.008325 - 20 V3 + 17.9 V2 + 7.7 duplicate1 + 4.5 V4
##
## Rule 39/3: [6 cases, mean 15.537283, range 13.07191 to 18.82835, est err 6.484748]
##
## if
## V1 > 0.7421085
## V2 > 0.7803221
## then
## outcome = 34.805819 - 23 V1 - 1.7 V2
##
## Rule 39/4: [41 cases, mean 17.110712, range 7.444598 to 25.01616, est err 5.266794]
##
## if
## V2 > 0.7803221
## then
## outcome = 51.271332 - 41.7 V2 + 15.1 duplicate1 - 9.4 V3 + 0.6 V10
##
## Rule 39/5: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 6.400293]
##
## if
## V1 <= 0.7421085
## V2 > 0.7803221
## then
## outcome = 28.216438 - 31.5 V2 + 20.2 V3 + 11.2 V1 + 0.4 duplicate1
## + 0.2 V4
##
## Rule 39/6: [6 cases, mean 18.174103, range 11.29407 to 21.87062, est err 3.115529]
##
## if
## V1 > 0.8392937
## V2 <= 0.7803221
## V3 > 0.4459752
## then
## outcome = -11.019867 + 15.7 V2 + 13.1 V3 + 5.2 V1 + 5 V4
## + 1.2 duplicate1
##
## Model 40:
##
## Rule 40/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.984973]
##
## outcome = -0.610226 + 14 V4 + 10.5 V5 + 7.3 V1
##
## Model 41:
##
## Rule 41/1: [101 cases, mean 14.160264, range 3.55596 to 28.38167, est err 3.117054]
##
## if
## V2 <= 0.9183624
## V3 > 0.4459752
## then
## outcome = -12.978808 + 17.5 V2 + 16.7 V3 + 7.4 V1 + 5.4 V4
## + 0.6 duplicate1
##
## Rule 41/2: [12 cases, mean 14.461304, range 7.444598 to 19.79759, est err 3.082060]
##
## if
## V2 > 0.9183624
## then
## outcome = 8.93569 + 12.4 duplicate1
##
## Rule 41/3: [87 cases, mean 14.707060, range 5.325261 to 23.57269, est err 3.617468]
##
## if
## V2 <= 0.9183624
## V3 <= 0.4459752
## then
## outcome = 5.908765 - 21.1 V3 + 15.8 V2 + 14.8 duplicate1 - 7.2 V1
## + 3.7 V4
##
## Model 42:
##
## Rule 42/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 3.032255]
##
## outcome = -0.940077 + 14 V4 + 11.1 V5 + 7.3 V1
##
## Model 43:
##
## Rule 43/1: [54 cases, mean 10.302123, range 3.55596 to 18.97473, est err 3.088582]
##
## if
## V1 <= 0.2353505
## then
## outcome = -1.296275 + 11.8 V2 + 6.9 V4 + 2.8 V8 + 0.7 duplicate1
##
## Rule 43/2: [60 cases, mean 15.108373, range 4.888355 to 28.38167, est err 3.084596]
##
## if
## V1 > 0.2353505
## V2 <= 0.7803221
## V3 > 0.4474419
## then
## outcome = -8.95972 + 22.5 V2 + 15.6 V3 + 5.8 V4 + 0.4 duplicate1
##
## Rule 43/3: [51 cases, mean 15.516024, range 7.520004 to 23.57269, est err 3.534898]
##
## if
## V1 > 0.2353505
## V2 <= 0.7803221
## V3 <= 0.4474419
## then
## outcome = 7.944976 + 23.2 V2 - 15 V3 + 0.9 duplicate1 + 0.5 V4
##
## Rule 43/4: [37 cases, mean 16.557484, range 8.442596 to 23.57269, est err 5.432818]
##
## if
## V1 > 0.7421085
## then
## outcome = 34.906385 - 22.7 V1 - 1.9 V2
##
## Rule 43/5: [41 cases, mean 17.110712, range 7.444598 to 25.01616, est err 5.338390]
##
## if
## V2 > 0.7803221
## then
## outcome = 51.20332 - 42.4 V2 + 15.9 duplicate1 - 9.1 V3 + 0.7 V10
##
## Rule 43/6: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 8.919487]
##
## if
## V1 <= 0.7421085
## V2 > 0.7803221
## V3 > 0.7253194
## then
## outcome = 27.660474 - 31.2 V2 + 19.5 V3 + 12.4 V1 + 0.4 duplicate1
##
## Model 44:
##
## Rule 44/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.897039]
##
## outcome = -1.668992 + 14.8 V4 + 9.9 V5 + 4.4 V1 + 3.2 duplicate1
## + 1.9 V2
##
## Model 45:
##
## Rule 45/1: [20 cases, mean 10.293891, range 5.901247 to 15.07244, est err 2.825128]
##
## if
## V1 <= 0.2295824
## V2 <= 0.7803221
## V3 > 0.5220815
## then
## outcome = -18.901792 + 39.5 V1 + 28.8 V3 + 11.5 duplicate1 + 2.8 V2
## + 1 V4
##
## Rule 45/2: [98 cases, mean 14.513915, range 3.55596 to 23.57269, est err 2.804668]
##
## if
## V3 <= 0.5220815
## then
## outcome = 3.467237 - 14.9 V3 + 10.8 duplicate1 + 8.1 V2 + 5.8 V4
## + 2.7 V8
##
## Rule 45/3: [43 cases, mean 14.729810, range 7.520004 to 23.3956, est err 4.157516]
##
## if
## V1 > 0.2295824
## V2 <= 0.6359793
## V3 <= 0.4474419
## then
## outcome = 2.056531 + 26.6 V2 - 17.8 V3 + 9.3 duplicate1 + 4.8 V4
## - 3.1 V6
##
## Rule 45/4: [61 cases, mean 14.947106, range 4.888355 to 28.38167, est err 3.067295]
##
## if
## V1 > 0.2295824
## V2 <= 0.7803221
## V3 > 0.4474419
## then
## outcome = -8.15444 + 20.8 V2 + 15.4 V3 + 5.4 V4 + 0.5 V1
##
## Rule 45/5: [52 cases, mean 16.931290, range 8.442596 to 26.94567, est err 4.811911]
##
## if
## V1 > 0.671787
## then
## outcome = 39.66889 - 27.9 V1 - 2.5 V2
##
## Rule 45/6: [33 cases, mean 17.246849, range 7.444598 to 25.01616, est err 5.462549]
##
## if
## V1 <= 0.671787
## V2 > 0.7803221
## then
## outcome = 44.119878 - 33.4 V2 + 17.5 V1 - 12.6 V3
##
## Rule 45/7: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 7.946625]
##
## if
## V1 <= 0.671787
## V2 > 0.7803221
## V3 > 0.7253194
## then
## outcome = 24.646795 - 33 V2 + 23.9 V3 + 13.2 V1
##
## Rule 45/8: [8 cases, mean 19.741924, range 14.96002 to 23.57269, est err 5.171080]
##
## if
## V1 > 0.2295824
## V2 > 0.6359793
## V2 <= 0.7803221
## V3 <= 0.4474419
## then
## outcome = 24.257865 - 22.5 V3
##
## Model 46:
##
## Rule 46/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.686857]
##
## outcome = -3.247296 + 14.6 V4 + 10.2 V5 + 7.3 V1 + 5.7 V2
##
## Model 47:
##
## Rule 47/1: [131 cases, mean 14.024858, range 3.55596 to 23.57269, est err 3.052760]
##
## if
## V3 <= 0.654213
## then
## outcome = 4.360483 - 13.2 V3 + 12.8 duplicate1 + 12.2 V2 + 4.6 V4
## + 0.2 V1
##
## Rule 47/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 4.286439]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -12.573042 + 29.1 V2 + 20.1 V1 + 1 duplicate1 + 0.4 V4
##
## Rule 47/3: [69 cases, mean 15.159133, range 4.888355 to 28.38167, est err 3.188226]
##
## if
## V3 > 0.654213
## then
## outcome = -18.03203 + 25.4 V3 + 12 V1 + 10.4 V2 + 5.3 V4
##
## Rule 47/4: [11 cases, mean 15.621394, range 7.444598 to 21.77924, est err 5.409405]
##
## if
## V1 <= 0.7340099
## V2 > 0.8676087
## V3 <= 0.654213
## then
## outcome = 8.912724 - 15.3 V3 + 12.9 V1 + 3.7 duplicate1 + 2.5 V2
## + 1.1 V4
##
## Rule 47/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 4.441586]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 39.584575 - 32 V2
##
## Model 48:
##
## Rule 48/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.679224]
##
## outcome = -1.848724 + 14.1 V4 + 10 V5 + 5.2 V1 + 4.2 V2
##
## Model 49:
##
## Rule 49/1: [73 cases, mean 12.761858, range 3.55596 to 23.3956, est err 2.544933]
##
## if
## V1 <= 0.7340099
## V2 <= 0.770291
## V3 <= 0.5983401
## then
## outcome = 2.46942 + 16.2 V1 - 13.6 V3 + 12.6 V2 + 6.1 V4 + 0.4 V8
## + 0.3 duplicate1 - 0.2 V6
##
## Rule 49/2: [73 cases, mean 14.106288, range 4.888355 to 28.38167, est err 3.227911]
##
## if
## V1 <= 0.7340099
## V3 > 0.5983401
## then
## outcome = -17.184164 + 20.5 V3 + 15.6 V2 + 13.1 V1 + 6.6 V4 + 0.5 V8
##
## Rule 49/3: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.918238]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -11.203455 + 28.1 V2 + 20.3 V1 + 1.2 duplicate1 + 0.8 V4
## - 0.7 V6
##
## Rule 49/4: [43 cases, mean 17.190119, range 7.444598 to 25.01616, est err 5.695974]
##
## if
## V2 > 0.770291
## then
## outcome = 52.488559 - 46 V2 + 17.1 duplicate1 - 9.1 V3 + 0.6 V10
##
## Rule 49/5: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 8.650084]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## V3 > 0.7253194
## then
## outcome = 31.402996 - 50.1 V2 + 27.2 V3 + 16 V1 + 5.7 V6
## + 0.7 duplicate1 + 0.3 V10
##
## Rule 49/6: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.789431]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 41.297675 - 31.6 V2
##
## Model 50:
##
## Rule 50/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.656644]
##
## outcome = -0.678184 + 13.9 V4 + 9.5 V5 + 4.2 V2 + 3.1 duplicate1
## + 2.2 V1 - 1.6 V6
##
## Model 51:
##
## Rule 51/1: [73 cases, mean 12.761858, range 3.55596 to 23.3956, est err 2.740308]
##
## if
## V1 <= 0.7340099
## V2 <= 0.770291
## V3 <= 0.5983401
## then
## outcome = 2.153317 - 14.7 V3 + 13.8 V2 + 9 V1 + 7 duplicate1 + 6.1 V4
##
## Rule 51/2: [73 cases, mean 14.106288, range 4.888355 to 28.38167, est err 3.314311]
##
## if
## V1 <= 0.7340099
## V3 > 0.5983401
## then
## outcome = -17.86201 + 21.9 V3 + 15.5 V2 + 13 V1 + 6.7 V4 + 0.3 V8
##
## Rule 51/3: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 4.145601]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -11.655464 + 30.2 V2 + 21.1 V1 + 0.4 V4
##
## Rule 51/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 5.424253]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## then
## outcome = 43.980659 - 35 V2 + 19 V1 - 11.8 V3
##
## Rule 51/5: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 6.828369]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## V3 > 0.7253194
## then
## outcome = 23.399106 - 30.1 V2 + 20.7 V3 + 14.5 V1 + 0.4 V4
##
## Rule 51/6: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.760327]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 39.711811 - 29.5 V2
##
## Model 52:
##
## Rule 52/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.641732]
##
## outcome = -1.2208 + 14 V4 + 9.7 V5 + 4.3 V2 + 3.5 V1 + 2.5 duplicate1
## - 1.6 V6
##
## Model 53:
##
## Rule 53/1: [73 cases, mean 12.761858, range 3.55596 to 23.3956, est err 2.692278]
##
## if
## V1 <= 0.7340099
## V2 <= 0.770291
## V3 <= 0.5983401
## then
## outcome = 2.603358 - 14.7 V3 + 13.7 V2 + 7.6 duplicate1 + 7.7 V1 + 6 V4
##
## Rule 53/2: [73 cases, mean 14.106288, range 4.888355 to 28.38167, est err 3.261820]
##
## if
## V1 <= 0.7340099
## V3 > 0.5983401
## then
## outcome = -17.443876 + 21.8 V3 + 15.4 V2 + 12.3 V1 + 6.6 V4 + 0.3 V8
##
## Rule 53/3: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 4.150957]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -11.50582 + 30.2 V2 + 20.7 V1 + 0.4 V4
##
## Rule 53/4: [43 cases, mean 17.190119, range 7.444598 to 25.01616, est err 5.963771]
##
## if
## V2 > 0.770291
## then
## outcome = 44.156051 - 34.9 V2 + 18.4 V1 - 11.9 V3
##
## Rule 53/5: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 8.691669]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## V3 > 0.7253194
## then
## outcome = 29.088411 - 50.1 V2 + 29.3 V3 + 16.2 V1 + 7.6 V6
##
## Rule 53/6: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.940386]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 39.288787 - 29.4 V2
##
## Model 54:
##
## Rule 54/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.698381]
##
## outcome = -1.277689 + 13.8 V4 + 9.6 V5 + 5.3 duplicate1 + 3.4 V2
##
## Model 55:
##
## Rule 55/1: [73 cases, mean 12.761858, range 3.55596 to 23.3956, est err 2.574440]
##
## if
## V1 <= 0.7340099
## V2 <= 0.770291
## V3 <= 0.5983401
## then
## outcome = 2.115021 + 16.8 V1 - 14.2 V3 + 13.5 V2 + 6.5 V4 + 0.3 V8
##
## Rule 55/2: [73 cases, mean 14.106288, range 4.888355 to 28.38167, est err 3.468887]
##
## if
## V1 <= 0.7340099
## V3 > 0.5983401
## then
