# Decision Trees Using R: Titanic Case Study

Hi MLEnthusiasts! Today, we will dive deeper into classification and will learn about Decision trees, how to analyse which variable is important among many given variables and how to make prediction for new data observations based on our analysis and model. Again, we will continue working on the titanic dataset. This will serve our two purposes. One is to learn how to implement classification using decision treess in R and other is by doing this, we will be able to come out with the comparison among the different classification algorithms, which one is better? So, like always, the first step is to set our working directory and import the dataset.

``````setwd("C:/Users/jyoti/Desktop/MachineLearning/Classification")

Let’s then find out the summary of this data.

``summary(titanicData)``
``````##      pclass        survived                                    name
##  Min.   :1.00   Min.   :0.0000   Connolly, Miss. Kate            :   2
##  1st Qu.:2.00   1st Qu.:0.0000   Kelly, Mr. James                :   2
##  Median :3.00   Median :0.0000   Abbing, Mr. Anthony             :   1
##  Mean   :2.31   Mean   :0.3827   Abbott, Master. Eugene Joseph   :   1
##  3rd Qu.:3.00   3rd Qu.:1.0000   Abbott, Mr. Rossmore Edward     :   1
##  Max.   :3.00   Max.   :1.0000   Abbott, Mrs. Stanton (Rosa Hunt):   1
##                                  (Other)                         :1249
##      sex           age            sibsp           parch
##  female:452   Min.   : 1.00   Min.   :0.000   Min.   :0.0000
##  male  :805   1st Qu.:21.00   1st Qu.:0.000   1st Qu.:0.0000
##               Median :28.00   Median :0.000   Median :0.0000
##               Mean   :29.07   Mean   :0.502   Mean   :0.3779
##               3rd Qu.:37.00   3rd Qu.:1.000   3rd Qu.:0.0000
##               Max.   :60.00   Max.   :8.000   Max.   :9.0000
##               NA's   :261
##       fare         embarked
##  Min.   :  0.000   C:256
##  1st Qu.:  7.896   Q:119
##  Median : 14.400   S:882
##  Mean   : 32.721
##  3rd Qu.: 31.000
##  Max.   :512.329
## ``````

As you can see, there are 261 missing values in the age column. Let’s fix that first. Let’s find out the distribution of age variable so that we can understand which value can be used to do missing value imputation.

``hist(titanicData\$age)``

The distribution is more or less normal in nature. Let’s then go ahead with replacing all the missing values by the mean of the age variable. This can be done by using the following R code.

``````titanicData\$age[is.na(titanicData\$age)] = 29.07
summary(titanicData)``````
``````##      pclass        survived                                    name
##  Min.   :1.00   Min.   :0.0000   Connolly, Miss. Kate            :   2
##  1st Qu.:2.00   1st Qu.:0.0000   Kelly, Mr. James                :   2
##  Median :3.00   Median :0.0000   Abbing, Mr. Anthony             :   1
##  Mean   :2.31   Mean   :0.3827   Abbott, Master. Eugene Joseph   :   1
##  3rd Qu.:3.00   3rd Qu.:1.0000   Abbott, Mr. Rossmore Edward     :   1
##  Max.   :3.00   Max.   :1.0000   Abbott, Mrs. Stanton (Rosa Hunt):   1
##                                  (Other)                         :1249
##      sex           age            sibsp           parch
##  female:452   Min.   : 1.00   Min.   :0.000   Min.   :0.0000
##  male  :805   1st Qu.:22.00   1st Qu.:0.000   1st Qu.:0.0000
##               Median :29.07   Median :0.000   Median :0.0000
##               Mean   :29.07   Mean   :0.502   Mean   :0.3779
##               3rd Qu.:34.00   3rd Qu.:1.000   3rd Qu.:0.0000
##               Max.   :60.00   Max.   :8.000   Max.   :9.0000
##
##       fare         embarked
##  Min.   :  0.000   C:256
##  1st Qu.:  7.896   Q:119
##  Median : 14.400   S:882
##  Mean   : 32.721
##  3rd Qu.: 31.000
##  Max.   :512.329
## ``````

Next step is to view how the dataset looks like.

``head(titanicData)``
``````##   pclass survived                                            name    sex
## 1      1        1                   Allen, Miss. Elisabeth Walton female
## 2      1        0                    Allison, Miss. Helen Loraine female
## 3      1        0            Allison, Mr. Hudson Joshua Creighton   male
## 4      1        0 Allison, Mrs. Hudson J C (Bessie Waldo Daniels) female
## 5      1        1                             Anderson, Mr. Harry   male
## 6      1        0                          Andrews, Mr. Thomas Jr   male
##   age sibsp parch     fare embarked
## 1  29     0     0 211.3375        S
## 2   2     1     2 151.5500        S
## 3  30     1     2 151.5500        S
## 4  25     1     2 151.5500        S
## 5  48     0     0  26.5500        S
## 6  39     0     0   0.0000        S``````

Let’s do some data manipulation to make the dataset useful for model making.

