Activity_9
whitewine <- read.csv("winequality-white.csv",sep = ";",
stringsAsFactors = TRUE)
str(whitewine)## 'data.frame': 4898 obs. of 12 variables:
## $ fixed.acidity : num 7 6.3 8.1 7.2 7.2 8.1 6.2 7 6.3 8.1 ...
## $ volatile.acidity : num 0.27 0.3 0.28 0.23 0.23 0.28 0.32 0.27 0.3 0.22 ...
## $ citric.acid : num 0.36 0.34 0.4 0.32 0.32 0.4 0.16 0.36 0.34 0.43 ...
## $ residual.sugar : num 20.7 1.6 6.9 8.5 8.5 6.9 7 20.7 1.6 1.5 ...
## $ chlorides : num 0.045 0.049 0.05 0.058 0.058 0.05 0.045 0.045 0.049 0.044 ...
## $ free.sulfur.dioxide : num 45 14 30 47 47 30 30 45 14 28 ...
## $ total.sulfur.dioxide: num 170 132 97 186 186 97 136 170 132 129 ...
## $ density : num 1.001 0.994 0.995 0.996 0.996 ...
## $ pH : num 3 3.3 3.26 3.19 3.19 3.26 3.18 3 3.3 3.22 ...
## $ sulphates : num 0.45 0.49 0.44 0.4 0.4 0.44 0.47 0.45 0.49 0.45 ...
## $ alcohol : num 8.8 9.5 10.1 9.9 9.9 10.1 9.6 8.8 9.5 11 ...
## $ quality : int 6 6 6 6 6 6 6 6 6 6 ...# the distribution of quality ratings
hist(whitewine$quality)
summary(whitewine)## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. : 3.800 Min. :0.0800 Min. :0.0000 Min. : 0.600
## 1st Qu.: 6.300 1st Qu.:0.2100 1st Qu.:0.2700 1st Qu.: 1.700
## Median : 6.800 Median :0.2600 Median :0.3200 Median : 5.200
## Mean : 6.855 Mean :0.2782 Mean :0.3342 Mean : 6.391
## 3rd Qu.: 7.300 3rd Qu.:0.3200 3rd Qu.:0.3900 3rd Qu.: 9.900
## Max. :14.200 Max. :1.1000 Max. :1.6600 Max. :65.800
## chlorides free.sulfur.dioxide total.sulfur.dioxide density
## Min. :0.00900 Min. : 2.00 Min. : 9.0 Min. :0.9871
## 1st Qu.:0.03600 1st Qu.: 23.00 1st Qu.:108.0 1st Qu.:0.9917
## Median :0.04300 Median : 34.00 Median :134.0 Median :0.9937
## Mean :0.04577 Mean : 35.31 Mean :138.4 Mean :0.9940
## 3rd Qu.:0.05000 3rd Qu.: 46.00 3rd Qu.:167.0 3rd Qu.:0.9961
## Max. :0.34600 Max. :289.00 Max. :440.0 Max. :1.0390
## pH sulphates alcohol quality
## Min. :2.720 Min. :0.2200 Min. : 8.00 Min. :3.000
## 1st Qu.:3.090 1st Qu.:0.4100 1st Qu.: 9.50 1st Qu.:5.000
## Median :3.180 Median :0.4700 Median :10.40 Median :6.000
## Mean :3.188 Mean :0.4898 Mean :10.51 Mean :5.878
## 3rd Qu.:3.280 3rd Qu.:0.5500 3rd Qu.:11.40 3rd Qu.:6.000
## Max. :3.820 Max. :1.0800 Max. :14.20 Max. :9.000whitewine_train <- whitewine[1:3750, ]
whitewine_test <- whitewine[3751:4898, ]Training a model on the data
library(rpart)
m.rpart <- rpart(quality ~ ., data = whitewine_train)# get basic information about the tree
m.rpart## n= 3750
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 3750 3140.06000 5.886933
## 2) alcohol< 10.85 2473 1510.66200 5.609381
## 4) volatile.acidity>=0.2425 1406 740.15080 5.402560
## 8) volatile.acidity>=0.4225 182 92.99451 4.994505 *
## 9) volatile.acidity< 0.4225 1224 612.34560 5.463235 *
## 5) volatile.acidity< 0.2425 1067 631.12090 5.881912 *
## 3) alcohol>=10.85 1277 1069.95800 6.424432
## 6) free.sulfur.dioxide< 11.5 93 99.18280 5.473118 *
## 7) free.sulfur.dioxide>=11.5 1184 879.99920 6.499155
## 14) alcohol< 11.85 611 447.38130 6.296236 *
## 15) alcohol>=11.85 573 380.63180 6.715532 *# get more detailed information about the tree
summary(m.rpart)## Call:
## rpart(formula = quality ~ ., data = whitewine_train)
## n= 3750
##
## CP nsplit rel error xerror xstd
## 1 0.17816211 0 1.0000000 1.0012045 0.02391262
## 2 0.04439109 1 0.8218379 0.8234799 0.02239999
## 3 0.02890893 2 0.7774468 0.7861089 0.02209662
## 4 0.01655575 3 0.7485379 0.7576577 0.02093863
## 5 0.01108600 4 0.7319821 0.7427597 0.02047926
## 6 0.01000000 5 0.7208961 0.7354229 0.02036136
##
## Variable importance
## alcohol density chlorides
## 38 23 12
## volatile.acidity total.sulfur.dioxide free.sulfur.dioxide
## 12 7 6
## sulphates pH residual.sugar
## 1 1 1
##
## Node number 1: 3750 observations, complexity param=0.1781621
## mean=5.886933, MSE=0.8373493
## left son=2 (2473 obs) right son=3 (1277 obs)
## Primary splits:
## alcohol < 10.85 to the