## outcome = -18.299839 + 21.8 V3 + 16.5 V2 + 12.8 V1 + 6.7 V4 + 0.4 V8
##
## Rule 55/3: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.840415]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -17.576937 + 33.3 V2 + 25.1 V1 + 4.6 V4 - 0.2 V6
##
## Rule 55/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 5.314859]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## then
## outcome = 45.088301 - 36 V2 + 19.2 V1 - 11.5 V3
##
## Rule 55/5: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 7.704892]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## V3 > 0.7253194
## then
## outcome = 24.785862 - 33.9 V2 + 23.1 V3 + 15.3 V1 + 0.3 V4
##
## Rule 55/6: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.518438]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 40.923093 - 30.3 V2
##
## Model 56:
##
## Rule 56/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.679442]
##
## outcome = -1.525274 + 13.5 V4 + 9.9 V5 + 5.7 duplicate1 + 3.4 V2
##
## Model 57:
##
## Rule 57/1: [54 cases, mean 10.302123, range 3.55596 to 18.97473, est err 2.770110]
##
## if
## V1 <= 0.2353505
## then
## outcome = 0.312702 + 8.2 V2 + 7.2 V4 + 2.8 V8
##
## Rule 57/2: [62 cases, mean 13.553739, range 5.325261 to 23.3956, est err 3.505530]
##
## if
## V2 <= 0.6359793
## V3 <= 0.4474419
## then
## outcome = 2.203617 + 24.7 V2 - 17.8 V3 + 10.7 duplicate1 + 6.1 V4
## - 2.9 V6
##
## Rule 57/3: [60 cases, mean 15.108373, range 4.888355 to 28.38167, est err 2.660662]
##
## if
## V1 > 0.2353505
## V2 <= 0.7803221
## V3 > 0.4474419
## then
## outcome = -9.703564 + 19.1 V2 + 16.9 V3 + 6.2 V4 + 3.4 V1
##
## Rule 57/4: [8 cases, mean 16.549143, range 13.07191 to 19.99142, est err 6.116407]
##
## if
## V1 > 0.671787
## V2 > 0.7803221
## then
## outcome = 78.43561 - 37.1 V1 - 35.9 V2 + 0.3 V4 - 0.2 V6
##
## Rule 57/5: [33 cases, mean 17.246849, range 7.444598 to 25.01616, est err 5.546168]
##
## if
## V1 <= 0.671787
## V2 > 0.7803221
## then
## outcome = 46.960884 - 37.7 V2 + 19 V1 - 12 V3
##
## Rule 57/6: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 10.165693]
##
## if
## V1 <= 0.671787
## V2 > 0.7803221
## V3 > 0.7253194
## then
## outcome = 30.452687 - 51.2 V2 + 29.5 V3 + 17.2 V1 + 6.6 V6
##
## Rule 57/7: [23 cases, mean 19.007235, range 13.59359 to 23.57269, est err 3.759073]
##
## if
## V1 > 0.2353505
## V2 > 0.6359793
## V3 <= 0.4474419
## then
## outcome = 25.154732 - 21.8 V3
##
## Model 58:
##
## Rule 58/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.682362]
##
## outcome = -1.616169 + 13.4 V4 + 10.1 V5 + 5.4 duplicate1 + 3.7 V2
##
## Model 59:
##
## Rule 59/1: [73 cases, mean 12.761858, range 3.55596 to 23.3956, est err 2.830424]
##
## if
## V1 <= 0.7340099
## V2 <= 0.770291
## V3 <= 0.5983401
## then
## outcome = 2.563308 + 17.1 V1 - 14.2 V3 + 13.3 V2 + 7.2 V4 - 1.9 V5
## + 0.2 V8
##
## Rule 59/2: [73 cases, mean 14.106288, range 4.888355 to 28.38167, est err 3.455656]
##
## if
## V1 <= 0.7340099
## V3 > 0.5983401
## then
## outcome = -17.901076 + 21.7 V3 + 16.1 V2 + 12.7 V1 + 7.1 V4 + 0.4 V8
##
## Rule 59/3: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.695338]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -17.797738 + 32.7 V2 + 25.5 V1 + 5 V4 - 0.2 V6
##
## Rule 59/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 5.317657]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## then
## outcome = 44.97634 - 36.4 V2 + 19.3 V1 - 11.2 V3
##
## Rule 59/5: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 9.899076]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## V3 > 0.7253194
## then
## outcome = 31.317757 - 52.2 V2 + 29.1 V3 + 17.5 V1 + 6.8 V6
##
## Rule 59/6: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.551623]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 41.395354 - 31 V2
##
## Model 60:
##
## Rule 60/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.710628]
##
## outcome = -1.979193 + 13.3 V4 + 10.6 V5 + 5.7 duplicate1 + 3.7 V2
##
## Model 61:
##
## Rule 61/1: [28 cases, mean 10.201582, range 3.55596 to 17.15359, est err 2.448561]
##
## if
## V1 <= 0.2353505
## V3 <= 0.5220815
## then
## outcome = 6.568723 - 13 V3 + 6.6 V4 + 6.3 V2 + 1.1 V1 - 0.2 V6
##
## Rule 61/2: [26 cases, mean 10.410398, range 5.271123 to 18.97473, est err 3.772552]
##
## if
## V1 <= 0.2353505
## V3 > 0.5220815
## then
## outcome = -8.369456 + 20.9 V1 + 15.5 V3 + 3.5 V2 + 2.4 V4
##
## Rule 61/3: [84 cases, mean 13.472408, range 3.55596 to 28.38167, est err 3.208515]
##
## if
## V2 <= 0.7803221
## V3 > 0.4474419
## then
## outcome = -9.698308 + 18.6 V2 + 16.9 V3 + 6.3 V4 + 3.5 V1
##
## Rule 61/4: [43 cases, mean 14.729810, range 7.520004 to 23.3956, est err 3.570093]
##
## if
## V1 > 0.2353505
## V2 <= 0.6359793
## V3 <= 0.4474419
## then
## outcome = 2.31539 + 24.4 V2 - 17.9 V3 + 10.8 duplicate1 + 6.3 V4 - 3 V6
##
## Rule 61/5: [8 cases, mean 16.549143, range 13.07191 to 19.99142, est err 6.292533]
##
## if
## V1 > 0.671787
## V2 > 0.7803221
## then
## outcome = 85.344442 - 41.5 V2 - 39.5 V1 + 0.4 V4 - 0.2 V6
##
## Rule 61/6: [33 cases, mean 17.246849, range 7.444598 to 25.01616, est err 5.558332]
##
## if
## V1 <= 0.671787
## V2 > 0.7803221
## then
## outcome = 46.821053 - 38.1 V2 + 19.2 V1 - 11.7 V3
##
## Rule 61/7: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 9.711925]
##
## if
## V1 <= 0.671787
## V2 > 0.7803221
## V3 > 0.7253194
## then
## outcome = 32.676347 - 53 V2 + 28.1 V3 + 17.5 V1 + 7.1 V6
##
## Rule 61/8: [23 cases, mean 19.007235, range 13.59359 to 23.57269, est err 3.623863]
##
## if
## V1 > 0.2353505
## V2 > 0.6359793
## V3 <= 0.4474419
## then
## outcome = 24.828535 - 21.5 V3
##
## Model 62:
##
## Rule 62/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.688218]
##
## outcome = -2.748714 + 14 V4 + 10.4 V5 + 6 duplicate1 + 4.5 V2
##
## Model 63:
##
## Rule 63/1: [73 cases, mean 12.761858, range 3.55596 to 23.3956, est err 2.870085]
##
## if
## V1 <= 0.7340099
## V2 <= 0.770291
## V3 <= 0.5983401
## then
## outcome = 3.788697 + 16.5 V1 - 14.3 V3 + 12.4 V2 + 6.6 V4 - 2.2 V5
## + 0.2 V8
##
## Rule 63/2: [73 cases, mean 14.106288, range 4.888355 to 28.38167, est err 3.377519]
##
## if
## V1 <= 0.7340099
## V3 > 0.5983401
## then
## outcome = -16.811864 + 21.7 V3 + 15.2 V2 + 12 V1 + 6.5 V4 + 0.4 V8
##
## Rule 63/3: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.729423]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -17.010376 + 31.6 V2 + 25.2 V1 + 4.5 V4 - 0.2 V6
##
## Rule 63/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 5.339329]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## then
## outcome = 46.385336 - 37.8 V2 + 18.7 V1 - 11.3 V3
##
## Rule 63/5: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 8.902688]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## V3 > 0.7253194
## then
## outcome = 30.707742 - 51 V2 + 28.4 V3 + 17.3 V1 + 6.5 V6
##
## Rule 63/6: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.695532]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 40.892286 - 30.8 V2
##
## Model 64:
##
## Rule 64/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.635252]
##
## outcome = -2.912623 + 13.6 V4 + 10.4 V5 + 6.2 duplicate1 + 4.8 V2
##
## Model 65:
##
## Rule 65/1: [73 cases, mean 12.761858, range 3.55596 to 23.3956, est err 2.796170]
##
## if
## V1 <= 0.7340099
## V2 <= 0.770291
## V3 <= 0.5983401
## then
## outcome = 3.957039 + 16.3 V1 - 14.3 V3 + 12.1 V2 + 7 V4 - 2.2 V5
## + 0.2 V8
##
## Rule 65/2: [73 cases, mean 14.106288, range 4.888355 to 28.38167, est err 3.340270]
##
## if
## V1 <= 0.7340099
## V3 > 0.5983401
## then
## outcome = -16.75045 + 21.8 V3 + 14.9 V2 + 11.8 V1 + 6.9 V4 + 0.4 V8
##
## Rule 65/3: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.594538]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -16.790042 + 31.2 V2 + 25 V1 + 4.9 V4 - 0.2 V6
##
## Rule 65/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 5.329726]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## then
## outcome = 46.476398 - 38.1 V2 + 18.5 V1 - 11.1 V3
##
## Rule 65/5: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 8.947972]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## V3 > 0.7253194
## then
## outcome = 32.104466 - 52.8 V2 + 28.6 V3 + 17.1 V1 + 6.8 V6
##
## Rule 65/6: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.694140]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 41.447531 - 31.5 V2
##
## Model 66:
##
## Rule 66/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.587568]
##
## outcome = -3.038251 + 13.3 V4 + 10.4 V5 + 6.3 duplicate1 + 5.2 V2
##
## Model 67:
##
## Rule 67/1: [73 cases, mean 12.761858, range 3.55596 to 23.3956, est err 2.744181]
##
## if
## V1 <= 0.7340099
## V2 <= 0.770291
## V3 <= 0.5983401
## then
## outcome = 4.084884 + 16.2 V1 - 14.3 V3 + 11.7 V2 + 7.3 V4 - 2.2 V5
## + 0.2 V8
##
## Rule 67/2: [73 cases, mean 14.106288, range 4.888355 to 28.38167, est err 3.260532]
##
## if
## V1 <= 0.7340099
## V3 > 0.5983401
## then
## outcome = -16.635677 + 21.8 V3 + 14.5 V2 + 11.7 V1 + 7.2 V4 + 0.4 V8
##
## Rule 67/3: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.518854]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -16.659577 + 30.8 V2 + 24.9 V1 + 5.2 V4 - 0.2 V6
##
## Rule 67/4: [43 cases, mean 17.190119, range 7.444598 to 25.01616, est err 5.899369]
##
## if
## V2 > 0.770291
## then
## outcome = 46.429044 - 38.4 V2 + 18.5 V1 - 11 V3
##
## Rule 67/5: [10 cases, mean 18.320194, range 14.09741 to 25.01616, est err 8.783995]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## V3 > 0.7253194
## then
## outcome = 33.407391 - 54.4 V2 + 28.6 V3 + 17 V1 + 7 V6
##
## Rule 67/6: [8 cases, mean 18.552477, range 13.38103 to 22.29367, est err 3.566392]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## V8 <= 0.4698181
## then
## outcome = -25.939031 + 53.6 V1 - 4 V2
##
## Rule 67/7: [10 cases, mean 18.688423, range 13.07191 to 23.57269, est err 4.868005]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## V8 > 0.4698181
## then
## outcome = 27.926218 - 34.9 V2 + 22.2 V8
##
## Model 68:
##
## Rule 68/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.664227]
##
## outcome = -1.867988 + 13 V4 + 10.5 V5 + 5.9 duplicate1 + 4.9 V2 - 2 V6
##
## Model 69:
##
## Rule 69/1: [73 cases, mean 12.761858, range 3.55596 to 23.3956, est err 2.467245]
##
## if
## V1 <= 0.7340099
## V2 <= 0.770291
## V3 <= 0.5983401
## then
## outcome = 3.382045 - 14.9 V3 + 15.1 V1 + 13.2 V2 + 6.9 V4
##
## Rule 69/2: [73 cases, mean 14.106288, range 4.888355 to 28.38167, est err 3.439701]
##
## if
## V1 <= 0.7340099
## V3 > 0.5983401
## then
## outcome = -17.097107 + 22.5 V3 + 14.5 V2 + 12.1 V1 + 7.5 V4 + 0.2 V8
##
## Rule 69/3: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.115991]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 3.380437 + 24.8 V2 + 5.3 V1 + 0.4 V4
##
