R Notebook: Estimating Red Wine Quality

setwd("~/Assignment1_files")

wine <- read.csv("winequality-red.csv")
head(wine)

# CCheck missing values
colSums(is.na(wine))

       fixed.acidity     volatile.acidity          citric.acid       residual.sugar 
                   0                    0                    0                    0 
           chlorides  free.sulfur.dioxide total.sulfur.dioxide              density 
                   0                    0                    0                    0 
                  pH            sulphates              alcohol              quality 
                   0                    0                    0                    0 

# examine data
str(wine)

'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(wine$quality, col="orange", main = "Histogram: Red Wine Quality", xlab="Quality", ylab="Frequency")

# summary statistics of the wine data
summary(wine)

 fixed.acidity   volatile.acidity  citric.acid    residual.sugar     chlorides      
 Min.   : 4.60   Min.   :0.1200   Min.   :0.000   Min.   : 0.900   Min.   :0.01200  
 1st Qu.: 7.10   1st Qu.:0.3900   1st Qu.:0.090   1st Qu.: 1.900   1st Qu.:0.07000  
 Median : 7.90   Median :0.5200   Median :0.260   Median : 2.200   Median :0.07900  
 Mean   : 8.32   Mean   :0.5278   Mean   :0.271   Mean   : 2.539   Mean   :0.08747  
 3rd Qu.: 9.20   3rd Qu.:0.6400   3rd Qu.:0.420   3rd Qu.: 2.600   3rd Qu.:0.09000  
 Max.   :15.90   Max.   :1.5800   Max.   :1.000   Max.   :15.500   Max.   :0.61100  
 free.sulfur.dioxide total.sulfur.dioxide    density             pH          sulphates     
 Min.   : 1.00       Min.   :  6.00       Min.   :0.9901   Min.   :2.740   Min.   :0.3300  
 1st Qu.: 7.00       1st Qu.: 22.00       1st Qu.:0.9956   1st Qu.:3.210   1st Qu.:0.5500  
 Median :14.00       Median : 38.00       Median :0.9968   Median :3.310   Median :0.6200  
 Mean   :15.87       Mean   : 46.47       Mean   :0.9967   Mean   :3.311   Mean   :0.6581  
 3rd Qu.:21.00       3rd Qu.: 62.00       3rd Qu.:0.9978   3rd Qu.:3.400   3rd Qu.:0.7300  
 Max.   :72.00       Max.   :289.00       Max.   :1.0037   Max.   :4.010   Max.   :2.0000  
    alcohol         quality     
 Min.   : 8.40   Min.   :3.000  
 1st Qu.: 9.50   1st Qu.:5.000  
 Median :10.20   Median :6.000  
 Mean   :10.42   Mean   :5.636  
 3rd Qu.:11.10   3rd Qu.:6.000  
 Max.   :14.90   Max.   :8.000  

set.seed(123)
train_index <- sample(1:nrow(wine), 0.8 * nrow(wine))

wine_train <- wine[train_index, ]
wine_test  <- wine[-train_index, ]

---

Training a model on the data

# regression tree using rpart
library(rpart)
m.rpart <- rpart(quality ~ ., data = wine_train)

# get basic information about the tree
m.rpart

n= 1279 

node), split, n, deviance, yval
      * denotes terminal node

 1) root 1279 864.63170 5.655981  
   2) alcohol< 10.525 768 346.71740 5.368490  
     4) sulphates< 0.555 259  79.28958 5.119691 *
     5) sulphates>=0.555 509 243.23770 5.495088  
      10) volatile.acidity>=0.365 439 190.87930 5.419134  
        20) total.sulfur.dioxide>=65.5 116  23.79310 5.137931 *
        21) total.sulfur.dioxide< 65.5 323 154.61920 5.520124 *
      11) volatile.acidity< 0.365 70  33.94286 5.971429 *
   3) alcohol>=10.525 511 359.03720 6.088063  
     6) sulphates< 0.585 140 107.39290 5.607143  
      12) volatile.acidity>=0.385 103  70.46602 5.388350  
        24) free.sulfur.dioxide< 5.5 21  15.80952 4.761905 *
        25) free.sulfur.dioxide>=5.5 82  44.30488 5.548780 *
      13) volatile.acidity< 0.385 37  18.27027 6.216216 *
     7) sulphates>=0.585 371 207.04580 6.269542  
      14) alcohol< 11.55 217 109.09680 6.064516 *
      15) alcohol>=11.55 154  75.97403 6.558442 *