left, improve=0.17816210, (0 missing)
## density < 0.992385 to the right, improve=0.11980970, (0 missing)
## chlorides < 0.0395 to the right, improve=0.08199995, (0 missing)
## total.sulfur.dioxide < 153.5 to the right, improve=0.03875440, (0 missing)
## free.sulfur.dioxide < 11.75 to the left, improve=0.03632119, (0 missing)
## Surrogate splits:
## density < 0.99201 to the right, agree=0.869, adj=0.614, (0 split)
## chlorides < 0.0375 to the right, agree=0.773, adj=0.334, (0 split)
## total.sulfur.dioxide < 102.5 to the right, agree=0.705, adj=0.132, (0 split)
## sulphates < 0.345 to the right, agree=0.670, adj=0.031, (0 split)
## fixed.acidity < 5.25 to the right, agree=0.662, adj=0.009, (0 split)
##
## Node number 2: 2473 observations, complexity param=0.04439109
## mean=5.609381, MSE=0.6108623
## left son=4 (1406 obs) right son=5 (1067 obs)
## Primary splits:
## volatile.acidity < 0.2425 to the right, improve=0.09227123, (0 missing)
## free.sulfur.dioxide < 13.5 to the left, improve=0.04177240, (0 missing)
## alcohol < 10.15 to the left, improve=0.03313802, (0 missing)
## citric.acid < 0.205 to the left, improve=0.02721200, (0 missing)
## pH < 3.325 to the left, improve=0.01860335, (0 missing)
## Surrogate splits:
## total.sulfur.dioxide < 111.5 to the right, agree=0.610, adj=0.097, (0 split)
## pH < 3.295 to the left, agree=0.598, adj=0.067, (0 split)
## alcohol < 10.05 to the left, agree=0.590, adj=0.049, (0 split)
## sulphates < 0.715 to the left, agree=0.584, adj=0.037, (0 split)
## residual.sugar < 1.85 to the right, agree=0.581, adj=0.029, (0 split)
##
## Node number 3: 1277 observations, complexity param=0.02890893
## mean=6.424432, MSE=0.8378682
## left son=6 (93 obs) right son=7 (1184 obs)
## Primary splits:
## free.sulfur.dioxide < 11.5 to the left, improve=0.08484051, (0 missing)
## alcohol < 11.85 to the left, improve=0.06149941, (0 missing)
## fixed.acidity < 7.35 to the right, improve=0.04259695, (0 missing)
## residual.sugar < 1.275 to the left, improve=0.02795662, (0 missing)
## total.sulfur.dioxide < 67.5 to the left, improve=0.02541719, (0 missing)
## Surrogate splits:
## total.sulfur.dioxide < 48.5 to the left, agree=0.937, adj=0.14, (0 split)
##
## Node number 4: 1406 observations, complexity param=0.011086
## mean=5.40256, MSE=0.526423
## left son=8 (182 obs) right son=9 (1224 obs)
## Primary splits:
## volatile.acidity < 0.4225 to the right, improve=0.04703189, (0 missing)
## free.sulfur.dioxide < 17.5 to the left, improve=0.04607770, (0 missing)
## total.sulfur.dioxide < 86.5 to the left, improve=0.02894310, (0 missing)
## alcohol < 10.25 to the left, improve=0.02890077, (0 missing)
## chlorides < 0.0455 to the right, improve=0.02096635, (0 missing)
## Surrogate splits:
## density < 0.99107 to the left, agree=0.874, adj=0.027, (0 split)
## citric.acid < 0.11 to the left, agree=0.873, adj=0.022, (0 split)
## fixed.acidity < 9.85 to the right, agree=0.873, adj=0.016, (0 split)
## chlorides < 0.206 to the right, agree=0.871, adj=0.005, (0 split)
##
## Node number 5: 1067 observations
## mean=5.881912, MSE=0.591491
##
## Node number 6: 93 observations
## mean=5.473118, MSE=1.066482
##
## Node number 7: 1184 observations, complexity param=0.01655575
## mean=6.499155, MSE=0.7432425
## left son=14 (611 obs) right son=15 (573 obs)
## Primary splits:
## alcohol < 11.85 to the left, improve=0.05907511, (0 missing)
## fixed.acidity < 7.35 to the right, improve=0.04400660, (0 missing)
## density < 0.991395 to the right, improve=0.02522410, (0 missing)
## residual.sugar < 1.225 to the left, improve=0.02503936, (0 missing)
## pH < 3.245 to the left, improve=0.02417936, (0 missing)
## Surrogate splits:
## density < 0.991115 to the right, agree=0.710, adj=0.401, (0 split)
## volatile.acidity < 0.2675 to the left, agree=0.665, adj=0.307, (0 split)
## chlorides < 0.0365 to the right, agree=0.631, adj=0.237, (0 