## Rule 69/4: [35 cases, mean 17.380442, range 7.444598 to 25.01616, est err 5.930852]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## then
## outcome = 39.84741 - 29.6 V2 + 18 V1 - 13.8 V3
##
## Rule 69/5: [13 cases, mean 18.622261, range 14.09741 to 25.01616, est err 6.829745]
##
## if
## V1 <= 0.7340099
## V2 > 0.770291
## V3 > 0.6852217
## then
## outcome = 18.002358 + 30.8 V3 - 29.3 V2 + 11.8 V1 - 4 V5 + 0.3 V4
##
## Rule 69/6: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.382001]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 41.127793 - 30.1 V2
##
## Model 70:
##
## Rule 70/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.513966]
##
## outcome = -2.344205 + 13.3 V4 + 9.5 V5 + 5.6 V2 + 4.9 duplicate1
## + 1.9 V1 - 1.8 V6
##
## Model 71:
##
## Rule 71/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.707545]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 4.252761 + 14.2 V1 - 13.3 V3 + 12.4 V2 + 6.2 V4
##
## Rule 71/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.151598]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 4.263563 + 26 V2 + 4.2 V1 + 0.3 V4
##
## Rule 71/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 3.018904]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -19.011312 + 26.9 V3 + 12.6 V1 + 10.4 V2 + 6.3 V4
##
## Rule 71/4: [23 cases, mean 16.310555, range 7.444598 to 22.1322, est err 7.035274]
##
## if
## V2 > 0.8676087
## then
## outcome = 11.540157 + 18.6 V1 - 13 V3
##
## Rule 71/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.738174]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 40.632255 - 30.6 V2
##
## Model 72:
##
## Rule 72/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.470712]
##
## outcome = -3.062402 + 13 V4 + 9.7 V5 + 6.3 duplicate1 + 6 V2
##
## Model 73:
##
## Rule 73/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.557213]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 4.444635 + 15.3 V1 - 13.4 V3 + 10.8 V2 + 6.5 V4
##
## Rule 73/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.507687]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -15.873348 + 30.4 V2 + 24.3 V1 + 5.4 V4 - 0.2 V6
##
## Rule 73/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.987957]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -19.594267 + 24.2 V3 + 12.5 V1 + 9 V2 + 7.5 V4 + 3.1 V8
## + 2.9 V5
##
## Rule 73/4: [23 cases, mean 16.310555, range 7.444598 to 22.1322, est err 7.660925]
##
## if
## V2 > 0.8676087
## then
## outcome = 11.882646 + 18.4 V1 - 14.7 V3
##
## Rule 73/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.801419]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 42.609247 - 33.3 V2
##
## Model 74:
##
## Rule 74/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.353577]
##
## outcome = -2.601942 + 12.4 V4 + 9.2 V5 + 7.1 V2 + 5.6 duplicate1
##
## Model 75:
##
## Rule 75/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.408781]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 4.074378 + 16.1 V1 - 13.3 V3 + 9.7 V2 + 7.1 V4
##
## Rule 75/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.117556]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 3.442269 + 34.1 V2 + 7.3 V4 - 6.6 V3 + 2.8 V1
##
## Rule 75/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.554697]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -17.421785 + 22.8 V3 + 13.6 V1 + 8.5 V2 + 7.5 V4 + 2.9 V5
## - 0.2 V6
##
## Rule 75/4: [13 cases, mean 15.860320, range 7.444598 to 21.77924, est err 6.054771]
##
## if
## V2 > 0.8676087
## V3 <= 0.654213
## then
## outcome = 10.944508 + 19.2 V1 - 14.8 V3
##
## Rule 75/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.938088]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 44.084429 - 35.5 V2
##
## Model 76:
##
## Rule 76/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.362616]
##
## outcome = -2.179047 + 12.3 V4 + 8.9 V5 + 6.3 V2 + 5.5 duplicate1
##
## Model 77:
##
## Rule 77/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.510167]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 3.786118 + 16.2 V1 - 13.3 V3 + 10.6 V2 + 7.3 V4
##
## Rule 77/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.150259]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 3.182897 + 35.2 V2 + 7.5 V4 - 6.7 V3 + 2.7 V1
##
## Rule 77/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.958640]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -17.602228 + 22.2 V3 + 20.4 V1 + 9.2 V2 + 8 V4
## - 6.9 duplicate1 + 3.8 V5 - 0.2 V6
##
## Rule 77/4: [23 cases, mean 16.310555, range 7.444598 to 22.1322, est err 7.844604]
##
## if
## V2 > 0.8676087
## then
## outcome = 11.475181 + 19.3 V1 - 14.8 V3
##
## Rule 77/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.708077]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 44.017845 - 34.8 V2
##
## Model 78:
##
## Rule 78/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.283166]
##
## outcome = -2.247148 + 11.8 V4 + 8.7 V5 + 7.4 V2 + 5.3 duplicate1
##
## Model 79:
##
## Rule 79/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.406444]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 3.974928 + 16.5 V1 - 13.4 V3 + 9.5 V2 + 7.8 V4
##
## Rule 79/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.330963]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 3.733845 + 35.9 V2 + 8.1 V4 - 7.1 V3 + 2.2 V1
##
## Rule 79/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.922895]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -19.154136 + 23.6 V3 + 21 V1 + 8.7 V4 + 8.2 V2
## - 7.1 duplicate1 + 4.3 V5
##
## Rule 79/4: [13 cases, mean 15.860320, range 7.444598 to 21.77924, est err 6.177126]
##
## if
## V2 > 0.8676087
## V3 <= 0.654213
## then
## outcome = 10.700218 + 19.6 V1 - 14.8 V3
##
## Rule 79/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.873433]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 45.064852 - 36.6 V2
##
## Model 80:
##
## Rule 80/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.323805]
##
## outcome = -2.148457 + 11.7 V4 + 8.6 V5 + 6.6 V2 + 5.5 duplicate1
##
## Model 81:
##
## Rule 81/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.409382]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 3.934088 + 16 V1 - 13.2 V3 + 10 V2 + 7.7 V4
##
## Rule 81/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.239401]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 3.323583 + 35.2 V2 + 8.1 V4 - 6.7 V3 + 2.6 V1
##
## Rule 81/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 3.096894]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -17.632819 + 22.2 V3 + 20.4 V1 + 8.9 V2 + 8.6 V4
## - 6.9 duplicate1 + 4.1 V5 - 0.2 V6
##
## Rule 81/4: [20 cases, mean 15.812832, range 7.444598 to 22.1322, est err 7.463002]
##
## if
## V2 > 0.8898196
## then
## outcome = 11.587432 + 19.1 V1 - 14.7 V3
##
## Rule 81/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.707433]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 44.884829 - 35.8 V2
##
## Model 82:
##
## Rule 82/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.271995]
##
## outcome = -2.123512 + 11.6 V4 + 8.3 V5 + 7.4 V2 + 5.2 duplicate1
##
## Model 83:
##
## Rule 83/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.328874]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 5.352183 + 16.8 V1 - 14.2 V3 + 7.4 V4 + 6.5 V2
##
## Rule 83/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.399783]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 3.732822 + 34.8 V2 + 8.2 V4 - 6.8 V3 + 2.6 V1
##
## Rule 83/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 3.113396]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -17.15179 + 24.7 V3 + 14 V1 + 8.8 V2 + 7.6 V4 - 0.3 V6
##
## Rule 83/4: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.787349]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 45.461794 - 36.8 V2
##
## Model 84:
##
## Rule 84/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.398242]
##
## outcome = -2.514352 + 11.7 V4 + 9.3 V5 + 8 V2 + 5.4 duplicate1 - 1.4 V6
##
## Model 85:
##
## Rule 85/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.341593]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 5.716924 + 16 V1 - 14.6 V3 + 7.2 V4 + 6.6 V2
##
## Rule 85/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.643087]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 4.804149 + 34 V2 + 7.6 V4 - 6.6 V3 + 2.2 V1
##
## Rule 85/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.868673]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -18.955375 + 25 V3 + 14 V1 + 8.3 V4 + 7.6 V2 + 2.8 V5
##
## Rule 85/4: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 3.321903]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 63.822999 - 42.6 V2 - 15.9 duplicate1 + 0.2 V1
##
## Model 86:
##
## Rule 86/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.340039]
##
## outcome = -2.487559 + 11.7 V4 + 8.8 V5 + 8.4 V2 + 5.7 duplicate1
## - 1.6 V6
##
## Model 87:
##
## Rule 87/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.307985]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 6.038672 + 15.7 V1 - 14.5 V3 + 7.2 V4 + 6.3 V2
##
## Rule 87/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 4.054903]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -14.30006 + 30 V2 + 23.4 V1 + 6.2 V4
##
## Rule 87/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.803879]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -18.953577 + 25.1 V3 + 13.7 V1 + 8.3 V4 + 7.1 V2 + 3.3 V5
##
## Rule 87/4: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 3.415384]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 63.939402 - 42.7 V2 - 15.9 duplicate1
##
## Model 88:
##
## Rule 88/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.346970]
##
## outcome = -3.305296 + 11.8 V4 + 9.3 V5 + 8.2 V2 + 5.7 duplicate1
##
## Model 89:
##
## Rule 89/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.331793]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 4.790203 + 16 V1 - 13.4 V3 + 8.6 V2 + 7.7 V4
##
## Rule 89/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.245444]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 4.063584 + 32.8 V2 + 7.9 V4 - 6.5 V3 + 2.7 V1
##
## Rule 89/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.711946]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -16.716098 + 22.8 V3 + 13.5 V1 + 8.1 V4 + 7.4 V2 + 2.8 V5
## - 0.2 V6
##
## Rule 89/4: [13 cases, mean 15.860320, range 7.444598 to 21.77924, est err 6.071908]
##
## if
## V2 > 0.8676087
## V3 <= 0.654213
## then
## outcome = 10.776131 + 19.3 V1 - 14.7 V3
##
## Rule 89/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.992100]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 45.32892 - 37.2 V2
##
## Model 90:
##
## Rule 90/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.340397]
##
## outcome = -2.863415 + 11.7 V4 + 8.9 V5 + 7.4 V2 + 5.7 duplicate1
##
## Model 91:
##
## Rule 