# get more detailed information about the tree
summary(m.rpart)

Call:
rpart(formula = quality ~ ., data = wine_train)
  n= 1279 

          CP nsplit rel error    xerror       xstd
1 0.18375119      0 1.0000000 1.0009026 0.04165519
2 0.05158092      1 0.8162488 0.8255477 0.03975751
3 0.02797740      2 0.7646679 0.7798956 0.03619021
4 0.02541547      3 0.7366905 0.7836549 0.03670417
5 0.02157747      4 0.7112750 0.7775538 0.03637259
6 0.02129877      5 0.6896975 0.7726727 0.03630100
7 0.01441882      6 0.6683988 0.7351590 0.03511256
8 0.01197228      7 0.6539799 0.7227261 0.03484660
9 0.01000000      8 0.6420077 0.7253546 0.03530394

Variable importance
             alcohol              density            sulphates     volatile.acidity 
                  34                   14                   13                   13 
           chlorides total.sulfur.dioxide        fixed.acidity  free.sulfur.dioxide 
                   7                    7                    5                    3 
         citric.acid                   pH 
                   2                    1 

Node number 1: 1279 observations,    complexity param=0.1837512
  mean=5.655981, MSE=0.6760217 
  left son=2 (768 obs) right son=3 (511 obs)
  Primary splits:
      alcohol          < 10.525   to the left,  improve=0.18375120, (0 missing)
      sulphates        < 0.645    to the left,  improve=0.11661770, (0 missing)
      volatile.acidity < 0.385    to the right, improve=0.10458550, (0 missing)
      citric.acid      < 0.305    to the left,  improve=0.07507874, (0 missing)
      density          < 0.995565 to the right, improve=0.05857806, (0 missing)
  Surrogate splits:
      density              < 0.99575  to the right, agree=0.760, adj=0.399, (0 split)
      chlorides            < 0.0685   to the right, agree=0.687, adj=0.217, (0 split)
      volatile.acidity     < 0.375    to the right, agree=0.658, adj=0.143, (0 split)
      fixed.acidity        < 6.75     to the right, agree=0.642, adj=0.104, (0 split)
      total.sulfur.dioxide < 17.5     to the right, agree=0.635, adj=0.086, (0 split)

Node number 2: 768 observations,    complexity param=0.0279774
  mean=5.36849, MSE=0.451455 
  left son=4 (259 obs) right son=5 (509 obs)
  Primary splits:
      sulphates            < 0.555    to the left,  improve=0.06976906, (0 missing)
      volatile.acidity     < 0.345    to the right, improve=0.05971706, (0 missing)
      alcohol              < 9.975    to the left,  improve=0.05678445, (0 missing)
      fixed.acidity        < 9.95     to the left,  improve=0.03851320, (0 missing)
      total.sulfur.dioxide < 83.5     to the right, improve=0.03270979, (0 missing)
  Surrogate splits:
      density              < 0.996225 to the left,  agree=0.702, adj=0.116, (0 split)
      volatile.acidity     < 0.7975   to the right, agree=0.681, adj=0.054, (0 split)
      fixed.acidity        < 6.05     to the left,  agree=0.673, adj=0.031, (0 split)
      total.sulfur.dioxide < 9.5      to the left,  agree=0.669, adj=0.019, (0 split)
      chlorides            < 0.046    to the left,  agree=0.665, adj=0.008, (0 split)

Node number 3: 511 observations,    complexity param=0.05158092
  mean=6.088063, MSE=0.7026168 
  left son=6 (140 obs) right son=7 (371 obs)
  Primary splits:
      sulphates        < 0.585    to the left,  improve=0.12421690, (0 missing)
      citric.acid      < 0.295    to the left,  improve=0.09324665, (0 missing)
      alcohol          < 11.55    to the left,  improve=0.09292045, (0 missing)
      volatile.acidity < 0.87     to the right, improve=0.08900247, (0 missing)
      pH               < 3.355    to the right, improve=0.06547522, (0 missing)
  Surrogate splits:
      volatile.acidity     < 0.7025   to the right, agree=0.746, adj=0.071, (0 split)
      total.sulfur.dioxide < 9.5      to the left,  agree=0.744, adj=0.064, (0 split)
      citric.acid          < 0.015    to the left,  agree=0.734, adj=0.029, (0 split)
      residual.sugar       < 7.65     to the right, agree=0.734, adj=0.029, (0 split)
      chlorides            < 0.023    to the left,  agree=0.730, adj=0.014, (0 split)