split)
## total.sulfur.dioxide < 126.5 to the right, agree=0.566, adj=0.103, (0 split)
## residual.sugar < 1.525 to the left, agree=0.560, adj=0.091, (0 split)
##
## Node number 8: 182 observations
## mean=4.994505, MSE=0.5109588
##
## Node number 9: 1224 observations
## mean=5.463235, MSE=0.5002823
##
## Node number 14: 611 observations
## mean=6.296236, MSE=0.7322117
##
## Node number 15: 573 observations
## mean=6.715532, MSE=0.6642788install.packages("rpart.plot")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.5'
## (as 'lib' is unspecified)# use the rpart.plot package to create a visualization
library(rpart.plot)# a basic decision tree diagram
rpart.plot(m.rpart, digits = 3)
# a few adjustments to the diagram
rpart.plot(m.rpart, digits = 4, fallen.leaves = TRUE, type = 3, extra = 101)
Evaluate model performance
# generate predictions
p.rpart <- predict(m.rpart, whitewine_test)# compare the distribution of predicted values vs actual values
summary(p.rpart)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.995 5.463 5.882 5.999 6.296 6.716summary(whitewine_test$quality)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.848 6.000 8.000# compare the correlation
cor(p.rpart, whitewine_test$quality)## [1] 0.4931608# function to calculate the mean absolute error
MAE <- function(actual, predicted) {
mean(abs(actual - predicted))
}# mean absolute error between predicted and actual values
MAE(p.rpart, whitewine_test$quality)## [1] 0.5732104# mean absolute error between actual values and mean value
mean(whitewine_train$quality) ## [1] 5.886933MAE(5.87, whitewine_test$quality)## [1] 0.5815679Improving model performance
install.packages("plyr")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.5'
## (as 'lib' is unspecified)install.packages("Cubist")## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.5'
## (as 'lib' is unspecified)library(Cubist)## Loading required package: latticem.cubist <- cubist(x = whitewine_train[-12], y = whitewine_train$quality)
m.cubist##
## Call:
## cubist.default(x = whitewine_train[-12], y = whitewine_train$quality)
##
## Number of samples: 3750
## Number of predictors: 11
##
## Number of committees: 1
## Number of rules: 10# display the tree itself
summary(m.cubist)##
## Call:
## cubist.default(x = whitewine_train[-12], y = whitewine_train$quality)
##
##
## Cubist [Release 2.07 GPL Edition] Tue Feb 3 02:02:40 2026
## ---------------------------------
##
## Target attribute `outcome'
##
## Read 3750 cases (12 attributes) from undefined.data
##
## Model:
##
## Rule 1: [918 cases, mean 5.3, range 3 to 7, est err 0.5]
##
## if
## volatile.acidity > 0.26
## alcohol <= 10.2
## then
## outcome = 66.6 + 0.187 alcohol + 0.041 residual.sugar - 65 density
## - 1.38 volatile.acidity + 0.5 pH + 0.0028 free.sulfur.dioxide
##
## Rule 2: [177 cases, mean 5.5, range 4 to 8, est err 0.5]
##
## if
## citric.acid > 0.42
## residual.sugar <= 14.05
## free.sulfur.dioxide > 49
## then
## outcome = 32.5 + 0.379 alcohol - 0.024 residual.sugar - 31 density
## - 0.54 volatile.acidity + 0.15 sulphates
## + 0.0003 total.sulfur.dioxide + 0.07 pH + 0.4 chlorides
## + 0.01 fixed.acidity
##
## Rule 3: [490 cases, mean 5.7, range 3 to 8, est err 0.5]
##
## if
## volatile.acidity <= 0.26
## residual.sugar <= 12.75
## free.sulfur.dioxide <= 49
## alcohol <= 10.2
## then
## outcome = 253.6 - 252 density + 0.102 residual.sugar
## - 2.63 volatile.acidity + 0.0149 free.sulfur.dioxide
## + 1.27 sulphates + 0.52 pH + 0.012 alcohol
##
## Rule 4: [71 cases, mean 5.8, range 5 to 7, est err 0.4]
##
## if
## fixed.acidity <= 7.5
## volatile.acidity <= 0.26
## residual.sugar > 14.05
## alcohol > 9.1
## then
## outcome = 127.2 - 125 density + 0.055 residual.sugar
## - 2.47 volatile.acidity + 0.24 fixed.acidity + 0.67 sulphates
## + 0.0017 total.sulfur.dioxide + 1.8 chlorides + 0.23 pH
## - 0.0015 free.sulfur.dioxide + 0.013 