``````titanicData\$female = ifelse(titanicData\$sex=="female", 1, 0)
titanicData\$embarked_c = ifelse(titanicData\$embarked=="C", 1, 0)
titanicData\$embarked_s = ifelse(titanicData\$embarked=="S", 1, 0)
titanicData\$pclass = as.factor(titanicData\$pclass)
titanicData\$survived = as.factor(titanicData\$survived)
``````##   pclass survived                                            name    sex
## 1      1        1                   Allen, Miss. Elisabeth Walton female
## 2      1        0                    Allison, Miss. Helen Loraine female
## 3      1        0            Allison, Mr. Hudson Joshua Creighton   male
## 4      1        0 Allison, Mrs. Hudson J C (Bessie Waldo Daniels) female
## 5      1        1                             Anderson, Mr. Harry   male
## 6      1        0                          Andrews, Mr. Thomas Jr   male
##   age sibsp parch     fare embarked female embarked_c embarked_s
## 1  29     0     0 211.3375        S      1          0          1
## 2   2     1     2 151.5500        S      1          0          1
## 3  30     1     2 151.5500        S      0          0          1
## 4  25     1     2 151.5500        S      1          0          1
## 5  48     0     0  26.5500        S      0          0          1
## 6  39     0     0   0.0000        S      0          0          1``````

Having done that, we also realize that the variables name, sex, embarked are no longer useful to us. So we remove them from our dataframe.

``titanicData <- titanicData[-c(3, 4, 9)]``

Let’s not see if the numerical variables like age and fare have expectile quantiles or that also needs manipulation.

``bx = boxplot(titanicData\$age)``

As you can see there are outliers which need to be handled.

``bx\$stats``
``````##       [,1]
## [1,]  4.00
## [2,] 22.00
## [3,] 29.07
## [4,] 34.00
## [5,] 52.00``````
``quantile(titanicData\$age, seq(0, 1, 0.02))``
``````##      0%      2%      4%      6%      8%     10%     12%     14%     16%
##  1.0000  3.0000  7.0000 11.0000 15.0000 17.0000 18.0000 18.0000 19.0000
##     18%     20%     22%     24%     26%     28%     30%     32%     34%
## 20.0000 21.0000 21.3200 22.0000 23.0000 24.0000 24.0000 25.0000 25.0000
##     36%     38%     40%     42%     44%     46%     48%     50%     52%
## 26.0000 27.0000 28.0000 29.0000 29.0448 29.0700 29.0700 29.0700 29.0700
##     54%     56%     58%     60%     62%     64%     66%     68%     70%
## 29.0700 29.0700 29.0700 29.0700 29.0700 29.0700 30.0000 30.5000 32.0000
##     72%     74%     76%     78%     80%     82%     84%     86%     88%
## 32.5000 34.0000 35.0000 36.0000 37.0000 39.0000 40.0000 42.0000 44.0000
##     90%     92%     94%     96%     98%    100%
## 45.0000 47.0000 50.0000 52.0000 55.4400 60.0000``````
``````titanicData\$age = ifelse(titanicData\$age >= 52, 52, titanicData\$age)
titanicData\$age = ifelse(titanicData\$age <= 4, 4, titanicData\$age)
boxplot(titanicData\$age)``````

Perfect! Let’s do the same for fare variable.

``bx = boxplot(titanicData\$fare)``

``bx\$stats``
``````##         [,1]
## [1,]  0.0000
## [2,]  7.8958
## [3,] 14.4000
## [4,] 31.0000
## [5,] 65.0000``````
``quantile(titanicData\$fare, seq(0, 1, 0.02))``
``````##         0%         2%         4%         6%         8%        10%
##   0.000000   6.495800   7.125000   7.229200   7.250000   7.550000
##        12%        14%        16%        18%        20%        22%
##   7.740524   7.750000   7.750000   7.775000   7.854200   7.879200
##        24%        26%        28%        30%        32%        34%
##   7.895800   7.895800   7.925000   8.050000   8.050000   8.662500
##        36%        38%        40%        42%        44%        46%
##   9.034672   9.838676  10.500000  11.760000  13.000000  13.000000
##        48%        50%        52%        54%        56%        58%
##  13.000000  14.400000  15.045800  15.550000  16.100000  20.212500
##        60%        62%        64%        66%        68%        70%
##  21.045000  23.250000  25.895672  26.000000  26.020000  26.550000
##        72%        74%        76%        78%        80%        82%
##  27.900000  30.000000  31.387500  36.350000  39.687500  50.456136
##        84%        86%        88%        90%        92%        94%
##  53.176000  59.400000  69.550000  76.952520  83.158300 108.009000
##        96%        98%       100%
## 136.504184 211.500000 512.329200``````