Node number 4: 259 observations
  mean=5.119691, MSE=0.3061374 

Node number 5: 509 observations,    complexity param=0.02129877
  mean=5.495088, MSE=0.4778737 
  left son=10 (439 obs) right son=11 (70 obs)
  Primary splits:
      volatile.acidity     < 0.365    to the right, improve=0.07571027, (0 missing)
      alcohol              < 9.85     to the left,  improve=0.06851443, (0 missing)
      total.sulfur.dioxide < 46.5     to the right, improve=0.06608195, (0 missing)
      fixed.acidity        < 9.95     to the left,  improve=0.04635665, (0 missing)
      pH                   < 3.535    to the right, improve=0.02682268, (0 missing)
  Surrogate splits:
      chlorides           < 0.0565   to the right, agree=0.872, adj=0.071, (0 split)
      citric.acid         < 0.685    to the left,  agree=0.864, adj=0.014, (0 split)
      free.sulfur.dioxide < 1.5      to the right, agree=0.864, adj=0.014, (0 split)

Node number 6: 140 observations,    complexity param=0.02157747
  mean=5.607143, MSE=0.7670918 
  left son=12 (103 obs) right son=13 (37 obs)
  Primary splits:
      volatile.acidity    < 0.385    to the right, improve=0.17372260, (0 missing)
      citric.acid         < 0.255    to the left,  improve=0.14724590, (0 missing)
      alcohol             < 11.45    to the left,  improve=0.12835050, (0 missing)
      pH                  < 3.365    to the right, improve=0.11277110, (0 missing)
      free.sulfur.dioxide < 26.5     to the left,  improve=0.08503115, (0 missing)
  Surrogate splits:
      citric.acid          < 0.315    to the left,  agree=0.864, adj=0.486, (0 split)
      pH                   < 3.275    to the right, agree=0.807, adj=0.270, (0 split)
      fixed.acidity        < 8.55     to the left,  agree=0.786, adj=0.189, (0 split)
      free.sulfur.dioxide  < 3.5      to the right, agree=0.771, adj=0.135, (0 split)
      total.sulfur.dioxide < 8.5      to the right, agree=0.771, adj=0.135, (0 split)

Node number 7: 371 observations,    complexity param=0.02541547
  mean=6.269542, MSE=0.558075 
  left son=14 (217 obs) right son=15 (154 obs)
  Primary splits:
      alcohol          < 11.55    to the left,  improve=0.10613600, (0 missing)
      volatile.acidity < 0.87     to the right, improve=0.05553900, (0 missing)
      sulphates        < 0.685    to the left,  improve=0.04775179, (0 missing)
      chlorides        < 0.0945   to the right, improve=0.03855994, (0 missing)
      citric.acid      < 0.295    to the left,  improve=0.03625129, (0 missing)
  Surrogate splits:
      density              < 0.994765 to the right, agree=0.714, adj=0.312, (0 split)
      fixed.acidity        < 5.7      to the right, agree=0.644, adj=0.143, (0 split)
      chlorides            < 0.0525   to the right, agree=0.628, adj=0.104, (0 split)
      pH                   < 3.535    to the left,  agree=0.623, adj=0.091, (0 split)
      total.sulfur.dioxide < 69.5     to the left,  agree=0.612, adj=0.065, (0 split)

Node number 10: 439 observations,    complexity param=0.01441882
  mean=5.419134, MSE=0.4348047 
  left son=20 (116 obs) right son=21 (323 obs)
  Primary splits:
      total.sulfur.dioxide < 65.5     to the right, improve=0.06531339, (0 missing)
      alcohol              < 9.975    to the left,  improve=0.05602606, (0 missing)
      fixed.acidity        < 9.95     to the left,  improve=0.02962558, (0 missing)
      pH                   < 3.535    to the right, improve=0.02752508, (0 missing)
      volatile.acidity     < 0.6175   to the right, improve=0.02592117, (0 missing)
  Surrogate splits:
      free.sulfur.dioxide < 19.5     to the right, agree=0.759, adj=0.086, (0 split)
      residual.sugar      < 3.25     to the right, agree=0.756, adj=0.078, (0 split)
      sulphates           < 1.6      to the right, agree=0.745, adj=0.034, (0 split)
      volatile.acidity    < 0.97     to the right, agree=0.743, adj=0.026, (0 split)
      density             < 1.00231  to the right, agree=0.740, adj=0.017, (0 split)