alcohol
##
## Rule 5: [446 cases, mean 5.8, range 3 to 9, est err 0.5]
##
## if
## citric.acid <= 0.42
## residual.sugar <= 14.05
## free.sulfur.dioxide > 49
## then
## outcome = 29.6 + 0.372 alcohol + 2.81 citric.acid
## - 2.94 volatile.acidity - 28 density + 0.013 residual.sugar
## + 0.13 sulphates + 0.0003 total.sulfur.dioxide
## + 0.01 fixed.acidity
##
## Rule 6: [451 cases, mean 5.9, range 3 to 8, est err 0.7]
##
## if
## free.sulfur.dioxide <= 20
## alcohol > 10.2
## then
## outcome = 16.2 + 0.0537 free.sulfur.dioxide + 0.311 alcohol
## - 2.63 volatile.acidity + 0.037 residual.sugar
## - 0.2 fixed.acidity - 13 density + 0.08 pH
##
## Rule 7: [113 cases, mean 5.9, range 5 to 7, est err 0.5]
##
## if
## fixed.acidity <= 7.5
## volatile.acidity <= 0.26
## residual.sugar > 14.05
## alcohol <= 9.1
## then
## outcome = -8.3 + 2.204 alcohol - 0.143 residual.sugar
## + 0.0066 total.sulfur.dioxide - 1.65 sulphates
## - 0.0092 free.sulfur.dioxide - 3 density
##
## Rule 8: [35 cases, mean 6.2, range 3 to 8, est err 0.8]
##
## if
## fixed.acidity > 7.5
## volatile.acidity <= 0.26
## residual.sugar > 14.05
## alcohol <= 10.2
## then
## outcome = 29.5 - 0.451 residual.sugar - 19.04 volatile.acidity
## - 0.804 alcohol - 39.4 chlorides + 0.0127 total.sulfur.dioxide
## - 0.64 fixed.acidity
##
## Rule 9: [46 cases, mean 6.3, range 5 to 7, est err 0.4]
##
## if
## volatile.acidity <= 0.26
## residual.sugar > 12.75
## residual.sugar <= 14.05
## free.sulfur.dioxide <= 49
## alcohol <= 10.2
## then
## outcome = 11.9 - 13.32 volatile.acidity + 0.0216 total.sulfur.dioxide
## - 8.01 sulphates - 0.0521 free.sulfur.dioxide - 16.2 chlorides
##
## Rule 10: [1410 cases, mean 6.4, range 3 to 9, est err 0.6]
##
## if
## free.sulfur.dioxide > 20
## alcohol > 10.2
## then
## outcome = 247.3 - 250 density + 0.11 residual.sugar + 1.26 pH
## + 0.116 alcohol + 1.04 sulphates + 0.11 fixed.acidity
## - 0.26 volatile.acidity + 0.0012 free.sulfur.dioxide
##
##
## Evaluation on training data (3750 cases):
##
## Average |error| 0.4
## Relative |error| 0.63
## Correlation coefficient 0.67
##
##
## Attribute usage:
## Conds Model
##
## 85% 99% alcohol
## 73% 84% free.sulfur.dioxide
## 40% 97% volatile.acidity
## 33% 99% residual.sugar
## 15% 11% citric.acid
## 5% 62% fixed.acidity
## 98% density
## 85% pH
## 66% sulphates
## 21% total.sulfur.dioxide
## 8% chlorides
##
##
## Time: 0.2 secs# generate predictions for the model
p.cubist <- predict(m.cubist, whitewine_test)summary(p.cubist)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.315 5.574 6.093 6.028 6.437 7.647# correlation between the predicted and true values
cor(p.cubist, whitewine_test$quality)## [1] 0.5683117# mean absolute error of predicted and true values
# (uses a custom function defined above)
MAE(whitewine_test$quality, p.cubist) ## [1] 0.5306253Red wine dataset
redwine <- read.csv("winequality-red.csv", stringsAsFactors = TRUE)
str(redwine)## 'data.frame': 1599 obs. of 12 variables:
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...# the distribution of quality ratings
hist(redwine$quality)
summary(redwine)## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. : 4.60 Min. :0.1200 Min. :0.000 Min. : 0.900
## 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090 1st Qu.: 1.900
## Median : 7.90 Median :0.5200 Median :0.260 Median : 2.200
## Mean : 8.32 Mean :0.5278 Mean :0.271 Mean : 2.539
## 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420 3rd Qu.: 2.600
## Max. :15.90 Max. :1.5800 Max. :1.000 Max. :15.500
## chlorides free.sulfur.dioxide total.sulfur.dioxide density
## Min. :0.01200 Min. : 1.00 Min. : 6.00 Min. :0.9901
## 1st Qu.:0.07000 1st Qu.: 7.00 1st Qu.: 22.00 1st Qu.:0.9956
## Median :0.07900 Median :14.00 Median : 38.00 Median :0.9968
## Mean :0.08747 Mean :15.87 Mean : 46.47 Mean :0.9967
## 3rd Qu.:0.09000 3rd Qu.:21.00 3rd Qu.: 62.00 3rd Qu.:0.9978
## Max. :0.61100 Max. :72.00 Max. :289.00 Max. :1.0037
## pH sulphates alcohol quality
## Min. :2.740 Min. :0.3300 Min. : 8.40 Min. :3.000
## 1st Qu.:3.210 1st Qu.:0.5500 1st Qu.: 9.50 1st Qu.:5.000
## Median :3.310 Median :0.6200 Median :10.20 Median :6.000
## Mean :3.311 Mean :0.6581 Mean :10.42 Mean :5.636
## 3rd Qu.:3.400 3rd Qu.:0.7300 3rd Qu.:11.10 3rd Qu.:6.000
## Max. :4.010 Max. :2.0000 Max. :14.90 Max. :8.000redwine_train <- redwine[1:3750, ]
redwine_test <- redwine[1201:1599, ]Training a model on the data
