Regression and Classification Trees
Dimitrios Zacharatos
library(rwf)Description
This shows the output of PART RPART functions from rwf.
Installation instructions for rwf can be found here These functions are not
installed by default they are in
/rwf/working_functions/OTHER/ML_TREE_RPART.R
infert_formula<-formula(factor(case)~age+parity+education+spontaneous+induced)
boston_formula<-formula(c("medv~",paste(names(MASS::Boston)[1:13],collapse="+")))## Warning in formula.character(c("medv~", paste(names(MASS::Boston)[1:13], : Using formula(x) is deprecated when x is a character vector of length > 1.
## Consider formula(paste(x, collapse = " ")) instead.print(infert_formula)## factor(case) ~ age + parity + education + spontaneous + induced
print(boston_formula)## medv ~ crim + zn + indus + chas + nox + rm + age + dis + rad + ## tax + ptratio + black + lstat
# kfolding
train_test_classification<-k_fold(df=infert,
model_formula=infert_formula)## Fold Cases: 1 Train: 223 Test: 25 Total: 248 Unique Train: 223 Unique Test: 25 ## Fold Cases: 2 Train: 223 Test: 25 Total: 248 Unique Train: 223 Unique Test: 25 ## Fold Cases: 3 Train: 223 Test: 25 Total: 248 Unique Train: 223 Unique Test: 25 ## Fold Cases: 4 Train: 224 Test: 24 Total: 248 Unique Train: 224 Unique Test: 24 ## Fold Cases: 5 Train: 223 Test: 25 Total: 248 Unique Train: 223 Unique Test: 25 ## Fold Cases: 6 Train: 223 Test: 25 Total: 248 Unique Train: 223 Unique Test: 25 ## Fold Cases: 7 Train: 224 Test: 24 Total: 248 Unique Train: 224 Unique Test: 24 ## Fold Cases: 8 Train: 223 Test: 25 Total: 248 Unique Train: 223 Unique Test: 25 ## Fold Cases: 9 Train: 223 Test: 25 Total: 248 Unique Train: 223 Unique Test: 25 ## Fold Cases: 10 Train: 223 Test: 25 Total: 248 Unique Train: 223 Unique Test: 25
train_test_regression<-k_fold(df=MASS::Boston,
model_formula=boston_formula)## Fold Cases: 1 Train: 455 Test: 51 Total: 506 Unique Train: 455 Unique Test: 51 ## Fold Cases: 2 Train: 455 Test: 51 Total: 506 Unique Train: 455 Unique Test: 51 ## Fold Cases: 3 Train: 456 Test: 50 Total: 506 Unique Train: 456 Unique Test: 50 ## Fold Cases: 4 Train: 455 Test: 51 Total: 506 Unique Train: 455 Unique Test: 51 ## Fold Cases: 5 Train: 456 Test: 50 Total: 506 Unique Train: 456 Unique Test: 50 ## Fold Cases: 6 Train: 455 Test: 51 Total: 506 Unique Train: 455 Unique Test: 51 ## Fold Cases: 7 Train: 456 Test: 50 Total: 506 Unique Train: 456 Unique Test: 50 ## Fold Cases: 8 Train: 455 Test: 51 Total: 506 Unique Train: 455 Unique Test: 51 ## Fold Cases: 9 Train: 456 Test: 50 Total: 506 Unique Train: 456 Unique Test: 50 ## Fold Cases: 10 Train: 455 Test: 51 Total: 506 Unique Train: 455 Unique Test: 51
# srpart models
rtree_classification<-rpart::rpart(infert_formula,
train_test_classification$f$train$f1,
model=TRUE,x=TRUE,y=TRUE)
rtree_regression<-rpart::rpart(boston_formula,
train_test_regression$f$train$f1,
model=TRUE,x=TRUE,y=TRUE)Rpart Classification
result<-data.frame(rtree_classification$cptable)
result$nsplit<-factor(result$nsplit+1)
minimun_size<-as.numeric(as.character(result[which.min(result[,"xerror"]),"nsplit"]))