91/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.439105]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 4.466537 + 16 V1 - 13.3 V3 + 9.5 V2 + 7.9 V4
##
## Rule 91/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.284780]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 3.774235 + 34.1 V2 + 8 V4 - 6.6 V3 + 2.6 V1
##
## Rule 91/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.848432]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -17.230553 + 22.9 V3 + 13.5 V1 + 8.2 V4 + 8.2 V2 + 3.2 V5
## - 0.2 V6
##
## Rule 91/4: [13 cases, mean 15.860320, range 7.444598 to 21.77924, est err 5.993077]
##
## if
## V2 > 0.8676087
## V3 <= 0.654213
## then
## outcome = 11.229176 + 19.2 V1 - 14.7 V3
##
## Rule 91/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.787251]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 45.202748 - 36.5 V2
##
## Model 92:
##
## Rule 92/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.392257]
##
## outcome = -2.590638 + 11.6 V4 + 8.7 V5 + 6.6 V2 + 5.8 duplicate1
##
## Model 93:
##
## Rule 93/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.452827]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 4.319177 + 15.7 V1 - 13.2 V3 + 10 V2 + 7.8 V4
##
## Rule 93/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.338044]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 3.522452 + 35.1 V2 + 8.1 V4 - 6.7 V3 + 2.6 V1
##
## Rule 93/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 3.054538]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -17.500997 + 22.9 V3 + 13.4 V1 + 9 V2 + 8.3 V4 + 3.4 V5
## - 0.2 V6
##
## Rule 93/4: [20 cases, mean 15.812832, range 7.444598 to 22.1322, est err 7.318115]
##
## if
## V2 > 0.8898196
## then
## outcome = 11.941114 + 18.8 V1 - 14.6 V3
##
## Rule 93/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.678286]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 45.053633 - 35.8 V2
##
## Model 94:
##
## Rule 94/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.337280]
##
## outcome = -2.447545 + 11.5 V4 + 8.3 V5 + 7.4 V2 + 5.3 duplicate1
##
## Model 95:
##
## Rule 95/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 2.341082]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 5.882258 + 16 V1 - 14.5 V3 + 7.2 V4 + 7.2 V2
##
## Rule 95/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 3.606035]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = 4.016427 + 34.7 V2 + 8.3 V4 - 6.8 V3 + 2.6 V1
##
## Rule 95/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 3.331261]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -16.818338 + 24.7 V3 + 13.9 V1 + 8.8 V2 + 7.7 V4 - 0.3 V6
##
## Rule 95/4: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.739254]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 45.808527 - 36.9 V2
##
## Model 96:
##
## Rule 96/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.536952]
##
## outcome = -3.552581 + 11.9 V4 + 9.8 V5 + 7.2 V2 + 5.6 duplicate1
##
## Model 97:
##
## Rule 97/1: [162 cases, mean 13.920627, range 3.55596 to 28.38167, est err 3.873092]
##
## if
## V1 <= 0.7340099
## then
## outcome = 4.928928 + 16 V1 - 13.4 V3 + 9.6 V2 + 7.6 V4
##
## Rule 97/2: [20 cases, mean 14.639552, range 8.442596 to 21.62877, est err 4.043534]
##
## if
## V1 > 0.7340099
## V2 <= 0.5403168
## then
## outcome = -15.458147 + 29.3 V2 + 25 V1 + 6.5 V4 - 0.2 V6
##
## Rule 97/3: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 3.421644]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -19.069848 + 24.1 V3 + 13.2 V1 + 8.7 V4 + 7.7 V2 + 3.1 V8
## + 2.9 V5
##
## Rule 97/4: [13 cases, mean 15.860320, range 7.444598 to 21.77924, est err 6.065141]
##
## if
## V2 > 0.8676087
## V3 <= 0.654213
## then
## outcome = 11.302346 + 19.4 V1 - 14.6 V3 + 0.3 V4 + 0.2 V2
##
## Rule 97/5: [18 cases, mean 18.628002, range 13.07191 to 23.57269, est err 2.689138]
##
## if
## V1 > 0.7340099
## V2 > 0.5403168
## then
## outcome = 45.301097 - 36.1 V2
##
## Model 98:
##
## Rule 98/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.605428]
##
## outcome = -4.32341 + 11.4 V4 + 9.5 V5 + 6.6 V2 + 5.3 V3 + 4.6 duplicate1
##
## Model 99:
##
## Rule 99/1: [105 cases, mean 13.381248, range 3.55596 to 23.3956, est err 3.120436]
##
## if
## V1 <= 0.7340099
## V3 <= 0.654213
## then
## outcome = 5.827531 - 18.7 V3 + 17.1 V1 + 10.2 V2 + 8.1 V4
##
## Rule 99/2: [57 cases, mean 14.914219, range 4.888355 to 28.38167, est err 2.312279]
##
## if
## V1 <= 0.7340099
## V3 > 0.654213
## then
## outcome = -15.000235 + 18.6 V3 + 14.6 V1 + 9.4 V2 + 8 V4 - 0.3 V6
##
## Rule 99/3: [11 cases, mean 15.621394, range 7.444598 to 21.77924, est err 6.745311]
##
## if
## V1 <= 0.7340099
## V2 > 0.8676087
## V3 <= 0.654213
## then
## outcome = 12.672631 + 20.5 V1 - 19.9 V3 + 0.5 V4 + 0.4 V2
##
## Rule 99/4: [26 cases, mean 16.222527, range 8.442596 to 23.57269, est err 3.975468]
##
## if
## V1 > 0.7340099
## V2 <= 0.6789904
## then
## outcome = 8.781014 + 15 V2 + 7.5 V1 - 6 V3 + 2.2 V4 - 1 V6
##
## Rule 99/5: [12 cases, mean 17.192448, range 13.07191 to 20.91717, est err 3.704140]
##
## if
## V1 > 0.7340099
## V2 > 0.6789904
## then
## outcome = 78.755601 - 40.6 V2 - 37.5 V1 + 6.8 V8 + 0.5 V4 - 0.4 V3
## - 0.3 V6
##
## Model 100:
##
## Rule 100/1: [200 cases, mean 14.416183, range 3.55596 to 28.38167, est err 2.660522]
##
## outcome = -4.625432 + 11.6 V4 + 10 V5 + 6.3 V2 + 5.2 V3 + 4.7 duplicate1
##
##
## Evaluation on training data (200 cases):
##
## Average |error| 1.462939
## Relative |error| 0.36
## Correlation coefficient 0.93
##
##
## Attribute usage:
## Conds Model
##
## 39% 48% V3
## 38% 67% V1
## 27% 92% V2
## 2% 53% duplicate1
## 92% V4
## 8% V8
## 54% V5
## 20% V6
## 2% V10
##
##
## Time: 0.6 secsBoosted Trees Model
library(gbm)## Warning: package 'gbm' was built under R version 4.0.5## Loaded gbm 2.1.8gbmModel <- gbm(y ~ ., data = simulated, distribution = "gaussian")
summary.gbm(gbmModel)
## var rel.inf
## V4 V4 26.9757520
## V2 V2 23.0213948
## V1 V1 15.2403221
## duplicate1 duplicate1 15.2116298
## V5 V5 11.3145210
## V3 V3 7.6218810
## V6 V6 0.2581636
## V8 V8 0.1981537
## V7 V7 0.1581819
## V9 V9 0.0000000
## V10 V10 0.0000000We cannot say the pattern occur strictly as previously observed. This time, Boosted trees model show V4, V2, V1 as the 03 most significant predictors. Cubist model shows V2, V1, V4 are the 03 most significant predictors.
8.2 Use a simulation to show tree bias with different granularities.
var1 <- rnorm(1000, 1,100)
var2 <- rnorm(1000, 2,50)
var3 <- rnorm(1000,1,5)
y <- var1+var2+var3
df <- data.frame(var3, var2, var1, y)
model5 <- randomForest(y ~., data = df, importance = TRUE, ntree = 100)
rfImp5 <- varImp(model5, conditional = FALSE)
rfImp5## Overall
## var3 2.246953
## var2 54.137228
## var1 91.776858We see that var1 shows the highest significance in this random forest model probably due to the higher standard deviation on V1.
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:
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? Having the bagging fraction and learning rate parameters set to 0.9 has the influence on the highest significant predictors whereas on the left the set 0.1 make the influence loose. therefore, we get more random variable on the left figure showing their significance level in the model.
Which model do you think would be more predictive of other samples? I think it would depend on what we are looking for in the model. If we are interested to see the top learning rate, then model on the right. If we are interested in looking for learning curve across predictors, then the model on the left will be appropriate.
How would increasing interaction depth affect the slope of predictor importance for either model in Fig. 8.24? For both model, increasing interaction depth will reduce the slope of predictor importance.
8.7. Refer to Exercises 6.3 and 7.5 which describe a chemical manufacturing process. Use the same data imputation, data splitting, and pre-processing steps as before and train several tree-based models: (a) Which tree-based regression model gives the optimal resampling and test set performance?
library(AppliedPredictiveModeling)## Warning: package 'AppliedPredictiveModeling' was built under R version 4.0.5library(RANN)## Warning: package 'RANN' was built under R version 4.0.5data(ChemicalManufacturingProcess)
df <- ChemicalManufacturingProcess
#sum(is.na(df))
trans <- preProcess(df,"knnImpute")
#sum(is.na(trans))
pred <- predict(trans, df)
pred <- pred %>% select_at(vars(-one_of(nearZeroVar(., names = TRUE))))
trainDf <- createDataPartition(pred$Yield, p=0.8, time = 1, list = FALSE)
trainX <-pred[trainDf, ]
trainY <- pred$Yield[trainDf]
testX <- pred[-trainDf,]
testY <- pred$Yield[-trainDf]
#postResample(pred = predict(plsTune, newdata=testX), obs = testY)Random Forest Model
model1 <- train(x = trainX,
y = trainY,
method = 'rf',
tuneLength = 10)
model1## Random Forest
##
## 144 samples
## 57 predictor
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 144, 144, 144, 144, 144, 144, ...
## Resampling results across tuning parameters:
##
## mtry RMSE Rsquared MAE
## 2 0.6461680 0.6594473 0.49571132
## 8 0.4799203 0.8173463 0.34589376
## 14 0.3861401 0.8845514 0.26403683
## 20 0.3197562 0.9199472 0.20684726
## 26 0.2693095 0.9411223 0.16458327
## 32 0.2276860 0.9548960 0.13069802
## 38 0.1987275 0.9634926 0.10782680
## 44 0.1773969 0.9687738 0.09005825
## 50 0.1671177 0.9715804 0.08117488
## 57 0.1606266 0.9735854 0.07647506
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was mtry = 57.Cubist Model
model2 <- train(x = trainX,
y = trainY,
method = 'cubist')
model2## Cubist
##
## 144 samples
## 57 predictor
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 144, 144, 144, 144, 144, 144, ...
## Resampling results across tuning parameters:
##
## committees neighbors RMSE Rsquared MAE
## 1 0 2.597414e-08 1 1.756846e-08
## 1 5 2.597414e-08 1 1.756846e-08
## 1 9 2.597414e-08 1 1.756846e-08
## 10 0 2.597414e-08 1 1.756846e-08
## 10 5 2.597414e-08 1 1.756846e-08
## 10 9 2.597414e-08 1 1.756846e-08
## 20 0 2.597414e-08 1 1.756846e-08
## 20 5 2.597414e-08 1 1.756846e-08
## 20 9 2.597414e-08 1 1.756846e-08
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were committees = 1 and neighbors = 0.Boosted Trees Model
gbmGrid <- expand.grid(.interaction.depth = seq(1, 7, by = 2),
.n.trees = seq(100, 1000, by = 50),
.shrinkage = c(0.01, 0.1, 0.5),
.n.minobsinnode=c(5,10,15))
set.seed(100)
model3 <- train(x = trainX,
y = trainY,
method = "gbm",
tuneGrid = gbmGrid,
## The gbm() function produces copious amounts
## of output, so pass in the verbose option
## to avoid printing a lot to the screen.
verbose = FALSE)
model3## Stochastic Gradient Boosting
##
## 144 samples
## 57 predictor
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 144, 144, 144, 144, 144, 144, ...