library(rpart)
m.rpart <- rpart(quality ~ ., data = redwine_train)# get basic information about the tree
m.rpart## n=1599 (2151 observations deleted due to missingness)
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 1599 1042.16500 5.636023
## 2) alcohol< 10.525 983 424.15870 5.366226
## 4) sulphates< 0.575 391 128.09720 5.150895 *
## 5) sulphates>=0.575 592 265.95780 5.508446
## 10) volatile.acidity>=0.405 448 175.87280 5.404018 *
## 11) volatile.acidity< 0.405 144 70.00000 5.833333 *
## 3) alcohol>=10.525 616 432.27110 6.066558
## 6) sulphates< 0.645 272 191.86760 5.727941
## 12) volatile.acidity>=1.015 10 6.00000 4.000000 *
## 13) volatile.acidity< 1.015 262 154.87020 5.793893
## 26) volatile.acidity>=0.495 146 73.67123 5.575342 *
## 27) volatile.acidity< 0.495 116 65.44828 6.068966 *
## 7) sulphates>=0.645 344 184.55520 6.334302
## 14) alcohol< 11.55 206 101.96600 6.121359
## 28) volatile.acidity>=0.395 111 37.42342 5.927928 *
## 29) volatile.acidity< 0.395 95 55.53684 6.347368
## 58) pH>=3.255 59 29.72881 6.067797 *
## 59) pH< 3.255 36 13.63889 6.805556 *
## 15) alcohol>=11.55 138 59.30435 6.652174 *# get more detailed information about the tree
summary(m.rpart)## Call:
## rpart(formula = quality ~ ., data = redwine_train)
## n=1599 (2151 observations deleted due to missingness)
##
## CP nsplit rel error xerror xstd
## 1 0.17822061 0 1.0000000 1.0009884 0.03792922
## 2 0.05358865 1 0.8217794 0.8363434 0.03654274
## 3 0.02974329 2 0.7681907 0.8079661 0.03419475
## 4 0.02888577 3 0.7384474 0.7883367 0.03371542
## 5 0.02234278 4 0.7095617 0.7597444 0.03163502
## 6 0.01927238 5 0.6872189 0.7364469 0.03042210
## 7 0.01511346 6 0.6679465 0.7138108 0.02942769
## 8 0.01015909 7 0.6528331 0.7004774 0.02834643
## 9 0.01000000 9 0.6325149 0.6956021 0.02861206
##
## Variable importance
## alcohol volatile.acidity density
## 31 17 13
## sulphates fixed.acidity chlorides
## 13 7 6
## citric.acid pH total.sulfur.dioxide
## 5 4 3
## free.sulfur.dioxide
## 1
##
## Node number 1: 1599 observations, complexity param=0.1782206
## mean=5.636023, MSE=0.6517605
## left son=2 (983 obs) right son=3 (616 obs)
## Primary splits:
## alcohol < 10.525 to the left, improve=0.17822060, (0 missing)
## sulphates < 0.645 to the left, improve=0.12565160, (0 missing)
## volatile.acidity < 0.425 to the right, improve=0.11400620, (0 missing)
## citric.acid < 0.295 to the left, improve=0.07225368, (0 missing)
## density < 0.99539 to the right, improve=0.06402980, (0 missing)
## Surrogate splits:
## density < 0.995575 to the right, agree=0.762, adj=0.383, (0 split)
## chlorides < 0.0685 to the right, agree=0.690, adj=0.195, (0 split)
## volatile.acidity < 0.3675 to the right, agree=0.662, adj=0.123, (0 split)
## fixed.acidity < 6.75 to the right, agree=0.654, adj=0.101, (0 split)
## total.sulfur.dioxide < 17.5 to the right, agree=0.641, adj=0.068, (0 split)
##
## Node number 2: 983 observations, complexity param=0.02888577
## mean=5.366226, MSE=0.4314941
## left son=4 (391 obs) right son=5 (592 obs)
## Primary splits:
## sulphates < 0.575 to the left, improve=0.07097282, (0 missing)
## volatile.acidity < 0.335 to the right, improve=0.06388554, (0 missing)
## alcohol < 9.85 to the left, improve=0.05212216, (0 missing)
## fixed.acidity < 10.85 to the left, improve=0.03084011, (0 missing)
## total.sulfur.dioxide < 83.5 to the right, improve=0.02749674, (0 