initial_model<-rtree_classification
model<-rpart::prune(rtree_classification,
cp=rtree_classification$cptable[which.min(rtree_classification$cptable[,"xerror"]),"CP"])
importance<-model$variable.importance
importance<-data.frame(names=names(importance),importance=importance)
importance$names<-factor(importance$names,levels=rev(as.character(importance$names)))
plot_importance<-ggplot(importance,aes(x=names,y=importance))+
geom_bar(stat='identity')+
labs(title="Importance Plot",y="Relative Influence",x="Predictor")+
theme_bw(base_size=10)+
scale_x_discrete(limits=rev(levels(names)))+
coord_flip()
plot_importance
rtree_classification## n= 223 ## ## node), split, n, loss, yval, (yprob) ## * denotes terminal node ## ## 1) root 223 75 0 (0.6636771 0.3363229) ## 2) spontaneous< 0.5 131 26 0 (0.8015267 0.1984733) * ## 3) spontaneous>=0.5 92 43 1 (0.4673913 0.5326087) ## 6) spontaneous< 1.5 58 26 0 (0.5517241 0.4482759) ## 12) parity>=1.5 31 8 0 (0.7419355 0.2580645) ## 24) induced< 0.5 11 0 0 (1.0000000 0.0000000) * ## 25) induced>=0.5 20 8 0 (0.6000000 0.4000000) ## 50) education=12+ yrs 8 1 0 (0.8750000 0.1250000) * ## 51) education=6-11yrs 12 5 1 (0.4166667 0.5833333) * ## 13) parity< 1.5 27 9 1 (0.3333333 0.6666667) * ## 7) spontaneous>=1.5 34 11 1 (0.3235294 0.6764706) ## 14) parity>=3.5 10 4 0 (0.6000000 0.4000000) * ## 15) parity< 3.5 24 5 1 (0.2083333 0.7916667) *
rpart::plotcp(model)
rpart::rsq.rpart(model)## ## Classification tree: ## rpart::rpart(formula = infert_formula, data = train_test_classification$f$train$f1, ## model = TRUE, x = TRUE, y = TRUE) ## ## Variables actually used in tree construction: ## [1] parity spontaneous ## ## Root node error: 75/223 = 0.33632 ## ## n= 223 ## ## CP nsplit rel error xerror xstd ## 1 0.093333 0 1.00000 1.00000 0.094069 ## 2 0.026667 3 0.72000 0.88000 0.090888 ## 3 0.013333 4 0.69333 0.77333 0.087346
## Warning in rpart::rsq.rpart(model): may not be applicable for this method
error<-data.frame(model$cptable)
error$nsplit<-factor(error$nsplit+1)
tree_size<-error[which.min(error[,"xerror"]),"nsplit"]
error<-reshape2::melt(error,id.vars="nsplit")
names(error)<-c("Split","Metric","value")
plot_prune<-ggplot(error,aes(x=Split,y=value,color=Metric))+
geom_line(aes(group=Metric))+
geom_point()+
labs(title=paste("Error Plot","Suggested Size:",tree_size),y="Metric value",x="Size of Tree")+
theme_bw(base_size=10)
plot_prune
rpart.plot::rpart.plot(model,type=1)
frame<-data.frame(model$frame)
cp<-data.frame(model$cptable)
parameters<-data.frame(parameters=unlist(model$control))
splits<-data.frame(name=row.names(model$splits),model$splits,row.names=NULL)
importance<-data.frame(importance=model$variable.importance)
ordered<-data.frame(ordered=model$ordered)
data<-data.frame(y=model$y,x=model$x,model=model$model)
call<-data.frame(call=call_to_string(model))
result<-list(frame=frame,cp=cp,parameters=parameters,splits=splits,importance=importance,ordered=ordered,call=call)