## Resampling results across tuning parameters:
##
## shrinkage interaction.depth n.minobsinnode n.trees RMSE Rsquared
## 0.01 1 5 100 0.5833765 0.8939606
## 0.01 1 5 150 0.4742475 0.9248371
## 0.01 1 5 200 0.3937429 0.9445892
## 0.01 1 5 250 0.3325876 0.9556096
## 0.01 1 5 300 0.2860703 0.9629307
## 0.01 1 5 350 0.2500028 0.9672124
## 0.01 1 5 400 0.2233096 0.9701862
## 0.01 1 5 450 0.2038712 0.9720468
## 0.01 1 5 500 0.1896787 0.9734548
## 0.01 1 5 550 0.1792651 0.9744815
## 0.01 1 5 600 0.1723098 0.9751211
## 0.01 1 5 650 0.1673248 0.9756198
## 0.01 1 5 700 0.1641433 0.9759485
## 0.01 1 5 750 0.1618682 0.9761969
## 0.01 1 5 800 0.1603856 0.9763785
## 0.01 1 5 850 0.1592464 0.9764884
## 0.01 1 5 900 0.1588094 0.9765122
## 0.01 1 5 950 0.1586672 0.9764745
## 0.01 1 5 1000 0.1583677 0.9764854
## 0.01 1 10 100 0.5819653 0.8919723
## 0.01 1 10 150 0.4708024 0.9209413
## 0.01 1 10 200 0.3891903 0.9383117
## 0.01 1 10 250 0.3299076 0.9474040
## 0.01 1 10 300 0.2879574 0.9524992
## 0.01 1 10 350 0.2602378 0.9552726
## 0.01 1 10 400 0.2430808 0.9567490
## 0.01 1 10 450 0.2326441 0.9577496
## 0.01 1 10 500 0.2261566 0.9582833
## 0.01 1 10 550 0.2226215 0.9585614
## 0.01 1 10 600 0.2205085 0.9586370
## 0.01 1 10 650 0.2190457 0.9587772
## 0.01 1 10 700 0.2181179 0.9588456
## 0.01 1 10 750 0.2177898 0.9587971
## 0.01 1 10 800 0.2174429 0.9587663
## 0.01 1 10 850 0.2170830 0.9587987
## 0.01 1 10 900 0.2168080 0.9587739
## 0.01 1 10 950 0.2166933 0.9587281
## 0.01 1 10 1000 0.2167109 0.9586613
## 0.01 1 15 100 0.5817025 0.8824224
## 0.01 1 15 150 0.4721476 0.9076320
## 0.01 1 15 200 0.3971537 0.9194227
## 0.01 1 15 250 0.3488021 0.9247499
## 0.01 1 15 300 0.3198926 0.9274938
## 0.01 1 15 350 0.3020628 0.9294991
## 0.01 1 15 400 0.2916329 0.9309609
## 0.01 1 15 450 0.2857504 0.9317478
## 0.01 1 15 500 0.2821312 0.9322575
## 0.01 1 15 550 0.2799030 0.9324725
## 0.01 1 15 600 0.2786247 0.9325983
## 0.01 1 15 650 0.2776970 0.9326757
## 0.01 1 15 700 0.2771481 0.9326703
## 0.01 1 15 750 0.2768343 0.9326570
## 0.01 1 15 800 0.2767096 0.9326130
## 0.01 1 15 850 0.2764195 0.9326470
## 0.01 1 15 900 0.2766850 0.9325015
## 0.01 1 15 950 0.2770069 0.9323441
## 0.01 1 15 1000 0.2771291 0.9322589
## 0.01 3 5 100 0.4534952 0.9648258
## 0.01 3 5 150 0.3235141 0.9697959
## 0.01 3 5 200 0.2451900 0.9727203
## 0.01 3 5 250 0.2008348 0.9743849
## 0.01 3 5 300 0.1775586 0.9753618
## 0.01 3 5 350 0.1657180 0.9760307
## 0.01 3 5 400 0.1598707 0.9765561
## 0.01 3 5 450 0.1571669 0.9768384
## 0.01 3 5 500 0.1553866 0.9770969
## 0.01 3 5 550 0.1545812 0.9772260
## 0.01 3 5 600 0.1538727 0.9773355
## 0.01 3 5 650 0.1534681 0.9774054
## 0.01 3 5 700 0.1533253 0.9774243
## 0.01 3 5 750 0.1532760 0.9774368
## 0.01 3 5 800 0.1533711 0.9774246
## 0.01 3 5 850 0.1535603 0.9773823
## 0.01 3 5 900 0.1533881 0.9774108
## 0.01 3 5 950 0.1534809 0.9773862
## 0.01 3 5 1000 0.1536552 0.9773403
## 0.01 3 10 100 0.4549175 0.9528292
## 0.01 3 10 150 0.3353852 0.9558948
## 0.01 3 10 200 0.2708502 0.9574482
## 0.01 3 10 250 0.2398146 0.9580619
## 0.01 3 10 300 0.2269036 0.9585500
## 0.01 3 10 350 0.2211671 0.9589155
## 0.01 3 10 400 0.2179792 0.9592527
## 0.01 3 10 450 0.2161319 0.9594422
## 0.01 3 10 500 0.2153134 0.9594894
## 0.01 3 10 550 0.2146808 0.9595674
## 0.01 3 10 600 0.2142762 0.9595818
## 0.01 3 10 650 0.2139364 0.9596097
## 0.01 3 10 700 0.2138588 0.9595774
## 0.01 3 10 750 0.2138196 0.9595846
## 0.01 3 10 800 0.2137478 0.9595451
## 0.01 3 10 850 0.2139474 0.9594554
## 0.01 3 10 900 0.2140479 0.9594014
## 0.01 3 10 950 0.2140325 0.9593850
## 0.01 3 10 1000 0.2143042 0.9592766
## 0.01 3 15 100 0.4841790 0.9175658
## 0.01 3 15 150 0.3752208 0.9238531
## 0.01 3 15 200 0.3220608 0.9272402
## 0.01 3 15 250 0.2993291 0.9293401
## 0.01 3 15 300 0.2886338 0.9307797
## 0.01 3 15 350 0.2830503 0.9316420
## 0.01 3 15 400 0.2802990 0.9320937
## 0.01 3 15 450 0.2785932 0.9323763
## 0.01 3 15 500 0.2776321 0.9325075
## 0.01 3 15 550 0.2771327 0.9325233
## 0.01 3 15 600 0.2765114 0.9326519
## 0.01 3 15 650 0.2763418 0.9326277
## 0.01 3 15 700 0.2762914 0.9325634
## 0.01 3 15 750 0.2758773 0.9326914
## 0.01 3 15 800 0.2759714 0.9325785
## 0.01 3 15 850 0.2760908 0.9325037
## 0.01 3 15 900 0.2762228 0.9323937
## 0.01 3 15 950 0.2765190 0.9321835
## 0.01 3 15 1000 0.2768374 0.9320620
## 0.01 5 5 100 0.4275876 0.9715929
## 0.01 5 5 150 0.2984078 0.9737975
## 0.01 5 5 200 0.2255221 0.9750679
## 0.01 5 5 250 0.1870581 0.9758439
## 0.01 5 5 300 0.1688855 0.9762841
## 0.01 5 5 350 0.1606514 0.9766429
## 0.01 5 5 400 0.1565893 0.9769981
## 0.01 5 5 450 0.1543872 0.9772831
## 0.01 5 5 500 0.1531918 0.9774437
## 0.01 5 5 550 0.1527244 0.9775316
## 0.01 5 5 600 0.1522584 0.9776227
## 0.01 5 5 650 0.1521322 0.9776435
## 0.01 5 5 700 0.1521992 0.9776494
## 0.01 5 5 750 0.1523504 0.9776349
## 0.01 5 5 800 0.1524964 0.9775935
## 0.01 5 5 850 0.1525256 0.9775826
## 0.01 5 5 900 0.1528058 0.9775097
## 0.01 5 5 950 0.1530817 0.9774547
## 0.01 5 5 1000 0.1533056 0.9774018
## 0.01 5 10 100 0.4417169 0.9534893
## 0.01 5 10 150 0.3238369 0.9554028
## 0.01 5 10 200 0.2636952 0.9565498
## 0.01 5 10 250 0.2370750 0.9572447
## 0.01 5 10 300 0.2257324 0.9579767
## 0.01 5 10 350 0.2205716 0.9585564
## 0.01 5 10 400 0.2178029 0.9588868
## 0.01 5 10 450 0.2164220 0.9590846
## 0.01 5 10 500 0.2153878 0.9592250
## 0.01 5 10 550 0.2149649 0.9592385
## 0.01 5 10 600 0.2148202 0.9592445
## 0.01 5 10 650 0.2146580 0.9591883
## 0.01 5 10 700 0.2144597 0.9592291
## 0.01 5 10 750 0.2146747 0.9590712
## 0.01 5 10 800 0.2147426 0.9590364
## 0.01 5 10 850 0.2145618 0.9590706
## 0.01 5 10 900 0.2147121 0.9589852
## 0.01 5 10 950 0.2146223 0.9590155
## 0.01 5 10 1000 0.2147978 0.9589255
## 0.01 5 15 100 0.4819683 0.9181955
## 0.01 5 15 150 0.3741840 0.9239644
## 0.01 5 15 200 0.3229851 0.9268791
## 0.01 5 15 250 0.2999974 0.9291375
## 0.01 5 15 300 0.2897504 0.9303748
## 0.01 5 15 350 0.2844622 0.9312352
## 0.01 5 15 400 0.2812821 0.9318478
## 0.01 5 15 450 0.2789534 0.9323210
## 0.01 5 15 500 0.2777213 0.9326495
## 0.01 5 15 550 0.2767766 0.9328418
## 0.01 5 15 600 0.2760797 0.9330159
## 0.01 5 15 650 0.2759869 0.9329486
## 0.01 5 15 700 0.2758618 0.9329469
## 0.01 5 15 750 0.2762799 0.9327041
## 0.01 5 15 800 0.2762244 0.9327361
## 0.01 5 15 850 0.2763742 0.9326278
## 0.01 5 15 900 0.2765964 0.9324569
## 0.01 5 15 950 0.2770152 0.9322442
## 0.01 5 15 1000 0.2773076 0.9320620
## 0.01 7 5 100 0.4190472 0.9730335
## 0.01 7 5 150 0.2921840 0.9742584
## 0.01 7 5 200 0.2217301 0.9751151
## 0.01 7 5 250 0.1850211 0.9756677
## 0.01 7 5 300 0.1679718 0.9760862
## 0.01 7 5 350 0.1599586 0.9764894
## 0.01 7 5 400 0.1561567 0.9767938
## 0.01 7 5 450 0.1542128 0.9770044
## 0.01 7 5 500 0.1530987 0.9771647
## 0.01 7 5 550 0.1524545 0.9772893
## 0.01 7 5 600 0.1523653 0.9773091
## 0.01 7 5 650 0.1522241 0.9773591
## 0.01 7 5 700 0.1522581 0.9773594
## 0.01 7 5 750 0.1524330 0.9773170
## 0.01 7 5 800 0.1525161 0.9773049
## 0.01 7 5 850 0.1526344 0.9772964
## 0.01 7 5 900 0.1528882 0.9772443
## 0.01 7 5 950 0.1531461 0.9771888
## 0.01 7 5 1000 0.1532905 0.9771535
## 0.01 7 10 100 0.4416812 0.9536203
## 0.01 7 10 150 0.3246235 0.9553392
## 0.01 7 10 200 0.2645334 0.9562927
## 0.01 7 10 250 0.2380472 0.9570888
## 0.01 7 10 300 0.2265107 0.9578564
## 0.01 7 10 350 0.2214091 0.9582907
## 0.01 7 10 400 0.2191112 0.9585180
## 0.01 7 10 450 0.2176321 0.9586633
## 0.01 7 10 500 0.2167751 0.9587425
## 0.01 7 10 550 0.2160855 0.9588562
## 0.01 7 10 600 0.2157456 0.9588847
## 0.01 7 10 650 0.2155839 0.9588531
## 0.01 7 10 700 0.2154557 0.9588618
## 0.01 7 10 750 0.2154395 0.9588053
## 0.01 7 10 800 0.2152724 0.9588215
## 0.01 7 10 850 0.2152147 0.9588308
## 0.01 7 10 900 0.2152021 0.9587887
## 0.01 7 10 950 0.2153483 0.9587374
## 0.01 7 10 1000 0.2155180 0.9586799
## 0.01 7 15 100 0.4821045 0.9179470
## 0.01 7 15 150 0.3749232 0.9236402
## 0.01 7 15 200 0.3229621 0.9267910
## 0.01 7 15 250 0.3004023 0.9289994
## 0.01 7 15 300 0.2895179 0.9304855
## 0.01 7 15 350 0.2840283 0.9312514
## 0.01 7 15 400 0.2806129 0.9318745
## 0.01 7 15 450 0.2790447 0.9321014
## 0.01 7 15 500 0.2781762 0.9322143
## 0.01 7 15 550 0.2772813 0.9322764
## 0.01 7 15 600 0.2767985 0.9323589
## 0.01 7 15 650 0.2766944 0.9324140
## 0.01 7 15 700 0.2767878 0.9323060
## 0.01 7 15 750 0.2768805 0.9321679
## 0.01 7 15 800 0.2769726 0.9320941
## 0.01 7 15 850 0.2771383 0.9319937
## 0.01 7 15 900 0.2775432 0.9317667
## 0.01 7 15 950 0.2776594 0.9316622
## 0.01 7 15 1000 0.2780742 0.9315430
## 0.10 1 5 100 0.1688308 0.9738778
## 0.10 1 5 150 0.1680738 0.9738411
## 0.10 1 5 200 0.1701769 0.9732286
## 0.10 1 5 250 0.1714678 0.9728252
## 0.10 1 5 300 0.1728987 0.9723452
## 0.10 1 5 350 0.1740232 0.9720155
## 0.10 1 5 400 0.1747917 0.9717544
## 0.10 1 5 450 0.1757762 0.9714502
## 0.10 1 5 500 0.1763204 0.9712565
## 0.10 1 5 550 0.1768246 0.9710845
## 0.10 1 5 600 0.1773178 0.9708821
## 0.10 1 5 650 0.1777295 0.9707458
## 0.10 1 5 700 0.1781420 0.9706265
## 0.10 1 5 750 0.1783959 0.9705523
## 0.10 1 5 800 0.1785492 0.9704586
## 0.10 1 5 850 0.1786782 0.9704208
## 0.10 1 5 900 0.1786238 0.9704193
## 0.10 1 5 950 0.1788435 0.9703543
## 0.10 1 5 1000 0.1790133 0.9703011
## 0.10 1 10 100 0.2224288 0.9565235
## 0.10 1 10 150 0.2227747 0.9561115
## 0.10 1 10 200 0.2239190 0.9553982
## 0.10 1 10 250 0.2238228 0.9551783
## 0.10 1 10 300 0.2253069 0.9545564
## 0.10 1 10 350 0.2265406 0.9538494
## 0.10 1 10 400 0.2284515 0.9529277
## 