missing)
## Surrogate splits:
## density < 0.996225 to the left, agree=0.662, adj=0.151, (0 split)
## volatile.acidity < 0.6525 to the right, agree=0.636, adj=0.084, (0 split)
## fixed.acidity < 6.05 to the left, agree=0.609, adj=0.018, (0 split)
## citric.acid < 0.115 to the left, agree=0.609, adj=0.018, (0 split)
## total.sulfur.dioxide < 9.5 to the left, agree=0.608, adj=0.015, (0 split)
##
## Node number 3: 616 observations, complexity param=0.05358865
## mean=6.066558, MSE=0.7017388
## left son=6 (272 obs) right son=7 (344 obs)
## Primary splits:
## sulphates < 0.645 to the left, improve=0.12919720, (0 missing)
## volatile.acidity < 0.87 to the right, improve=0.11482610, (0 missing)
## citric.acid < 0.295 to the left, improve=0.10819510, (0 missing)
## alcohol < 11.55 to the left, improve=0.10309310, (0 missing)
## pH < 3.355 to the right, improve=0.07557599, (0 missing)
## Surrogate splits:
## citric.acid < 0.245 to the left, agree=0.683, adj=0.283, (0 split)
## fixed.acidity < 7.85 to the left, agree=0.666, adj=0.243, (0 split)
## volatile.acidity < 0.5875 to the right, agree=0.653, adj=0.213, (0 split)
## density < 0.994915 to the left, agree=0.635, adj=0.173, (0 split)
## pH < 3.405 to the right, agree=0.630, adj=0.162, (0 split)
##
## Node number 4: 391 observations
## mean=5.150895, MSE=0.3276143
##
## Node number 5: 592 observations, complexity param=0.01927238
## mean=5.508446, MSE=0.449253
## left son=10 (448 obs) right son=11 (144 obs)
## Primary splits:
## volatile.acidity < 0.405 to the right, improve=0.07551952, (0 missing)
## total.sulfur.dioxide < 81.5 to the right, improve=0.05845854, (0 missing)
## alcohol < 9.85 to the left, improve=0.05386312, (0 missing)
## fixed.acidity < 10.95 to the left, improve=0.05335172, (0 missing)
## chlorides < 0.0975 to the right, improve=0.03262428, (0 missing)
## Surrogate splits:
## fixed.acidity < 10.45 to the left, agree=0.787, adj=0.125, (0 split)
## chlorides < 0.0565 to the right, agree=0.765, adj=0.035, (0 split)
## citric.acid < 0.365 to the left, agree=0.764, adj=0.028, (0 split)
## free.sulfur.dioxide < 2.5 to the right, agree=0.764, adj=0.028, (0 split)
## alcohol < 8.6 to the right, agree=0.758, adj=0.007, (0 split)
##
## Node number 6: 272 observations, complexity param=0.02974329
## mean=5.727941, MSE=0.7053958
## left son=12 (10 obs) right son=13 (262 obs)
## Primary splits:
## volatile.acidity < 1.015 to the right, improve=0.16155630, (0 missing)
## alcohol < 11.45 to the left, improve=0.11901850, (0 missing)
## citric.acid < 0.255 to the left, improve=0.11313180, (0 missing)
## pH < 3.365 to the right, improve=0.09055459, (0 missing)
## sulphates < 0.585 to the left, improve=0.04970438, (0 missing)
##
## Node number 7: 344 observations, complexity param=0.02234278
## mean=6.334302, MSE=0.5364978
## left son=14 (206 obs) right son=15 (138 obs)
## Primary splits:
## alcohol < 11.55 to the left, improve=0.12616750, (0 missing)
## chlorides < 0.0785 to the right, improve=0.05765389, (0 missing)
## total.sulfur.dioxide < 101.5 to the right, improve=0.05496021, (0 missing)
## density < 0.99537 to the right, improve=0.04412990, (0 missing)
## volatile.acidity < 0.425 to the right, improve=0.04136603, (0 missing)
## Surrogate splits:
## density < 0.994875 to the right, agree=0.701, adj=0.254, (0 split)
## chlorides < 0.053 to the right, agree=0.651, adj=0.130, (0 split)
## fixed.acidity < 5.55 to the right, agree=0.640, adj=0.101, (0 split)
## residual.sugar < 4.25 to the left, agree=0.628, adj=0.072, (0 split)
## citric.acid < 0.635 to the left, agree=0.622, adj=0.058, (0 split)
##
## Node number 10: 448 observations
## mean=5.404018, MSE=0.3925731
##
## Node number 11: 144 observations
## mean=5.833333, MSE=0.4861111
##
## Node number 12: 10 observations
## mean=4, MSE=0.6
##
## Node number 13: 262 observations, complexity param=0.01511346