print(result)## $frame ## var n wt dev yval complexity ncompete nsurrogate yval2.V1 yval2.V2 yval2.V3 yval2.V4 yval2.V5 yval2.nodeprob ## 1 spontaneous 223 223 75 1 0.09333333 4 3 1.00000000 148.00000000 75.00000000 0.66367713 0.33632287 1.00000000 ## 2131 131 26 1 0.00000000 0 0 1.00000000 105.00000000 26.00000000 0.80152672 0.19847328 0.58744395 ## 3 spontaneous 92 92 43 2 0.09333333 4 3 2.00000000 43.00000000 49.00000000 0.46739130 0.53260870 0.41255605 ## 6 parity 58 58 26 1 0.09333333 3 3 1.00000000 32.00000000 26.00000000 0.55172414 0.44827586 0.26008969 ## 12 31 31 8 1 0.01333333 0 0 1.00000000 23.00000000 8.00000000 0.74193548 0.25806452 0.13901345 ## 13 27 27 9 2 0.00000000 0 0 2.00000000 9.00000000 18.00000000 0.33333333 0.66666667 0.12107623 ## 7 parity 34 34 11 2 0.02666667 3 2 2.00000000 11.00000000 23.00000000 0.32352941 0.67647059 0.15246637 ## 14 10 10 4 1 0.01000000 0 0 1.00000000 6.00000000 4.00000000 0.60000000 0.40000000 0.04484305 ## 15 24 24 5 2 0.00000000 0 0 2.00000000 5.00000000 19.00000000 0.20833333 0.79166667 0.10762332 ## ## $cp ## CP nsplit rel.error xerror xstd ## 1 0.09333333 0 1.0000000 1.0000000 0.09406927 ## 2 0.02666667 3 0.7200000 0.8800000 0.09088832 ## 3 0.01333333 4 0.6933333 0.7733333 0.08734585 ## ## $parameters ## parameters ## minsplit 20.00 ## minbucket 7.00 ## cp 0.01 ## maxcompete 4.00 ## maxsurrogate 5.00 ## usesurrogate 2.00 ## surrogatestyle 0.00 ## maxdepth 30.00 ## xval 10.00 ## ## $splits ## name count ncat improve index adj ## 1 spontaneous 223 -1 12.06783237 0.5 0.00000000 ## 2 parity 223 -1 0.21444673 2.5 0.00000000 ## 3 age 223 -1 0.11411177 33.0 0.00000000 ## 4 education 223 3 0.08490284 1.0 0.00000000 ## 5 induced 223 -1 0.07061948 0.5 0.00000000 ## 6 parity 0 -1 0.64573991 2.5 0.14130435 ## 7 age 0 1 0.59192825 22.0 0.01086957 ## 8 induced 0 1 0.59192825 0.5 0.01086957 ## 9 spontaneous 92 -1 2.23233971 1.5 0.00000000 ## 10 parity 92 1 2.16115534 3.5 0.00000000 ## 11 age 92 -1 2.05434783 37.5 0.00000000 ## 12 education 92 3 0.09276390 2.0 0.00000000 ## 13 induced 92 1 0.01517404 0.5 0.00000000 ## 14 age 0 -1 0.67391304 37.5 0.11764706 ## 15 parity 0 -1 0.67391304 4.5 0.11764706 ## 16 education 0 3 0.65217391 3.0 0.05882353 ## 17 parity 58 1 4.81868743 1.5 0.00000000 ## 18 age 58 -1 0.45207941 30.5 0.00000000 ## 19 induced 58 1 0.14228675 0.5 0.00000000 ## 20 education 58 3 0.13793103 4.0 0.00000000 ## 21 induced 0 1 0.81034483 0.5 0.59259259 ## 22 education 0 3 0.65517241 5.0 0.25925926 ## 23 age 0 1 0.63793103 25.5 0.22222222 ## 24 parity 34 1 2.16568627 3.5 0.00000000 ## 25 age 34 -1 1.11846405 30.5 0.00000000 ## 26 education 34 3 1.11846405 6.0 0.00000000 ## 27 induced 34 -1 0.57547463 0.5 0.00000000 ## 28 education 0 3 0.76470588 7.0 0.20000000 ## 29 induced 0 1 0.73529412 0.5 0.10000000 ## ## $importance ## importance ## spontaneous 14.300172 ## parity 8.952239 ## induced 3.203259 ## education 1.813741 ## age 1.464620 ## ## $ordered ## ordered ## age FALSE ## parity FALSE ## education FALSE ## spontaneous FALSE ## induced FALSE ## ## $call ## call ## 1 rpart::rpart(formula=infert_formula,data=train_test_classification$f$train$f1,,model=TRUE,x=TRUE,y=TRUE)