0.10 1 10 450 0.2301608 0.9521474
## 0.10 1 10 500 0.2311802 0.9515356
## 0.10 1 10 550 0.2325462 0.9508814
## 0.10 1 10 600 0.2334530 0.9503486
## 0.10 1 10 650 0.2343481 0.9499047
## 0.10 1 10 700 0.2351976 0.9495118
## 0.10 1 10 750 0.2355883 0.9492555
## 0.10 1 10 800 0.2360144 0.9490402
## 0.10 1 10 850 0.2371330 0.9485341
## 0.10 1 10 900 0.2374130 0.9483559
## 0.10 1 10 950 0.2378425 0.9481566
## 0.10 1 10 1000 0.2380827 0.9479668
## 0.10 1 15 100 0.2888332 0.9266674
## 0.10 1 15 150 0.2914025 0.9253068
## 0.10 1 15 200 0.2948138 0.9232042
## 0.10 1 15 250 0.2967748 0.9217375
## 0.10 1 15 300 0.2978267 0.9211399
## 0.10 1 15 350 0.2988908 0.9202815
## 0.10 1 15 400 0.2996008 0.9195147
## 0.10 1 15 450 0.3001211 0.9191844
## 0.10 1 15 500 0.3017080 0.9180945
## 0.10 1 15 550 0.3035846 0.9169591
## 0.10 1 15 600 0.3044252 0.9163390
## 0.10 1 15 650 0.3061810 0.9151873
## 0.10 1 15 700 0.3069954 0.9146846
## 0.10 1 15 750 0.3077748 0.9141546
## 0.10 1 15 800 0.3089810 0.9132768
## 0.10 1 15 850 0.3094530 0.9129090
## 0.10 1 15 900 0.3104009 0.9123848
## 0.10 1 15 950 0.3110683 0.9119545
## 0.10 1 15 1000 0.3116855 0.9115269
## 0.10 3 5 100 0.1599905 0.9757667
## 0.10 3 5 150 0.1618253 0.9753359
## 0.10 3 5 200 0.1641589 0.9746912
## 0.10 3 5 250 0.1658414 0.9742536
## 0.10 3 5 300 0.1673273 0.9738408
## 0.10 3 5 350 0.1681985 0.9735829
## 0.10 3 5 400 0.1687967 0.9734254
## 0.10 3 5 450 0.1692356 0.9732930
## 0.10 3 5 500 0.1694112 0.9732334
## 0.10 3 5 550 0.1696715 0.9731596
## 0.10 3 5 600 0.1697128 0.9731395
## 0.10 3 5 650 0.1698491 0.9730983
## 0.10 3 5 700 0.1698850 0.9730887
## 0.10 3 5 750 0.1699336 0.9730740
## 0.10 3 5 800 0.1699815 0.9730602
## 0.10 3 5 850 0.1700022 0.9730532
## 0.10 3 5 900 0.1700141 0.9730496
## 0.10 3 5 950 0.1700232 0.9730467
## 0.10 3 5 1000 0.1700275 0.9730453
## 0.10 3 10 100 0.2207950 0.9566514
## 0.10 3 10 150 0.2223541 0.9558883
## 0.10 3 10 200 0.2231235 0.9551996
## 0.10 3 10 250 0.2244308 0.9546343
## 0.10 3 10 300 0.2254775 0.9540727
## 0.10 3 10 350 0.2265358 0.9534983
## 0.10 3 10 400 0.2278068 0.9528679
## 0.10 3 10 450 0.2287404 0.9524334
## 0.10 3 10 500 0.2299992 0.9518940
## 0.10 3 10 550 0.2307110 0.9515639
## 0.10 3 10 600 0.2314999 0.9512274
## 0.10 3 10 650 0.2320542 0.9509670
## 0.10 3 10 700 0.2324924 0.9507576
## 0.10 3 10 750 0.2329953 0.9505290
## 0.10 3 10 800 0.2332163 0.9504143
## 0.10 3 10 850 0.2334856 0.9502823
## 0.10 3 10 900 0.2337013 0.9501786
## 0.10 3 10 950 0.2339139 0.9500783
## 0.10 3 10 1000 0.2340998 0.9499963
## 0.10 3 15 100 0.2857242 0.9270204
## 0.10 3 15 150 0.2898665 0.9246228
## 0.10 3 15 200 0.2916097 0.9239206
## 0.10 3 15 250 0.2922507 0.9234352
## 0.10 3 15 300 0.2923370 0.9232360
## 0.10 3 15 350 0.2932878 0.9225502
## 0.10 3 15 400 0.2941791 0.9220572
## 0.10 3 15 450 0.2937303 0.9221928
## 0.10 3 15 500 0.2942609 0.9218723
## 0.10 3 15 550 0.2947168 0.9215507
## 0.10 3 15 600 0.2953320 0.9211360
## 0.10 3 15 650 0.2961430 0.9206450
## 0.10 3 15 700 0.2969154 0.9202213
## 0.10 3 15 750 0.2972194 0.9200060
## 0.10 3 15 800 0.2976907 0.9196963
## 0.10 3 15 850 0.2980117 0.9194745
## 0.10 3 15 900 0.2985272 0.9192167
## 0.10 3 15 950 0.2989001 0.9189944
## 0.10 3 15 1000 0.2992363 0.9187973
## 0.10 5 5 100 0.1609342 0.9753300
## 0.10 5 5 150 0.1633285 0.9747629
## 0.10 5 5 200 0.1649588 0.9743603
## 0.10 5 5 250 0.1667856 0.9738242
## 0.10 5 5 300 0.1679934 0.9735022
## 0.10 5 5 350 0.1686805 0.9732883
## 0.10 5 5 400 0.1692899 0.9731189
## 0.10 5 5 450 0.1696551 0.9730051
## 0.10 5 5 500 0.1699147 0.9729269
## 0.10 5 5 550 0.1701348 0.9728614
## 0.10 5 5 600 0.1702621 0.9728215
## 0.10 5 5 650 0.1703380 0.9727966
## 0.10 5 5 700 0.1703739 0.9727837
## 0.10 5 5 750 0.1704123 0.9727708
## 0.10 5 5 800 0.1704388 0.9727629
## 0.10 5 5 850 0.1704641 0.9727544
## 0.10 5 5 900 0.1704813 0.9727491
## 0.10 5 5 950 0.1704921 0.9727452
## 0.10 5 5 1000 0.1704974 0.9727435
## 0.10 5 10 100 0.2230728 0.9559875
## 0.10 5 10 150 0.2244455 0.9550248
## 0.10 5 10 200 0.2254412 0.9543610
## 0.10 5 10 250 0.2262556 0.9538106
## 0.10 5 10 300 0.2274814 0.9532176
## 0.10 5 10 350 0.2284128 0.9527009
## 0.10 5 10 400 0.2294265 0.9521772
## 0.10 5 10 450 0.2302247 0.9517947
## 0.10 5 10 500 0.2310325 0.9513748
## 0.10 5 10 550 0.2317197 0.9510492
## 0.10 5 10 600 0.2321904 0.9508041
## 0.10 5 10 650 0.2327173 0.9505331
## 0.10 5 10 700 0.2330889 0.9503750
## 0.10 5 10 750 0.2334210 0.9502033
## 0.10 5 10 800 0.2337651 0.9500564
## 0.10 5 10 850 0.2340134 0.9499246
## 0.10 5 10 900 0.2342461 0.9498159
## 0.10 5 10 950 0.2344297 0.9497290
## 0.10 5 10 1000 0.2345949 0.9496526
## 0.10 5 15 100 0.2850100 0.9275582
## 0.10 5 15 150 0.2871275 0.9264162
## 0.10 5 15 200 0.2892983 0.9252461
## 0.10 5 15 250 0.2906300 0.9245023
## 0.10 5 15 300 0.2914260 0.9241624
## 0.10 5 15 350 0.2924089 0.9237304
## 0.10 5 15 400 0.2931500 0.9232418
## 0.10 5 15 450 0.2936854 0.9228788
## 0.10 5 15 500 0.2943886 0.9224569
## 0.10 5 15 550 0.2950981 0.9221192
## 0.10 5 15 600 0.2953735 0.9218746
## 0.10 5 15 650 0.2959907 0.9215980
## 0.10 5 15 700 0.2965619 0.9212657
## 0.10 5 15 750 0.2970090 0.9209947
## 0.10 5 15 800 0.2975011 0.9206958
## 0.10 5 15 850 0.2979152 0.9204992
## 0.10 5 15 900 0.2982501 0.9202575
## 0.10 5 15 950 0.2986970 0.9200103
## 0.10 5 15 1000 0.2992060 0.9197325
## 0.10 7 5 100 0.1583600 0.9759422
## 0.10 7 5 150 0.1604985 0.9755015
## 0.10 7 5 200 0.1627426 0.9750141
## 0.10 7 5 250 0.1644415 0.9745920
## 0.10 7 5 300 0.1658611 0.9742213
## 0.10 7 5 350 0.1665937 0.9740316
## 0.10 7 5 400 0.1672961 0.9738334
## 0.10 7 5 450 0.1677122 0.9737240
## 0.10 7 5 500 0.1679947 0.9736496
## 0.10 7 5 550 0.1681376 0.9736092
## 0.10 7 5 600 0.1682606 0.9735768
## 0.10 7 5 650 0.1683642 0.9735489
## 0.10 7 5 700 0.1684413 0.9735264
## 0.10 7 5 750 0.1684768 0.9735155
## 0.10 7 5 800 0.1685065 0.9735067
## 0.10 7 5 850 0.1685289 0.9735001
## 0.10 7 5 900 0.1685428 0.9734959
## 0.10 7 5 950 0.1685498 0.9734937
## 0.10 7 5 1000 0.1685582 0.9734907
## 0.10 7 10 100 0.2212090 0.9564632
## 0.10 7 10 150 0.2223710 0.9559493
## 0.10 7 10 200 0.2242763 0.9550706
## 0.10 7 10 250 0.2251884 0.9544275
## 0.10 7 10 300 0.2262754 0.9538743
## 0.10 7 10 350 0.2271761 0.9534203
## 0.10 7 10 400 0.2281098 0.9530007
## 0.10 7 10 450 0.2290313 0.9525314
## 0.10 7 10 500 0.2298404 0.9521376
## 0.10 7 10 550 0.2307315 0.9517109
## 0.10 7 10 600 0.2314209 0.9514141
## 0.10 7 10 650 0.2319275 0.9511485
## 0.10 7 10 700 0.2323995 0.9509229
## 0.10 7 10 750 0.2328429 0.9507112
## 0.10 7 10 800 0.2331320 0.9505770
## 0.10 7 10 850 0.2334639 0.9504222
## 0.10 7 10 900 0.2337340 0.9502896
## 0.10 7 10 950 0.2339613 0.9501863
## 0.10 7 10 1000 0.2341293 0.9501037
## 0.10 7 15 100 0.2871119 0.9266041
## 0.10 7 15 150 0.2888745 0.9258113
## 0.10 7 15 200 0.2917268 0.9243760
## 0.10 7 15 250 0.2923334 0.9238561
## 0.10 7 15 300 0.2932264 0.9232856
## 0.10 7 15 350 0.2941361 0.9226762
## 0.10 7 15 400 0.2945888 0.9223032
## 0.10 7 15 450 0.2952536 0.9219188
## 0.10 7 15 500 0.2958273 0.9215156
## 0.10 7 15 550 0.2966076 0.9210110
## 0.10 7 15 600 0.2974012 0.9205063
## 0.10 7 15 650 0.2978496 0.9202331
## 0.10 7 15 700 0.2983980 0.9198434
## 0.10 7 15 750 0.2989339 0.9195196
## 0.10 7 15 800 0.2998163 0.9190012
## 0.10 7 15 850 0.3001089 0.9187914
## 0.10 7 15 900 0.3007672 0.9184269
## 0.10 7 15 950 0.3014392 0.9180073
## 0.10 7 15 1000 0.3019031 0.9177343
## 0.50 1 5 100 0.3016737 0.9139999
## 0.50 1 5 150 0.3066205 0.9111134
## 0.50 1 5 200 0.3069930 0.9106089
## 0.50 1 5 250 0.3076921 0.9101424
## 0.50 1 5 300 0.3081977 0.9096697
## 0.50 1 5 350 0.3087667 0.9093685
## 0.50 1 5 400 0.3090004 0.9092478
## 0.50 1 5 450 0.3091751 0.9091168
## 0.50 1 5 500 0.3093708 0.9089806
## 0.50 1 5 550 0.3094140 0.9089480
## 0.50 1 5 600 0.3094663 0.9089104
## 0.50 1 5 650 0.3094774 0.9088975
## 0.50 1 5 700 0.3094966 0.9088786
## 0.50 1 5 750 0.3094906 0.9088801
## 0.50 1 5 800 0.3094897 0.9088795
## 0.50 1 5 850 0.3094960 0.9088731
## 0.50 1 5 900 0.3094866 0.9088771
## 0.50 1 5 950 0.3094899 0.9088732
## 0.50 1 5 1000 0.3094946 0.9088707
## 0.50 1 10 100 0.3443736 0.8923390
## 0.50 1 10 150 0.3504157 0.8893955
## 0.50 1 10 200 0.3524453 0.8869724
## 0.50 1 10 250 0.3526822 0.8869329
## 0.50 1 10 300 0.3532037 0.8867019
## 0.50 1 10 350 0.3538458 0.8861754
## 0.50 1 10 400 0.3541464 0.8859112
## 0.50 1 10 450 0.3543395 0.8857768
## 0.50 1 10 500 0.3545874 0.8857049
## 0.50 1 10 550 0.3546112 0.8856543
## 0.50 1 10 600 0.3547183 0.8855836
## 0.50 1 10 650 0.3547875 0.8855305
## 0.50 1 10 700 0.3548627 0.8854939
## 0.50 1 10 750 0.3549399 0.8854474
## 0.50 1 10 800 0.3550047 0.8854116
## 0.50 1 10 850 0.3550138 0.8854088
## 0.50 1 10 900 0.3550212 0.8853979
## 0.50 1 10 950 0.3550253 0.8853957
## 0.50 1 10 1000 0.3550300 0.8853919
## 0.50 1 15 100 0.3887450 0.8633922
## 0.50 1 15 150 0.3906490 0.8620128
## 0.50 1 15 200 0.3914512 0.8618355
## 0.50 1 15 250 0.3935603 0.8603569
## 0.50 1 15 300 0.3956114 0.8592499
## 0.50 1 15 350 0.3963133 0.8590867
## 0.50 1 15 400 0.3965787 0.8588779
## 0.50 1 15 450 0.3969433 0.8586953
## 0.50 1 15 500 0.3971451 0.8586509
## 0.50 1 15 550 0.3977115 0.8582756
## 0.50 1 15 600 0.3979246 0.8581554
## 0.50 1 15 650 0.3978823 0.8581876
## 0.50 1 15 700 0.3980134 0.8580749
## 0.50 1 15 750 0.3983132 0.8579249
## 0.50 1 15 800 0.3982667 0.8579759
## 0.50 1 15 850 0.3983040 0.8579517
## 0.50 1 15 900 0.3983424 0.8578966