## mean=5.793893, MSE=0.5911077
## left son=26 (146 obs) right son=27 (116 obs)
## Primary splits:
## volatile.acidity < 0.495 to the right, improve=0.10170270, (0 missing)
## alcohol < 11.45 to the left, improve=0.09838534, (0 missing)
## citric.acid < 0.255 to the left, improve=0.09415346, (0 missing)
## pH < 3.295 to the right, improve=0.07618253, (0 missing)
## density < 0.995155 to the right, improve=0.05214905, (0 missing)
## Surrogate splits:
## citric.acid < 0.235 to the left, agree=0.866, adj=0.698, (0 split)
## pH < 3.305 to the right, agree=0.733, adj=0.397, (0 split)
## fixed.acidity < 7.85 to the left, agree=0.691, adj=0.302, (0 split)
## alcohol < 11.85 to the left, agree=0.641, adj=0.190, (0 split)
## total.sulfur.dioxide < 12.5 to the right, agree=0.637, adj=0.181, (0 split)
##
## Node number 14: 206 observations, complexity param=0.01015909
## mean=6.121359, MSE=0.4949807
## left son=28 (111 obs) right son=29 (95 obs)
## Primary splits:
## volatile.acidity < 0.395 to the right, improve=0.08832113, (0 missing)
## total.sulfur.dioxide < 49.5 to the right, improve=0.06808035, (0 missing)
## chlorides < 0.0945 to the right, improve=0.05079896, (0 missing)
## citric.acid < 0.295 to the left, improve=0.05051307, (0 missing)
## free.sulfur.dioxide < 25.5 to the right, improve=0.03611908, (0 missing)
## Surrogate splits:
## citric.acid < 0.285 to the left, agree=0.733, adj=0.421, (0 split)
## sulphates < 0.765 to the left, agree=0.655, adj=0.253, (0 split)
## chlorides < 0.0675 to the right, agree=0.617, adj=0.168, (0 split)
## residual.sugar < 1.85 to the right, agree=0.612, adj=0.158, (0 split)
## fixed.acidity < 7.05 to the left, agree=0.597, adj=0.126, (0 split)
##
## Node number 15: 138 observations
## mean=6.652174, MSE=0.4297417
##
## Node number 26: 146 observations
## mean=5.575342, MSE=0.5045975
##
## Node number 27: 116 observations
## mean=6.068966, MSE=0.5642093
##
## Node number 28: 111 observations
## mean=5.927928, MSE=0.337148
##
## Node number 29: 95 observations, complexity param=0.01015909
## mean=6.347368, MSE=0.5845983
## left son=58 (59 obs) right son=59 (36 obs)
## Primary splits:
## pH < 3.255 to the right, improve=0.21911830, (0 missing)
## total.sulfur.dioxide < 56.5 to the right, improve=0.18528400, (0 missing)
## fixed.acidity < 10 to the left, improve=0.12899290, (0 missing)
## free.sulfur.dioxide < 24.5 to the right, improve=0.11666000, (0 missing)
## alcohol < 10.75 to the left, improve=0.05498168, (0 missing)
## Surrogate splits:
## fixed.acidity < 9.7 to the left, agree=0.737, adj=0.306, (0 split)
## total.sulfur.dioxide < 28.5 to the right, agree=0.737, adj=0.306, (0 split)
## free.sulfur.dioxide < 9.5 to the right, agree=0.716, adj=0.250, (0 split)
## chlorides < 0.0635 to the right, agree=0.663, adj=0.111, (0 split)
## sulphates < 0.935 to the left, agree=0.663, adj=0.111, (0 split)
##
## Node number 58: 59 observations
## mean=6.067797, MSE=0.5038782
##
## Node number 59: 36 observations
## mean=6.805556, MSE=0.378858# use the rpart.plot package to create a visualization
library(rpart.plot)# a basic decision tree diagram
rpart.plot(m.rpart, digits = 3)
# a few adjustments to the diagram
rpart.plot(m.rpart, digits = 4, fallen.leaves = TRUE, type = 3, extra = 101)
Evaluate model performance
# generate predictions
p.rpart <- predict(m.rpart, redwine_test)# compare the distribution of predicted values vs actual values
summary(p.rpart)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.000 5.151 5.404 5.614 5.928 6.806summary(redwine_test$quality)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.549 6.000 8.000# compare the correlation
cor(p.rpart, redwine_test$quality)## [1] 0.5588764# function to calculate the mean absolute error
MAE <- function(actual, predicted) {
mean(abs(actual - predicted))
}# mean absolute error between predicted and actual values