Node number 11: 70 observations
  mean=5.971429, MSE=0.484898 

Node number 12: 103 observations,    complexity param=0.01197228
  mean=5.38835, MSE=0.6841361 
  left son=24 (21 obs) right son=25 (82 obs)
  Primary splits:
      free.sulfur.dioxide  < 5.5      to the left,  improve=0.14690230, (0 missing)
      alcohol              < 11.45    to the left,  improve=0.09834283, (0 missing)
      volatile.acidity     < 0.9125   to the right, improve=0.09768146, (0 missing)
      total.sulfur.dioxide < 27.5     to the left,  improve=0.06906661, (0 missing)
      pH                   < 3.355    to the right, improve=0.04596367, (0 missing)
  Surrogate splits:
      total.sulfur.dioxide < 10.5     to the left,  agree=0.854, adj=0.286, (0 split)
      volatile.acidity     < 1.1375   to the right, agree=0.825, adj=0.143, (0 split)
      fixed.acidity        < 7.9      to the right, agree=0.816, adj=0.095, (0 split)
      density              < 0.996995 to the right, agree=0.806, adj=0.048, (0 split)
      pH                   < 3.62     to the right, agree=0.806, adj=0.048, (0 split)

Node number 13: 37 observations
  mean=6.216216, MSE=0.4937911 

Node number 14: 217 observations
  mean=6.064516, MSE=0.5027501 

Node number 15: 154 observations
  mean=6.558442, MSE=0.4933378 

Node number 20: 116 observations
  mean=5.137931, MSE=0.205113 

Node number 21: 323 observations
  mean=5.520124, MSE=0.4786972 

Node number 24: 21 observations
  mean=4.761905, MSE=0.7528345 

Node number 25: 82 observations
  mean=5.54878, MSE=0.5403034 

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 for the testing dataset
p.rpart <- predict(m.rpart, wine_test)

# compare the distribution of predicted values vs. actual values
summary(p.rpart)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  4.762   5.138   5.520   5.599   6.065   6.558 

summary(wine_test$quality)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  3.000   5.000   5.500   5.556   6.000   8.000 

# compare the correlation
cor(p.rpart, wine_test$quality)

[1] 0.5381298

# 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, wine_test$quality)

[1] 0.4738731

# mean absolute error between actual values and mean value
mean(wine_train$quality) 

[1] 5.655981

MAE(5.87, wine_test$quality)

[1] 0.6375

Improving model performance

library(Cubist)
library(plyr)

m.cubist <- cubist(x = wine_train[-12], y = wine_train$quality)

# display basic information about the model tree
m.cubist

Call:
cubist.default(x = wine_train[-12], y = wine_train$quality)

Number of samples: 1279 
Number of predictors: 11 

Number of committees: 1 
Number of rules: 4 

# display the tree itself
summary(m.cubist)

Call:
cubist.default(x = wine_train[-12], y = wine_train$quality)


Cubist [Release 2.07 GPL Edition]  Thu Feb  5 14:23:13 2026
---------------------------------

    Target attribute `outcome'

Read 1279 cases (12 attributes) from undefined.data

Model:

  Rule 1: [385 cases, mean 5.2, range 3 to 7, est err 0.3]

    if
    alcohol <= 9.6
    then
    outcome = 5

  Rule 2: [320 cases, mean 5.3, range 3 to 7, est err 0.4]

    if
    total.sulfur.dioxide <= 105
    sulphates <= 0.92
    alcohol <= 9.6
    then
    outcome = 4.3 + 1.47 sulphates - 0.24 volatile.acidity
              - 0.0012 total.sulfur.dioxide + 0.016 alcohol

  Rule 3: [65 cases, mean 5.6, range 4 to 8, est err 0.7]

    if
    sulphates > 0.92
    then
    outcome = -22.6 - 0.002 total.sulfur.dioxide + 28 density
              - 0.28 volatile.acidity

  Rule 4: [894 cases, mean 5.8, range 3 to 8, est err 0.6]

    if
    alcohol > 9.6
    then
    outcome = 4.8 + 0.299 alcohol - 1.03 volatile.acidity + 0.9 sulphates
              - 0.004 total.sulfur.dioxide - 0.64 pH
              + 0.0065 free.sulfur.dioxide - 1.3 chlorides


Evaluation on training data (1279 cases):

    Average  |error|                0.5
    Relative |error|               0.66
    Correlation coefficient        0.59


    Attribute usage:
      Conds  Model

       96%    73%    alcohol
       23%    73%    sulphates
       19%    77%    total.sulfur.dioxide
              77%    volatile.acidity
              54%    chlorides
              54%    free.sulfur.dioxide
              54%    pH
               4%    density


Time: 0.0 secs

# generate predictions for the model
p.cubist <- predict(m.cubist, wine_test)

# summary statistics about the predictions
summary(p.cubist)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  4.634   5.082   5.373   5.502   5.832   6.781 

# correlation between the predicted and true values
cor(p.cubist, wine_test$quality)

[1] 0.5765034

# mean absolute error of predicted and true values
MAE(wine_test$quality, p.cubist)