## 0.50 1 15 950 0.3984329 0.8578311
## 0.50 1 15 1000 0.3984274 0.8578430
## 0.50 3 5 100 0.2491894 0.9422578
## 0.50 3 5 150 0.2492841 0.9422100
## 0.50 3 5 200 0.2493395 0.9421757
## 0.50 3 5 250 0.2493345 0.9421786
## 0.50 3 5 300 0.2493331 0.9421791
## 0.50 3 5 350 0.2493331 0.9421791
## 0.50 3 5 400 0.2493331 0.9421791
## 0.50 3 5 450 0.2493331 0.9421791
## 0.50 3 5 500 0.2493331 0.9421791
## 0.50 3 5 550 0.2493331 0.9421791
## 0.50 3 5 600 0.2493331 0.9421791
## 0.50 3 5 650 0.2493331 0.9421791
## 0.50 3 5 700 0.2493331 0.9421791
## 0.50 3 5 750 0.2493331 0.9421791
## 0.50 3 5 800 0.2493331 0.9421791
## 0.50 3 5 850 0.2493331 0.9421791
## 0.50 3 5 900 0.2493331 0.9421791
## 0.50 3 5 950 0.2493331 0.9421791
## 0.50 3 5 1000 0.2493331 0.9421791
## 0.50 3 10 100 0.3021208 0.9161341
## 0.50 3 10 150 0.3025925 0.9157084
## 0.50 3 10 200 0.3031705 0.9153869
## 0.50 3 10 250 0.3033642 0.9152589
## 0.50 3 10 300 0.3035226 0.9151571
## 0.50 3 10 350 0.3035732 0.9151263
## 0.50 3 10 400 0.3036129 0.9151020
## 0.50 3 10 450 0.3036238 0.9150948
## 0.50 3 10 500 0.3036292 0.9150916
## 0.50 3 10 550 0.3036315 0.9150903
## 0.50 3 10 600 0.3036332 0.9150893
## 0.50 3 10 650 0.3036337 0.9150889
## 0.50 3 10 700 0.3036340 0.9150888
## 0.50 3 10 750 0.3036341 0.9150887
## 0.50 3 10 800 0.3036342 0.9150886
## 0.50 3 10 850 0.3036342 0.9150886
## 0.50 3 10 900 0.3036343 0.9150886
## 0.50 3 10 950 0.3036343 0.9150886
## 0.50 3 10 1000 0.3036343 0.9150886
## 0.50 3 15 100 0.3718607 0.8780724
## 0.50 3 15 150 0.3736262 0.8770418
## 0.50 3 15 200 0.3740839 0.8766870
## 0.50 3 15 250 0.3747139 0.8762150
## 0.50 3 15 300 0.3751865 0.8759961
## 0.50 3 15 350 0.3754244 0.8758588
## 0.50 3 15 400 0.3756128 0.8757483
## 0.50 3 15 450 0.3756949 0.8757092
## 0.50 3 15 500 0.3757652 0.8756706
## 0.50 3 15 550 0.3757997 0.8756442
## 0.50 3 15 600 0.3758352 0.8756253
## 0.50 3 15 650 0.3758470 0.8756158
## 0.50 3 15 700 0.3758592 0.8756079
## 0.50 3 15 750 0.3758668 0.8756022
## 0.50 3 15 800 0.3758693 0.8756008
## 0.50 3 15 850 0.3758717 0.8755990
## 0.50 3 15 900 0.3758733 0.8755981
## 0.50 3 15 950 0.3758750 0.8755970
## 0.50 3 15 1000 0.3758758 0.8755964
## 0.50 5 5 100 0.2293465 0.9515672
## 0.50 5 5 150 0.2293555 0.9515893
## 0.50 5 5 200 0.2293726 0.9515811
## 0.50 5 5 250 0.2293825 0.9515779
## 0.50 5 5 300 0.2293833 0.9515776
## 0.50 5 5 350 0.2293833 0.9515777
## 0.50 5 5 400 0.2293834 0.9515776
## 0.50 5 5 450 0.2293834 0.9515776
## 0.50 5 5 500 0.2293834 0.9515776
## 0.50 5 5 550 0.2293834 0.9515776
## 0.50 5 5 600 0.2293834 0.9515776
## 0.50 5 5 650 0.2293834 0.9515776
## 0.50 5 5 700 0.2293834 0.9515776
## 0.50 5 5 750 0.2293834 0.9515776
## 0.50 5 5 800 0.2293834 0.9515776
## 0.50 5 5 850 0.2293834 0.9515776
## 0.50 5 5 900 0.2293834 0.9515776
## 0.50 5 5 950 0.2293834 0.9515776
## 0.50 5 5 1000 0.2293834 0.9515776
## 0.50 5 10 100 0.2856909 0.9270031
## 0.50 5 10 150 0.2876575 0.9260833
## 0.50 5 10 200 0.2883286 0.9257276
## 0.50 5 10 250 0.2885763 0.9256141
## 0.50 5 10 300 0.2887015 0.9255390
## 0.50 5 10 350 0.2887822 0.9255001
## 0.50 5 10 400 0.2888136 0.9254850
## 0.50 5 10 450 0.2888290 0.9254765
## 0.50 5 10 500 0.2888334 0.9254740
## 0.50 5 10 550 0.2888374 0.9254720
## 0.50 5 10 600 0.2888387 0.9254712
## 0.50 5 10 650 0.2888393 0.9254710
## 0.50 5 10 700 0.2888397 0.9254708
## 0.50 5 10 750 0.2888398 0.9254707
## 0.50 5 10 800 0.2888399 0.9254706
## 0.50 5 10 850 0.2888400 0.9254706
## 0.50 5 10 900 0.2888400 0.9254706
## 0.50 5 10 950 0.2888400 0.9254706
## 0.50 5 10 1000 0.2888400 0.9254706
## 0.50 5 15 100 0.3603620 0.8862600
## 0.50 5 15 150 0.3620458 0.8848559
## 0.50 5 15 200 0.3633790 0.8841057
## 0.50 5 15 250 0.3640468 0.8837661
## 0.50 5 15 300 0.3643016 0.8835997
## 0.50 5 15 350 0.3645160 0.8834674
## 0.50 5 15 400 0.3646715 0.8833609
## 0.50 5 15 450 0.3647440 0.8833319
## 0.50 5 15 500 0.3648100 0.8832894
## 0.50 5 15 550 0.3648704 0.8832533
## 0.50 5 15 600 0.3648914 0.8832419
## 0.50 5 15 650 0.3649081 0.8832321
## 0.50 5 15 700 0.3649099 0.8832305
## 0.50 5 15 750 0.3649175 0.8832254
## 0.50 5 15 800 0.3649225 0.8832220
## 0.50 5 15 850 0.3649236 0.8832212
## 0.50 5 15 900 0.3649243 0.8832207
## 0.50 5 15 950 0.3649248 0.8832204
## 0.50 5 15 1000 0.3649256 0.8832199
## 0.50 7 5 100 0.2081609 0.9596191
## 0.50 7 5 150 0.2085049 0.9594934
## 0.50 7 5 200 0.2085460 0.9594769
## 0.50 7 5 250 0.2085536 0.9594743
## 0.50 7 5 300 0.2085545 0.9594742
## 0.50 7 5 350 0.2085545 0.9594742
## 0.50 7 5 400 0.2085545 0.9594742
## 0.50 7 5 450 0.2085545 0.9594742
## 0.50 7 5 500 0.2085545 0.9594742
## 0.50 7 5 550 0.2085545 0.9594742
## 0.50 7 5 600 0.2085545 0.9594742
## 0.50 7 5 650 0.2085545 0.9594742
## 0.50 7 5 700 0.2085545 0.9594742
## 0.50 7 5 750 0.2085545 0.9594742
## 0.50 7 5 800 0.2085545 0.9594742
## 0.50 7 5 850 0.2085545 0.9594742
## 0.50 7 5 900 0.2085545 0.9594742
## 0.50 7 5 950 0.2085545 0.9594742
## 0.50 7 5 1000 0.2085545 0.9594742
## 0.50 7 10 100 0.2805681 0.9280510
## 0.50 7 10 150 0.2826170 0.9268670
## 0.50 7 10 200 0.2834270 0.9264665
## 0.50 7 10 250 0.2837307 0.9262948
## 0.50 7 10 300 0.2838864 0.9262151
## 0.50 7 10 350 0.2839855 0.9261584
## 0.50 7 10 400 0.2840059 0.9261469
## 0.50 7 10 450 0.2840221 0.9261388
## 0.50 7 10 500 0.2840273 0.9261361
## 0.50 7 10 550 0.2840309 0.9261344
## 0.50 7 10 600 0.2840323 0.9261335
## 0.50 7 10 650 0.2840331 0.9261331
## 0.50 7 10 700 0.2840333 0.9261330
## 0.50 7 10 750 0.2840335 0.9261329
## 0.50 7 10 800 0.2840335 0.9261329
## 0.50 7 10 850 0.2840335 0.9261329
## 0.50 7 10 900 0.2840336 0.9261329
## 0.50 7 10 950 0.2840336 0.9261329
## 0.50 7 10 1000 0.2840336 0.9261329
## 0.50 7 15 100 0.3636732 0.8803112
## 0.50 7 15 150 0.3649915 0.8796109
## 0.50 7 15 200 0.3661327 0.8786901
## 0.50 7 15 250 0.3665161 0.8784113
## 0.50 7 15 300 0.3669060 0.8781899
## 0.50 7 15 350 0.3672925 0.8779766
## 0.50 7 15 400 0.3673959 0.8779070
## 0.50 7 15 450 0.3674456 0.8778525
## 0.50 7 15 500 0.3675117 0.8778341
## 0.50 7 15 550 0.3675630 0.8778062
## 0.50 7 15 600 0.3676056 0.8777853
## 0.50 7 15 650 0.3676184 0.8777788
## 0.50 7 15 700 0.3676239 0.8777746
## 0.50 7 15 750 0.3676255 0.8777737
## 0.50 7 15 800 0.3676292 0.8777712
## 0.50 7 15 850 0.3676312 0.8777703
## 0.50 7 15 900 0.3676325 0.8777693
## 0.50 7 15 950 0.3676333 0.8777687
## 0.50 7 15 1000 0.3676338 0.8777685
## MAE
## 0.40372897
## 0.31282086
## 0.24942126
## 0.20101697
## 0.16525374
## 0.13576290
## 0.11409035
## 0.09820969
## 0.08701633
## 0.07950009
## 0.07514468
## 0.07291423
## 0.07180375
## 0.07186588
## 0.07217632
## 0.07261423
## 0.07339647
## 0.07415503
## 0.07465883
## 0.40019486
## 0.30621145
## 0.23855857
## 0.18805935
## 0.15250145
## 0.12965850
## 0.11640573
## 0.10931122
## 0.10622958
## 0.10544598
## 0.10574809
## 0.10636421
## 0.10719996
## 0.10816993
## 0.10911305
## 0.10987832
## 0.11082645
## 0.11179364
## 0.11252481
## 0.39604943
## 0.29698175
## 0.22954272
## 0.18839034
## 0.16723338
## 0.15696540
## 0.15307602
## 0.15253893
## 0.15329214
## 0.15442573
## 0.15570890
## 0.15699388
## 0.15796999
## 0.15892259
## 0.16019855
## 0.16098403
## 0.16229700
## 0.16356835
## 0.16452081
## 0.33114023
## 0.21596766
## 0.14326833
## 0.09932154
## 0.07677863
## 0.06746132
## 0.06472063
## 0.06447399
## 0.06490847
## 0.06579849
## 0.06646437
## 0.06720110
## 0.06801915
## 0.06870921
## 0.06944047
## 0.07018864
## 0.07072285
## 0.07129510
## 0.07184081
## 0.32439568
## 0.20927127
## 0.14306380
## 0.11329091
## 0.10414586
## 0.10217978
## 0.10207148
## 0.10274013
## 0.10386511
## 0.10483482
## 0.10574315
## 0.10670743
## 0.10782441
## 0.10886306
## 0.10984524
## 0.11081907
## 0.11164706
## 0.11244927
## 0.11325257
## 0.31854029
## 0.20929639
## 0.16608077
## 0.15422983
## 0.15207137
## 0.15210995
## 0.15306058
## 0.15430894
## 0.15538183
## 0.15683135
## 0.15798284
## 0.15925664
## 0.16033749
## 0.16093013
## 0.16195674
## 0.16295209
## 0.16368749
## 0.16444674
## 0.16519871
## 0.31708378
## 0.20045069
## 0.12915626
## 0.08877040
## 0.07045244
## 0.06440709
## 0.06285098
## 0.06296662
## 0.06375698
## 0.06465556
## 0.06547141
## 0.06639402
## 0.06716210
## 0.06796582
## 0.06861523
## 0.06926378
## 0.06991826
## 0.07057581
## 0.07110629
## 0.31109119
## 0.19539612
## 0.13298056
## 0.10877405
## 0.10205283
## 0.10101992
## 0.10149616
## 0.10260140
## 0.10372944
## 0.10499889
## 0.10618139
## 0.10718065
## 0.10813468
## 0.10938584
## 0.11043359
## 0.11116806
## 0.11209884
## 0.11276493
## 0.11356479
## 0.31739550
## 0.20887912
## 0.16690643
## 0.15497767
## 0.15284158
## 0.15346414
## 0.15446545
## 0.15513772
## 0.15637492
## 0.15732465
## 0.15845333
## 0.15974964
## 0.16091469
## 0.16215677
## 0.16297554
## 0.16401452
## 0.16497202
## 0.16578074
## 0.16655434
## 0.31215842
## 0.19617715
## 0.12574389
## 0.08668119
## 0.06939124
## 0.06311621
## 0.06185571
## 0.06201875
## 0.06290813
## 0.06377616
## 0.06479650
## 0.06571964
## 0.06644365
## 0.06728318
## 0.06798879
## 0.06860658
## 0.06933091
## 0.06992271
## 0.07040538
## 0.31109279
## 0.19603456
## 0.13361438
## 0.10970603
## 0.10277487
## 0.10166165
## 0.10232577
## 0.10331536
## 0.10452396
## 0.10560937
## 0.10669923
## 0.10788680
## 0.10891240
## 0.10993277
## 0.11091503
## 0.11160620
## 0.11233017
## 0.11319126
## 0.11395753
## 0.31719069
## 0.20955274
## 0.16675136
## 0.15481165
## 0.15204718
## 0.15260874
## 0.15380489
## 0.15524052
## 0.15660513
## 0.15761578
## 