To avoid data loss, let’s limit the significance level to 96%.

``````titanicData\$fare = ifelse(titanicData\$fare >= 136, 136, titanicData\$fare)
boxplot(titanicData\$fare)``````

Let’s now start the bivariate analysis of our dataset. First let’s do the boxplot analysis of survived with age and survived with fare.

``boxplot(titanicData\$age~titanicData\$survived, main="Boxplot for age variable")``

It looks like people who died were mainly of middle age as the whiskers for 0 start at 10 and end at 48 approximately.

``boxplot(titanicData\$fare~titanicData\$survived, main="Boxplot for fare variable")``

It looks like people who died had also soe relation with fare! Those who died had paid lower(though there are outliers too). Those who survived had paid comparatively higher fare. For categorical variables, we will do bivariate analysis using mosaic plot.

``mosaicplot(titanicData\$pclass~titanicData\$survived, main="Boxplot for pclass variable", color="skyblue")``

This indeed reveals a useful trend. 1. People of 1st class had a better survival rate among all the classes. 2. People of 3sr class had the worst survival rate.

``mosaicplot(titanicData\$female~titanicData\$survived, main="Boxplot for gender vs survival analysis", color="skyblue")``

Male passengers had worse survival rate than the females. It seems like females were saved first when the mishap happened.

``mosaicplot(titanicData\$embarked_c~titanicData\$survived, main="Boxplot for embarkment as C variable", color="skyblue")``

It looks like the survival rate for the embarkment other than port “C” is worse than port “C”.

``mosaicplot(titanicData\$embarked_s~titanicData\$survived, main="Boxplot for embarkment as S variable", color="skyblue")``

It looks like the survival rate for port “S” was very very good, far better than the other two ports. Let’s now do the correlation analysis of the above data. As the cor() function takes only numerical data, let’s first convert all the categorical columns into numerical and store it into new dataframe.

``````titanicDataNumerical = data.frame(titanicData)
titanicDataNumerical\$pclass = as.numeric(titanicData\$pclass)
titanicDataNumerical\$survived = as.numeric(titanicData\$survived)
titanicDataNumerical\$sibsp = as.numeric(titanicData\$sibsp)
titanicDataNumerical\$parch = as.numeric(titanicData\$parch)
titanicDataNumerical\$female = as.numeric(titanicData\$female)
titanicDataNumerical\$embarked_c = as.numeric(titanicData\$embarked_c)
titanicDataNumerical\$embarked_s = as.numeric(titanicData\$embarked_s)
titanicDataNumerical\$age = titanicData\$age
titanicDataNumerical\$fare = titanicData\$fare``````

Now, let’s find the correlation among all of them.

``library(corrplot)``
``## corrplot 0.84 loaded``
``cor(titanicDataNumerical)``
``````##                 pclass    survived         age       sibsp       parch
## pclass      1.00000000 -0.32725083 -0.35309876  0.06180422  0.02620263
## survived   -0.32725083  1.00000000 -0.01493079 -0.03480143  0.07444689
## age        -0.35309876 -0.01493079  1.00000000 -0.20017298 -0.12191168
## sibsp       0.06180422 -0.03480143 -0.20017298  1.00000000  0.37679176
## parch       0.02620263  0.07444689 -0.12191168  0.37679176  1.00000000
## fare       -0.67866086  0.29736533  0.18218451  0.22825539  0.24633570
## female     -0.13406341  0.52881727 -0.04420916  0.10218247  0.22136893
## embarked_c -0.28849436  0.19525216  0.09624283 -0.05332157 -0.01313978
## embarked_s  0.10529179 -0.16636744 -0.06024244  0.07613393  0.07398385
##                  fare      female  embarked_c  embarked_s
## pclass     -0.6786609 -0.13406341 -0.28849436  0.10529179
## survived    0.2973653  0.52881727  0.19525216 -0.16636744
## age         0.1821845 -0.04420916  0.09624283 -0.06024244
## sibsp       0.2282554  0.10218247 -0.05332157  0.07613393
## parch       0.2463357  0.22136893 -0.01313978  0.07398385
## fare        1.0000000  0.22875075  0.31638709 -0.17604836
## female      0.2287507  1.00000000  0.06564176 -0.12013483
## embarked_c  0.3163871  0.06564176  1.00000000 -0.77557107
## embarked_s -0.1760484 -0.12013483 -0.77557107  1.00000000``````
``corrplot(cor(titanicDataNumerical), method="circle")``

So, we can say that survival is mainly related to age, pclass, fare, female, embarked_c and embarked_S. Let’s do the splitting of dataset between training and test sets.

