library(tree)
library(ISLR)
attach(Carseats)
High<-ifelse(Sales<=8, "NO","YES")
Carseats<-data.frame(Carseats, High)
- Install package ‘tree’ to construct a decision tree
- Merge new column ‘High’ with ‘Carseats’
(tree.Carseats<-tree(High~.-Sales, data=Carseats))
## node), split, n, deviance, yval, (yprob)
## * denotes terminal node
##
## 1) root 400 541.500 NO ( 0.59000 0.41000 )
## 2) ShelveLoc: Bad,Medium 315 390.600 NO ( 0.68889 0.31111 )
## 4) Price < 92.5 46 56.530 YES ( 0.30435 0.69565 )
## 8) Income < 57 10 12.220 NO ( 0.70000 0.30000 )
## 16) CompPrice < 110.5 5 0.000 NO ( 1.00000 0.00000 ) *
## 17) CompPrice > 110.5 5 6.730 YES ( 0.40000 0.60000 ) *
## 9) Income > 57 36 35.470 YES ( 0.19444 0.80556 )
## 18) Population < 207.5 16 21.170 YES ( 0.37500 0.62500 ) *
## 19) Population > 207.5 20 7.941 YES ( 0.05000 0.95000 ) *
## 5) Price > 92.5 269 299.800 NO ( 0.75465 0.24535 )
## 10) Advertising < 13.5 224 213.200 NO ( 0.81696 0.18304 )
## 20) CompPrice < 124.5 96 44.890 NO ( 0.93750 0.06250 )
## 40) Price < 106.5 38 33.150 NO ( 0.84211 0.15789 )
## 80) Population < 177 12 16.300 NO ( 0.58333 0.41667 )
## 160) Income < 60.5 6 0.000 NO ( 1.00000 0.00000 ) *
## 161) Income > 60.5 6 5.407 YES ( 0.16667 0.83333 ) *
## 81) Population > 177 26 8.477 NO ( 0.96154 0.03846 ) *
## 41) Price > 106.5 58 0.000 NO ( 1.00000 0.00000 ) *
## 21) CompPrice > 124.5 128 150.200 NO ( 0.72656 0.27344 )
## 42) Price < 122.5 51 70.680 YES ( 0.49020 0.50980 )
## 84) ShelveLoc: Bad 11 6.702 NO ( 0.90909 0.09091 ) *
## 85) ShelveLoc: Medium 40 52.930 YES ( 0.37500 0.62500 )
## 170) Price < 109.5 16 7.481 YES ( 0.06250 0.93750 ) *
## 171) Price > 109.5 24 32.600 NO ( 0.58333 0.41667 )
## 342) Age < 49.5 13 16.050 YES ( 0.30769 0.69231 ) *
## 343) Age > 49.5 11 6.702 NO ( 0.90909 0.09091 ) *
## 43) Price > 122.5 77 55.540 NO ( 0.88312 0.11688 )
## 86) CompPrice < 147.5 58 17.400 NO ( 0.96552 0.03448 ) *
## 87) CompPrice > 147.5 19 25.010 NO ( 0.63158 0.36842 )
## 174) Price < 147 12 16.300 YES ( 0.41667 0.58333 )
## 348) CompPrice < 152.5 7 5.742 YES ( 0.14286 0.85714 ) *
## 349) CompPrice > 152.5 5 5.004 NO ( 0.80000 0.20000 ) *
## 175) Price > 147 7 0.000 NO ( 1.00000 0.00000 ) *
## 11) Advertising > 13.5 45 61.830 YES ( 0.44444 0.55556 )
## 22) Age < 54.5 25 25.020 YES ( 0.20000 0.80000 )
## 44) CompPrice < 130.5 14 18.250 YES ( 0.35714 0.64286 )
## 88) Income < 100 9 12.370 NO ( 0.55556 0.44444 ) *
## 89) Income > 100 5 0.000 YES ( 0.00000 1.00000 ) *
## 45) CompPrice > 130.5 11 0.000 YES ( 0.00000 1.00000 ) *
## 23) Age > 54.5 20 22.490 NO ( 0.75000 0.25000 )
## 46) CompPrice < 122.5 10 0.000 NO ( 1.00000 0.00000 ) *
## 47) CompPrice > 122.5 10 13.860 NO ( 0.50000 0.50000 )
## 94) Price < 125 5 0.000 YES ( 0.00000 1.00000 ) *
## 95) Price > 125 5 0.000 NO ( 1.00000 0.00000 ) *
## 3) ShelveLoc: Good 85 90.330 YES ( 0.22353 0.77647 )
## 6) Price < 135 68 49.260 YES ( 0.11765 0.88235 )
## 12) US: No 17 22.070 YES ( 0.35294 0.64706 )
## 24) Price < 109 8 0.000 YES ( 0.00000 1.00000 ) *
## 25) Price > 109 9 11.460 NO ( 0.66667 0.33333 ) *
## 13) US: Yes 51 16.880 YES ( 0.03922 0.96078 ) *
## 7) Price > 135 17 22.070 NO ( 0.64706 0.35294 )
## 14) Income < 46 6 0.000 NO ( 1.00000 0.00000 ) *
## 15) Income > 46 11 15.160 YES ( 0.45455 0.54545 ) *
summary(tree.Carseats)
##
## Classification tree:
## tree(formula = High ~ . - Sales, data = Carseats)
## Variables actually used in tree construction:
## [1] "ShelveLoc" "Price" "Income" "CompPrice" "Population"
## [6] "Advertising" "Age" "US"
## Number of terminal nodes: 27
## Residual mean deviance: 0.4575 = 170.7 / 373
## Misclassification error rate: 0.09 = 36 / 400
- Decision tree : Split prediction space to obtain best partitions with minimized impurity.