MAE(p.rpart, redwine_test$quality)## [1] 0.5137012# mean absolute error between actual values and mean value
mean(redwine_train$quality) ## [1] NAMAE(5.87, redwine_test$quality)## [1] 0.6521554Improving model performance
library(Cubist)m.cubist <- cubist(x = redwine_train[-12], y = redwine_train$quality)
m.cubist##
## Call:
## cubist.default(x = redwine_train[-12], y = redwine_train$quality)
##
## Number of samples: 3750
## Number of predictors: 11
##
## Number of committees: 1
## Number of rules: 7# display the tree itself
summary(m.cubist)##
## Call:
## cubist.default(x = redwine_train[-12], y = redwine_train$quality)
##
##
## Cubist [Release 2.07 GPL Edition] Tue Feb 3 02:02:41 2026
## ---------------------------------
##
## Target attribute `outcome'
##
## *** Ignoring cases with unknown or N/A target value
##
## Read 1599 cases (12 attributes) from undefined.data
##
## Model:
##
## Rule 1: [630 cases, mean 5.3, range 3 to 8, est err 0.4]
##
## if
## alcohol <= 9.8
## then
## outcome = 5 - 0.79 volatile.acidity - 0.099 alcohol
## + 0.052 fixed.acidity - 0.31 citric.acid + 0.33 sulphates
## + 0.29 pH - 0.0031 free.sulfur.dioxide
## - 0.0007 total.sulfur.dioxide - 0.4 chlorides
##
## Rule 2: [589 cases, mean 5.3, range 3 to 8, est err 0.4]
##
## if
## sulphates <= 0.92
## alcohol <= 9.8
## then
## outcome = 5.5 + 1.28 sulphates - 0.9 volatile.acidity - 0.33 citric.acid
## + 0.029 fixed.acidity - 0.033 alcohol
## - 0.0008 total.sulfur.dioxide - 0.0023 free.sulfur.dioxide
## - 0.4 chlorides - 0.1 pH
##
## Rule 3: [80 cases, mean 5.3, range 3 to 7, est err 0.7]
##
## if
## volatile.acidity > 0.31
## total.sulfur.dioxide <= 14
## sulphates <= 0.63
## alcohol > 9.8
## then
## outcome = 0.5 + 0.549 alcohol - 1.61 volatile.acidity + 0.36 sulphates
## - 0.18 pH - 0.0005 total.sulfur.dioxide - 0.07 citric.acid
## + 0.001 free.sulfur.dioxide
##
## Rule 4: [340 cases, mean 5.6, range 4 to 7, est err 0.5]
##
## if
## volatile.acidity > 0.31
## total.sulfur.dioxide > 14
## sulphates <= 0.63
## alcohol > 9.8
## then
## outcome = 5.1 + 2.85 sulphates + 0.19 alcohol - 0.74 citric.acid
## - 0.69 volatile.acidity - 0.74 pH
## - 0.0027 total.sulfur.dioxide + 0.0013 free.sulfur.dioxide
##
## Rule 5: [407 cases, mean 6.1, range 3 to 8, est err 0.6]
##
## if
## volatile.acidity > 0.31
## sulphates > 0.63
## alcohol > 9.8
## then
## outcome = 7.6 + 0.309 alcohol - 0.0073 total.sulfur.dioxide - 1.12 pH
## - 0.81 volatile.acidity - 0.079 fixed.acidity + 0.22 sulphates
## + 0.002 free.sulfur.dioxide
##
## Rule 6: [71 cases, mean 6.2, range 5 to 8, est err 0.5]
##
## if
## volatile.acidity <= 0.31
## sulphates <= 0.73
## alcohol > 9.8
## then
## outcome = 131.4 + 4.85 volatile.acidity - 124 density - 1.35 pH
## + 0.056 fixed.acidity + 0.54 sulphates + 0.036 alcohol
## + 0.021 residual.sugar
##
## Rule 7: [85 cases, mean 6.5, range 5 to 8, est err 0.4]
##
## if
## volatile.acidity <= 0.31
## sulphates > 0.73
## then
## outcome = 17 + 0.39 alcohol + 0.113 fixed.acidity
## + 0.25 volatile.acidity - 16 density + 0.14 sulphates
##
##
## Evaluation on training data (1599 cases):
##
## Average |error| 0.4
## Relative |error| 0.62
## Correlation coefficient 0.62
##
##
## Attribute usage:
## Conds Model
##
## 96% 100% alcohol
## 71% 100% sulphates
## 45% 100% volatile.acidity
## 19% 93% total.sulfur.dioxide
## 96% pH
## 93% free.sulfur.dioxide
## 81% fixed.acidity
## 74% citric.acid
## 55% chlorides
## 7% density
## 3% residual.sugar
##
##
## Time: 0.0 secs# generate predictions for the model
p.cubist <- predict(m.cubist, redwine_test)summary(p.cubist)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.455 5.109 5.639 5.592 5.974 7.045# correlation between the predicted and true values
cor(p.cubist, redwine_test$quality)## [1] 0.6402049# mean absolute error of predicted and true values
# (uses a custom function defined above)
MAE(redwine_test$quality, p.cubist) ## [1] 0.4606379