Rpart Regression
result<-data.frame(rtree_regression$cptable)
result$nsplit<-factor(result$nsplit+1)
minimun_size<-as.numeric(as.character(result[which.min(result[,"xerror"]),"nsplit"]))
initial_model<-rtree_regression
model<-rpart::prune(rtree_regression,cp=rtree_regression$cptable[which.min(rtree_regression$cptable[,"xerror"]),"CP"])
importance<-model$variable.importance
importance<-data.frame(names=names(importance),importance=importance)
importance$names<-factor(importance$names,levels=rev(as.character(importance$names)))
plot_importance<-ggplot(importance,aes(x=names,y=importance))+
geom_bar(stat='identity')+
labs(title="Importance Plot",y="Relative Influence",x="Predictor")+
theme_bw(base_size=10)+
scale_x_discrete(limits=rev(levels(names)))+
coord_flip()
plot_importance
rtree_regression## n= 455 ## ## node), split, n, deviance, yval ## * denotes terminal node ## ## 1) root 455 37518.1000 22.77714 ## 2) rm< 7.0105 397 15982.5900 20.38892 ## 4) lstat>=14.4 153 2791.3460 15.16536 ## 8) nox>=0.607 93 1144.4070 13.17204 ## 16) lstat>=19.645 45 326.8520 10.81333 * ## 17) lstat< 19.645 48 332.4867 15.38333 * ## 9) nox< 0.607 60 704.6685 18.25500 * ## 5) lstat< 14.4 244 6398.8200 23.66434 ## 10) lstat>=5.41 214 3854.0590 22.68178 ## 20) lstat>=9.725 107 700.1824 20.99159 * ## 21) lstat< 9.725 107 2542.5360 24.37196 ## 42) age< 89.45 99 1077.6180 23.70404 * ## 43) age>=89.45 8 874.1988 32.63750 * ## 11) lstat< 5.41 30 864.3787 30.67333 * ## 3) rm>=7.0105 58 3772.1660 39.12414 ## 6) rm< 7.437 31 837.2684 33.11935 * ## 7) rm>=7.437 27 533.7407 46.01852 *
rpart::plotcp(model)
rpart::rsq.rpart(model)## ## Regression tree: ## rpart::rpart(formula = boston_formula, data = train_test_regression$f$train$f1, ## model = TRUE, x = TRUE, y = TRUE) ## ## Variables actually used in tree construction: ## [1] age lstat nox rm ## ## Root node error: 37518/455 = 82.457 ## ## n= 455 ## ## CP nsplit rel error xerror xstd ## 1 0.473461 0 1.00000 1.00312 0.088717 ## 2 0.181044 1 0.52654 0.58030 0.058757 ## 3 0.064000 2 0.34550 0.39662 0.047970 ## 4 0.044789 3 0.28150 0.31518 0.042157 ## 5 0.025115 4 0.23671 0.28337 0.041015 ## 6 0.016295 5 0.21159 0.26362 0.041056 ## 7 0.015745 6 0.19530 0.26679 0.041138 ## 8 0.012929 7 0.17955 0.26516 0.043149 ## 9 0.010000 8 0.16662 0.26008 0.043140
error<-data.frame(model$cptable)
error$nsplit<-factor(error$nsplit+1)
tree_size<-error[which.min(error[,"xerror"]),"nsplit"]
error<-reshape2::melt(error,id.vars="nsplit")
names(error)<-c("Split","Metric","value")
plot_prune<-ggplot(error,aes(x=Split,y=value,color=Metric))+
geom_line(aes(group=Metric))+
geom_point()+
labs(title=paste("Error Plot","Suggested Size:",tree_size),y="Metric value",x="Size of Tree")+
theme_bw(base_size=10)
plot_prune
rpart.plot::rpart.plot(model,type=1)
frame<-data.frame(model$frame)
cp<-data.frame(model$cptable)
parameters<-data.frame(parameters=unlist(model$control))
splits<-data.frame(name=row.names(model$splits),model$splits,row.names=NULL)
importance<-data.frame(importance=model$variable.importance)
ordered<-data.frame(ordered=model$ordered)