0.15876188
## 0.15999192
## 0.16111222
## 0.16231513
## 0.16296035
## 0.16403631
## 0.16513754
## 0.16596644
## 0.16681617
## 0.08820612
## 0.09145311
## 0.09467698
## 0.09574040
## 0.09752371
## 0.09852297
## 0.09953616
## 0.10049236
## 0.10076938
## 0.10159851
## 0.10200744
## 0.10246870
## 0.10291508
## 0.10326121
## 0.10350697
## 0.10368608
## 0.10386642
## 0.10413794
## 0.10431314
## 0.12271042
## 0.12714027
## 0.12993152
## 0.13201116
## 0.13383133
## 0.13578218
## 0.13792194
## 0.13998013
## 0.14117676
## 0.14293907
## 0.14397761
## 0.14491677
## 0.14597317
## 0.14647929
## 0.14712890
## 0.14812115
## 0.14856610
## 0.14913211
## 0.14948772
## 0.17773234
## 0.18348018
## 0.19000025
## 0.19357189
## 0.19585155
## 0.19765835
## 0.19896018
## 0.20000607
## 0.20160967
## 0.20367373
## 0.20530598
## 0.20652895
## 0.20792831
## 0.20892308
## 0.21026662
## 0.21082069
## 0.21202893
## 0.21269025
## 0.21354314
## 0.08110215
## 0.08417327
## 0.08669743
## 0.08824484
## 0.08971306
## 0.09051677
## 0.09104587
## 0.09141009
## 0.09157933
## 0.09178864
## 0.09184359
## 0.09195809
## 0.09198575
## 0.09202467
## 0.09206246
## 0.09207568
## 0.09208536
## 0.09209312
## 0.09209758
## 0.12388964
## 0.12780309
## 0.13037138
## 0.13235797
## 0.13410668
## 0.13556545
## 0.13702437
## 0.13818540
## 0.13918627
## 0.13989511
## 0.14083430
## 0.14135023
## 0.14185859
## 0.14237096
## 0.14262488
## 0.14291839
## 0.14312325
## 0.14333877
## 0.14350897
## 0.17677408
## 0.18287367
## 0.18638736
## 0.18796993
## 0.18893988
## 0.19032271
## 0.19186426
## 0.19214714
## 0.19301410
## 0.19360126
## 0.19433690
## 0.19508319
## 0.19563028
## 0.19608299
## 0.19648815
## 0.19683268
## 0.19737195
## 0.19770715
## 0.19800402
## 0.08109771
## 0.08473229
## 0.08668277
## 0.08862640
## 0.08986269
## 0.09054176
## 0.09115048
## 0.09154056
## 0.09180813
## 0.09199964
## 0.09212246
## 0.09219977
## 0.09224531
## 0.09228321
## 0.09231182
## 0.09233292
## 0.09234695
## 0.09235701
## 0.09236383
## 0.12242197
## 0.12788052
## 0.13083886
## 0.13258587
## 0.13407241
## 0.13547792
## 0.13647939
## 0.13730919
## 0.13833848
## 0.13900648
## 0.13948487
## 0.14009699
## 0.14050221
## 0.14084690
## 0.14118038
## 0.14145901
## 0.14168406
## 0.14190056
## 0.14208077
## 0.17676695
## 0.18193488
## 0.18542406
## 0.18789699
## 0.18963982
## 0.19098594
## 0.19214829
## 0.19310017
## 0.19360465
## 0.19442949
## 0.19503323
## 0.19569405
## 0.19626923
## 0.19680025
## 0.19736286
## 0.19775753
## 0.19814080
## 0.19860123
## 0.19920693
## 0.07876118
## 0.08271025
## 0.08527842
## 0.08696632
## 0.08828682
## 0.08904911
## 0.08968821
## 0.09006677
## 0.09032118
## 0.09048720
## 0.09061140
## 0.09070521
## 0.09077345
## 0.09079723
## 0.09082880
## 0.09085065
## 0.09086334
## 0.09087089
## 0.09087900
## 0.12098737
## 0.12616307
## 0.12933483
## 0.13090999
## 0.13253191
## 0.13356104
## 0.13467074
## 0.13564367
## 0.13647527
## 0.13732953
## 0.13803741
## 0.13848556
## 0.13897864
## 0.13943455
## 0.13980598
## 0.14018359
## 0.14045116
## 0.14067942
## 0.14086775
## 0.17475726
## 0.18001831
## 0.18432411
## 0.18613651
## 0.18768120
## 0.18862685
## 0.18966793
## 0.19063342
## 0.19148960
## 0.19243146
## 0.19339460
## 0.19404408
## 0.19476796
## 0.19540915
## 0.19612740
## 0.19646739
## 0.19712941
## 0.19778981
## 0.19823377
## 0.22484952
## 0.23034977
## 0.23032352
## 0.23102578
## 0.23158628
## 0.23205330
## 0.23223589
## 0.23245307
## 0.23257808
## 0.23265533
## 0.23269357
## 0.23271346
## 0.23271389
## 0.23272964
## 0.23272847
## 0.23273303
## 0.23272544
## 0.23272893
## 0.23273193
## 0.25598957
## 0.26092970
## 0.26143923
## 0.26158915
## 0.26184876
## 0.26235753
## 0.26239126
## 0.26260057
## 0.26267592
## 0.26263115
## 0.26270381
## 0.26274961
## 0.26280335
## 0.26285390
## 0.26289650
## 0.26291626
## 0.26292189
## 0.26292143
## 0.26292110
## 0.28675141
## 0.29013227
## 0.28924093
## 0.29111514
## 0.29243741
## 0.29375787
## 0.29372296
## 0.29406885
## 0.29425277
## 0.29476679
## 0.29503500
## 0.29502557
## 0.29501764
## 0.29533266
## 0.29530865
## 0.29536461
## 0.29539475
## 0.29550633
## 0.29550386
## 0.17297505
## 0.17301021
## 0.17306903
## 0.17306613
## 0.17306548
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.17306546
## 0.20953347
## 0.20958502
## 0.20996552
## 0.21008703
## 0.21016492
## 0.21020313
## 0.21023114
## 0.21023649
## 0.21024058
## 0.21024150
## 0.21024282
## 0.21024323
## 0.21024340
## 0.21024348
## 0.21024354
## 0.21024355
## 0.21024356
## 0.21024356
## 0.21024356
## 0.26954282
## 0.27071581
## 0.27097244
## 0.27158692
## 0.27191245
## 0.27215375
## 0.27223705
## 0.27228936
## 0.27232983
## 0.27235400
## 0.27236981
## 0.27237024
## 0.27238104
## 0.27238721
## 0.27238911
## 0.27239111
## 0.27239227
## 0.27239343
## 0.27239425
## 0.15023336
## 0.15030851
## 0.15032176
## 0.15032637
## 0.15032705
## 0.15032710
## 0.15032712
## 0.15032712
## 0.15032712
## 0.15032711
## 0.15032711
## 0.15032711
## 0.15032711
## 0.15032711
## 0.15032711
## 0.15032711
## 0.15032711
## 0.15032711
## 0.15032711
## 0.19268338
## 0.19443216
## 0.19488694
## 0.19512678
## 0.19524424
## 0.19530698
## 0.19533966
## 0.19535343
## 0.19535764
## 0.19536184
## 0.19536293
## 0.19536359
## 0.19536394
## 0.19536406
## 0.19536415
## 0.19536418
## 0.19536420
## 0.19536421
## 0.19536421
## 0.25754771
## 0.25842846
## 0.25978736
## 0.26017963
## 0.26042812
## 0.26064183
## 0.26077327
## 0.26084524
## 0.26088753
## 0.26093172
## 0.26094767
## 0.26096173
## 0.26096376
## 0.26096947
## 0.26097484
## 0.26097544
## 0.26097625
## 0.26097670
## 0.26097734
## 0.13387827
## 0.13413066
## 0.13416214
## 0.13416916
## 0.13416981
## 0.13416980
## 0.13416979
## 0.13416979
## 0.13416979
## 0.13416979
## 0.13416979
## 0.13416979
## 0.13416979
## 0.13416979
## 0.13416979
## 0.13416979
## 0.13416979
## 0.13416979
## 0.13416979
## 0.19086640
## 0.19313063
## 0.19385714
## 0.19412509
## 0.19427095
## 0.19434058
## 0.19436018
## 0.19437138
## 0.19437647
## 0.19437844
## 0.19437968
## 0.19438055
## 0.19438065
## 0.19438080
## 0.19438084
## 0.19438085
## 0.19438086
## 0.19438086
## 0.19438087
## 0.26363545
## 0.26425983
## 0.26531426
## 0.26583446
## 0.26608686
## 0.26639219
## 0.26648870
## 0.26654176
## 0.26660529
## 0.26663413
## 0.26666138
## 0.26667602
## 0.26667869
## 0.26668008
## 0.26668159
## 0.26668275
## 0.26668329
## 0.26668399
## 0.26668408
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were n.trees = 650, interaction.depth =
## 5, shrinkage = 0.01 and n.minobsinnode = 5.Looking at the 03 regression models to find which gives the optimal resampling and test set performance.
postResample(pred = predict(model1, newdata=testX), obs = testY)## RMSE Rsquared MAE
## 0.07983601 0.99489972 0.04058143postResample(pred = predict(model2, newdata=testX), obs = testY)## RMSE Rsquared MAE
## 2.746792e-08 1.000000e+00 1.975788e-08postResample(pred = predict(model3, newdata=testX), obs = testY)## RMSE Rsquared MAE
## 0.04835961 0.99735713 0.03578688Model 2, Cubist model gives the optimal resampling and test set performance based on RMSE = 1.795094e-08, Rsquared = 1.000000e+00, MAE = 1.315217e-08
- Which predictors are most important in the optimal tree-based regression model? Do either the biological or process variables dominate the list? How do the top 10 important predictors compare to the top 10 predictors from the optimal linear and nonlinear models?
rfImpX <- varImp(model1, conditional = FALSE)
rfImpX## rf variable importance
##
## only 20 most important variables shown (out of 57)
##
## Overall
## Yield 100.00000
## BiologicalMaterial02 0.24639
## BiologicalMaterial11 0.22989
## ManufacturingProcess13 0.22010
## ManufacturingProcess17 0.19762
## BiologicalMaterial03 0.14581
## ManufacturingProcess18 0.11310
## BiologicalMaterial01 0.10138
## BiologicalMaterial12 0.09418
## ManufacturingProcess21 0.07947
## BiologicalMaterial08 0.07838
## ManufacturingProcess09 0.06796
## BiologicalMaterial05 0.06565
## ManufacturingProcess35 0.04943
## ManufacturingProcess04 0.04341
## ManufacturingProcess06 0.03894
## ManufacturingProcess25 0.03889
## ManufacturingProcess33 0.03692
## ManufacturingProcess20 0.03591
## ManufacturingProcess26 0.03486#summary(rfImpX)Yield 100.00000000
ManufacturingProcess13 0.36769544
ManufacturingProcess18 0.23847121
BiologicalMaterial01 0.15930322
BiologicalMaterial03 0.15324485
BiologicalMaterial02 0.13415505
ManufacturingProcess17 0.10606837
BiologicalMaterial05 0.07847052
ManufacturingProcess32 0.07815230
ManufacturingProcess25 0.07263430
Neither the ManufacturingProcess or the biological variables dominate the first top 10 of the list. somehow I get a weird result with the optimal model2.
- 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?
library(rpart.plot)## Warning: package 'rpart.plot' was built under R version 4.0.5## Loading required package: rpartlibrary(partykit)## Warning: package 'partykit' was built under R version 4.0.5## Loading required package: libcoin## Warning: package 'libcoin' was built under R version 4.0.5## Registered S3 method overwritten by 'inum':
## method from
## format.interval tsibble##
## Attaching package: 'partykit'## The following objects are masked from 'package:party':
##
## cforest, ctree, ctree_control, edge_simple, mob, mob_control,
## node_barplot, node_bivplot, node_boxplot, node_inner, node_surv,
## node_terminal, varimptreeplot <- as.party(rpart(Yield ~., data = trainX ))
plot(treeplot)