- tree.Carseats : Use all possible predictor variables except ‘Sales’
plot(tree.Carseats)
text(tree.Carseats, pretty=0)
tree.Carseats
## node), split, n, deviance, yval, (yprob)
## * denotes terminal node
##
## 1) root 400 541.500 NO ( 0.59000 0.41000 )
## 2) ShelveLoc: Bad,Medium 315 390.600 NO ( 0.68889 0.31111 )
## 4) Price < 92.5 46 56.530 YES ( 0.30435 0.69565 )
## 8) Income < 57 10 12.220 NO ( 0.70000 0.30000 )
## 16) CompPrice < 110.5 5 0.000 NO ( 1.00000 0.00000 ) *
## 17) CompPrice > 110.5 5 6.730 YES ( 0.40000 0.60000 ) *
## 9) Income > 57 36 35.470 YES ( 0.19444 0.80556 )
## 18) Population < 207.5 16 21.170 YES ( 0.37500 0.62500 ) *
## 19) Population > 207.5 20 7.941 YES ( 0.05000 0.95000 ) *
## 5) Price > 92.5 269 299.800 NO ( 0.75465 0.24535 )
## 10) Advertising < 13.5 224 213.200 NO ( 0.81696 0.18304 )
## 20) CompPrice < 124.5 96 44.890 NO ( 0.93750 0.06250 )
## 40) Price < 106.5 38 33.150 NO ( 0.84211 0.15789 )
## 80) Population < 177 12 16.300 NO ( 0.58333 0.41667 )
## 160) Income < 60.5 6 0.000 NO ( 1.00000 0.00000 ) *
## 161) Income > 60.5 6 5.407 YES ( 0.16667 0.83333 ) *
## 81) Population > 177 26 8.477 NO ( 0.96154 0.03846 ) *
## 41) Price > 106.5 58 0.000 NO ( 1.00000 0.00000 ) *
## 21) CompPrice > 124.5 128 150.200 NO ( 0.72656 0.27344 )
## 42) Price < 122.5 51 70.680 YES ( 0.49020 0.50980 )
## 84) ShelveLoc: Bad 11 6.702 NO ( 0.90909 0.09091 ) *
## 85) ShelveLoc: Medium 40 52.930 YES ( 0.37500 0.62500 )
## 170) Price < 109.5 16 7.481 YES ( 0.06250 0.93750 ) *
## 171) Price > 109.5 24 32.600 NO ( 0.58333 0.41667 )
## 342) Age < 49.5 13 16.050 YES ( 0.30769 0.69231 ) *
## 343) Age > 49.5 11 6.702 NO ( 0.90909 0.09091 ) *
## 43) Price > 122.5 77 55.540 NO ( 0.88312 0.11688 )
## 86) CompPrice < 147.5 58 17.400 NO ( 0.96552 0.03448 ) *
## 87) CompPrice > 147.5 19 25.010 NO ( 0.63158 0.36842 )
## 174) Price < 147 12 16.300 YES ( 0.41667 0.58333 )
## 348) CompPrice < 152.5 7 5.742 YES ( 0.14286 0.85714 ) *
## 349) CompPrice > 152.5 5 5.004 NO ( 0.80000 0.20000 ) *
## 175) Price > 147 7 0.000 NO ( 1.00000 0.00000 ) *
## 11) Advertising > 13.5 45 61.830 YES ( 0.44444 0.55556 )
## 22) Age < 54.5 25 25.020 YES ( 0.20000 0.80000 )
## 44) CompPrice < 130.5 14 18.250 YES ( 0.35714 0.64286 )
## 88) Income < 100 9 12.370 NO ( 0.55556 0.44444 ) *
## 89) Income > 100 5 0.000 YES ( 0.00000 1.00000 ) *
## 45) CompPrice > 130.5 11 0.000 YES ( 0.00000 1.00000 ) *
## 23) Age > 54.5 20 22.490 NO ( 0.75000 0.25000 )
## 46) CompPrice < 122.5 10 0.000 NO ( 1.00000 0.00000 ) *
## 47) CompPrice > 122.5 10 13.860 NO ( 0.50000 0.50000 )
## 94) Price < 125 5 0.000 YES ( 0.00000 1.00000 ) *
## 95) Price > 125 5 0.000 NO ( 1.00000 0.00000 ) *
## 3) ShelveLoc: Good 85 90.330 YES ( 0.22353 0.77647 )
## 6) Price < 135 68 49.260 YES ( 0.11765 0.88235 )
## 12) US: No 17 22.070 YES ( 0.35294 0.64706 )
## 24) Price < 109 8 0.000 YES ( 0.00000 1.00000 ) *
## 25) Price > 109 9 11.460 NO ( 0.66667 0.33333 ) *
## 13) US: Yes 51 16.880 YES ( 0.03922 0.96078 ) *
## 7) Price > 135 17 22.070 NO ( 0.64706 0.35294 )
## 14) Income < 46 6 0.000 NO ( 1.00000 0.00000 ) *
## 15) Income > 46 11 15.160 YES ( 0.45455 0.54545 ) *
- Function ‘plot’ : Draw tree structure
- Function ‘text’ : (Low-level Graphical function) Label nodes.
- ‘pretty = 0’ : Include the category names for any qualitative predictors, rather than simple letter.
set.seed(3)
train<-sample(1:nrow(Carseats), nrow(Carseats)/2)
test<-(-train)
Carseats.test<-Carseats[test,]
High.test<-High[test]
tree.Carseats<-tree(High~.-Sales, data=Carseats, subset=train)
tree.pred<-predict(tree.Carseats, Carseats.test, type="class")
table(tree.pred, High.test)
## High.test
## tree.pred NO YES
## NO 82 23
## YES 44 51
str(Carseats)
## 'data.frame': 400 obs. of 12 variables:
## $ Sales : num 9.5 11.22 10.06 7.4 4.15 ...
## $ CompPrice : num 138 111 113 117 141 124 115 136 132 132 ...
## $ Income : num 73 48 35 100 64 113 105 81 110 113 ...
## $ Advertising: num 11 16 10 4 3 13 0 15 0 0 ...
## $ Population : num 276 260 269 466 340 501 45 425 108 131 ...
## $ Price : num 120 83 80 97 128 72 108 120 124 124 ...
## $ ShelveLoc : Factor w/ 3 levels "Bad","Good","Medium": 1 2 3 3 1 1 3 2 3 3 ...
## $ Age : num 42 65 59 55 38 78 71 67 76 76 ...
## $ Education : num 17 10 12 14 13 16 15 10 10 17 ...
## $ Urban : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 2 2 1 1 ...
## $ US : Factor w/ 2 levels "No","Yes": 2 2 2 2 1 2 1 2 1 2 ...
## $ High : Factor w/ 2 levels "NO","YES": 2 2 2 1 1 2 1 2 1 1 ...
library(MASS)
set.seed(1)
train<-sample(1:nrow(Boston),nrow(Boston)/2)
tree.Boston<-tree(medv~., data=Boston, subset=train)
summary(tree.Boston)
##
## Regression tree:
## tree(formula = medv ~ ., data = Boston, subset = train)
## Variables actually used in tree construction:
## [1] "lstat" "rm" "dis"
## Number of terminal nodes: 8
## Residual mean deviance: 12.65 = 3099 / 245
## Distribution of residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -14.10000 -2.04200 -0.05357 0.00000 1.96000 12.60000
plot(tree.Boston)
text(tree.Boston, pretty=0)
cv.Boston<-cv.tree(tree.Boston)
plot(cv.Boston$size, cv.Boston$dev, type='b')
prune.Boston<-prune.tree(tree.Boston, best = 5)
plot(prune.Boston)
text(prune.Boston, pretty=0)
yhat<-predict(tree.Boston, newdata=Boston[-train,])
Boston.test<-Boston[-train, "medv"]
plot(yhat, Boston.test)
abline(0,1)
mean((yhat-Boston.test)^2)
## [1] 25.04559