data<-data.frame(y=model$y,x=model$x,model=model$model)
call<-data.frame(call=call_to_string(model))
result<-list(frame=frame,cp=cp,parameters=parameters,splits=splits,importance=importance,ordered=ordered,call=call)
print(result)## $frame ## var n wt dev yval complexity ncompete nsurrogate ## 1 rm 455 455 37518.1023 22.77714 0.473460643 4 5 ## 2 lstat 397 397 15982.5912 20.38892 0.181043939 4 5 ## 4 nox 153 153 2791.3464 15.16536 0.025115092 4 5 ## 8 lstat 93 93 1144.4073 13.17204 0.012928923 4 5 ## 1645 45 326.8520 10.81333 0.010000000 0 0 ## 17 48 48 332.4867 15.38333 0.010000000 0 0 ## 9 60 60 704.6685 18.25500 0.004693425 0 0 ## 5 lstat 244 244 6398.8198 23.66434 0.044788571 4 3 ## 10 lstat 214 214 3854.0589 22.68178 0.016294550 4 5 ## 20 107 107 700.1824 20.99159 0.001963850 0 0 ## 21 age 107 107 2542.5359 24.37196 0.015744900 4 5 ## 42 99 99 1077.6184 23.70404 0.008387714 0 0 ## 43 8 8 874.1988 32.63750 0.010000000 0 0 ## 11 30 30 864.3787 30.67333 0.004038209 0 0 ## 3 rm 58 58 3772.1662 39.12414 0.063999961 4 5 ## 6 31 31 837.2684 33.11935 0.003017580 0 0 ## 7 27 27 533.7407 46.01852 0.004804938 0 0 ## ## $cp ## CP nsplit rel.error xerror xstd ## 1 0.47346064 0 1.0000000 1.0031192 0.08871684 ## 2 0.18104394 1 0.5265394 0.5803040 0.05875669 ## 3 0.06399996 2 0.3454954 0.3966223 0.04796970 ## 4 0.04478857 3 0.2814955 0.3151798 0.04215714 ## 5 0.02511509 4 0.2367069 0.2833655 0.04101530 ## 6 0.01629455 5 0.2115918 0.2636155 0.04105647 ## 7 0.01574490 6 0.1952972 0.2667909 0.04113817 ## 8 0.01292892 7 0.1795523 0.2651643 0.04314947 ## 9 0.01000000 8 0.1666234 0.2600830 0.04313979 ## ## $parameters ## parameters ## minsplit 20.00 ## minbucket 7.00 ## cp 0.01 ## maxcompete 4.00 ## maxsurrogate 5.00 ## usesurrogate 2.00 ## surrogatestyle 0.00 ## maxdepth 30.00 ## xval 10.00 ## ## $splits ## name count ncat improve index adj ## 1 rm 455 -1 0.47346064 7.010500 0.00000000 ## 2 lstat 455 1 0.43594812 9.725000 0.00000000 ## 3 indus 455 1 0.25311926 6.660000 0.00000000 ## 4 ptratio 455 1 0.24122713 19.900000 0.00000000 ## 5 nox 455 1 0.21087719 0.669500 0.00000000 ## 6 lstat 0 1 0.90549451 4.150000 0.25862069 ## 7 ptratio 0 1 0.89890110 14.550000 0.20689655 ## 8 zn 0 -1 0.88131868 87.500000 0.06896552 ## 9 indus 0 1 0.88131868 1.605000 0.06896552 ## 10 crim 0 1 0.87692308 0.013355 0.03448276 ## 11 lstat 397 1 0.42498897 14.400000 0.00000000 ## 12 nox 397 1 0.26514757 0.669500 0.00000000 ## 13 ptratio 397 1 0.22430246 19.900000 0.00000000 ## 14 crim 397 1 0.22018148 5.848030 0.00000000 ## 15 age 397 1 0.20548981 75.750000 0.00000000 ## 16 age 0 1 0.81863980 91.150000 0.52941176 ## 17 tax 0 1 0.77833753 434.500000 0.42483660 ## 18 dis 0 -1 0.77581864 2.239350 0.41830065 ## 19 crim 0 1 0.77329975 4.067905 0.41176471 ## 20 indus 0 1 0.77329975 16.570000 0.41176471 ## 21 nox 153 1 0.33756849 0.607000 0.00000000 ## 22 crim 153 1 0.30454235 6.992370 0.00000000 ## 23 dis 153 -1 0.28243585 2.003700 0.00000000 ## 24 tax 153 1 0.25929100 567.500000 0.00000000 ## 25 lstat 153 1 0.25537353 21.490000 0.00000000 ## 26 indus 0 1 0.88235294 16.010000 0.70000000 ## 27 tax 0 1 0.87581699 397.000000 0.68333333 ## 28 dis 0 -1 0.84967320 2.384050 0.61666667 ## 29 crim 0 1 0.82352941 1.400920 0.55000000 ## 30 rad 0 1 0.75816993 16.000000 0.38333333 ## 31 lstat 93 1 0.42386014 19.645000 0.00000000 ## 32 crim 93 1 0.38301367 11.369150 0.00000000 ## 33 dis 93 -1 0.19498794 2.003700 0.00000000 ## 34 tax 93 1 0.14693985 551.500000 0.00000000 ## 35 rm 93 -1 0.13771335 5.453500 0.00000000 ## 36 dis 0 -1 0.79569892 1.668650 0.57777778 ## 37 crim 0 1 0.73118280 9.084990 0.44444444 ## 38 rm 0 -1 0.73118280 5.586500 0.44444444 ## 39 age 0 1 0.70967742 98.850000 0.40000000 ## 40 nox 0 -1 0.65591398 0.706500 0.28888889 ## 41 lstat 244 1 0.26260815 5.410000 0.00000000 ## 42 rm 244 -1 0.24420279 6.543000 0.00000000 ## 43 dis 244 1 0.11343084 1.611700 0.00000000 ## 44 tax 244 1 0.07857446 222.500000 0.00000000 ## 45 age 244 -1 0.07027078 99.450000 0.00000000 ## 46 zn 0 -1 0.88934426 87.500000 0.10000000 ## 47 crim 0 1 0.88114754 0.014700 0.03333333 ## 48 rm 0 -1 0.88114754 6.797000 0.03333333 ## 49 lstat 214 1 0.15862254 9.725000 0.00000000 ## 50 rm 214 -1 0.13369709 6.544500 0.00000000 ## 51 crim 214 -1 0.11943304 7.247120 0.00000000 ## 52 dis 214 1 0.11435385 1.615600 0.00000000 ## 53 age 214 -1 0.05987248 99.450000 0.00000000 ## 54 nox 0 1 0.71962617 0.519000 0.43925234 ## 55 rm 0 -1 0.70093458 6.260000 0.40186916 ## 56 indus 0 1 0.69626168 7.625000 0.39252336 ## 57 crim 0 1 0.68691589 0.130245 0.37383178 ## 58 dis 0 -1 0.67757009 4.480250 0.35514019 ## 59 age 107 -1 0.23233448 89.450000 0.00000000 ## 60 dis 107 1 0.22810109 2.089100 0.00000000 ## 61 nox 107 -1 0.20573659 0.589000 0.00000000 ## 62 crim 107 -1 0.17012999 1.308150 0.00000000 ## 63 indus 107 -1 0.16559151 16.570000 0.00000000 ## 64 dis 0 1 0.98130841 2.227500 0.75000000 ## 65 nox 0 -1 0.96261682 0.589000 0.50000000 ## 66 ptratio 0 1 0.96261682 14.750000 0.50000000 ## 67 indus 0 -1 0.95327103 18.840000 0.37500000 ## 68 black 0 1 0.95327103 354.295000 0.37500000 ## 69 rm 58 -1 0.63654594 7.437000 0.00000000 ## 70 lstat 58 1 0.39191315 4.680000 0.00000000 ## 71 black 58 1 0.15346650 392.790000 0.00000000 ## 72 ptratio 58 1 0.11944861 14.750000 0.00000000 ## 73 dis 58 1 0.09704531 6.687000 0.00000000 ## 74 lstat 0 1 0.81034483 4.680000 0.59259259 ## 75 black 0 1 0.67241379 391.410000 0.29629630 ## 76 crim 0 -1 0.63793103 0.112760 0.22222222 ## 77 ptratio 0 1 0.62068966 14.750000 0.18518519 ## 78 zn 0 1 0.60344828 27.500000 0.14814815 ## ## $importance ## importance ## rm 20681.7797 ## lstat 15586.0929 ## indus 5143.0136 ## crim 4961.3867 ## ptratio 4415.1929 ## age 4380.7359 ## dis 4362.7553 ## tax 3529.5557 ## zn 1748.8235 ## nox 1646.2937 ## black 932.9735 ## rad 361.2037 ## ## $ordered ## ordered ## crim FALSE ## zn FALSE ## indus FALSE ## chas FALSE ## nox FALSE ## rm FALSE ## age FALSE ## dis FALSE ## rad FALSE ## tax FALSE ## ptratio FALSE ## black FALSE ## lstat FALSE ## ## $call ## call ## 1 rpart::rpart(formula=boston_formula,data=train_test_regression$f$train$f1,,model=TRUE,x=TRUE,y=TRUE)