``````set.seed(1234)
split = sample(1:nrow(titanicData), 0.7*nrow(titanicData))
trainSplit = titanicData[split, ]
testSplit = titanicData[-split,]
print(table(trainSplit\$survived))``````
``````##
##   0   1
## 527 352``````
``print(table(testSplit\$survived))``
``````##
##   0   1
## 249 129``````

Now let’s check for event rate.

``prop.table(table(trainSplit\$survived))``
``````##
##         0         1
## 0.5995449 0.4004551``````
``prop.table(table(testSplit\$survived))``
``````##
##         0         1
## 0.6587302 0.3412698``````

So, the probabilities are approx same in both train and test datasets. We can now start building our decision tree using rpart algorithm.

``````library(rpart)
library(rpart.plot)
fit = rpart(survived~., data=trainSplit, method="class", control=rpart.control(minsplit=10, cp=0.008))
rpart.plot(fit)``````

Thus, total 13 nodes get created in this case. Each node shows: 1. the predicted class(0 for not survived, 1 for survived) 2. predicted probability of survival 3. The percentage of observations in each of the node.

``summary(fit)``
``````## Call:
## rpart(formula = survived ~ ., data = trainSplit, method = "class",
##     control = rpart.control(minsplit = 10, cp = 0.008))
##   n= 879
##
##            CP nsplit rel error    xerror       xstd
## 1 0.451704545      0 1.0000000 1.0000000 0.04127048
## 2 0.022727273      1 0.5482955 0.5482955 0.03486612
## 3 0.009943182      3 0.5028409 0.5284091 0.03440218
## 4 0.008049242      6 0.4715909 0.5539773 0.03499518
## 5 0.008000000     12 0.4232955 0.5511364 0.03493084
##
## Variable importance
##     female       fare     pclass        age      parch      sibsp
##         44         20         15          8          7          4
## embarked_c embarked_s
##          1          1
##
## Node number 1: 879 observations,    complexity param=0.4517045
##   predicted class=0  expected loss=0.4004551  P(node) =1
##     class counts:   527   352
##    probabilities: 0.600 0.400
##   left son=2 (558 obs) right son=3 (321 obs)
##   Primary splits:
##       female     < 0.5      to the left,  improve=121.91870, (0 missing)
##       fare       < 50.7396  to the left,  improve= 37.66640, (0 missing)
##       pclass     splits as  RLL,          improve= 34.90510, (0 missing)
##       embarked_c < 0.5      to the left,  improve= 17.17411, (0 missing)
##       embarked_s < 0.5      to the right, improve= 11.27987, (0 missing)
##   Surrogate splits:
##       parch < 0.5      to the left,  agree=0.675, adj=0.109, (0 split)
##       fare  < 75.7667  to the left,  agree=0.675, adj=0.109, (0 split)
##       age   < 9.5      to the right, agree=0.644, adj=0.025, (0 split)
##
## Node number 2: 558 observations,    complexity param=0.008049242
##   predicted class=0  expected loss=0.2007168  P(node) =0.6348123
##     class counts:   446   112
##    probabilities: 0.799 0.201
##   left son=4 (451 obs) right son=5 (107 obs)
##   Primary splits:
##       pclass     splits as  RLL,          improve=7.934882, (0 missing)
##       fare       < 26.26875 to the left,  improve=5.945697, (0 missing)
##       embarked_c < 0.5      to the left,  improve=5.110501, (0 missing)
##       age        < 13.5     to the right, improve=4.484881, (0 missing)
##       embarked_s < 0.5      to the right, improve=2.662998, (0 missing)
##   Surrogate splits:
##       fare < 26.26875 to the left,  agree=0.889, adj=0.421, (0 split)
##       age  < 44.5     to the left,  agree=0.841, adj=0.168, (0 split)
##
## Node number 3: 321 observations,    complexity param=0.02272727
##   predicted class=1  expected loss=0.2523364  P(node) =0.3651877
##     class counts:    81   240
##    probabilities: 0.252 0.748
##   left son=6 (145 obs) right son=7 (176 obs)
##   Primary splits:
##       pclass     splits as  RRL,          improve=29.788890, (0 missing)
##       fare       < 48.2021  to the left,  improve=12.223650, (0 missing)
##       embarked_c < 0.5      to the left,  improve= 7.004200, (0 missing)
##       sibsp      < 2.5      to the right, improve= 4.677233, (0 missing)
##       parch      < 3.5      to the right, improve= 4.063987, (0 missing)
##   Surrogate splits:
##       fare       < 22.67915 to the left,  agree=0.819, adj=0.600, (0 split)
##       age        < 29.535   to the left,  agree=0.667, adj=0.262, (0 split)
##       sibsp      < 1.5      to the right, agree=0.579, adj=0.069, (0 split)
##       parch      < 2.5      to the right, agree=0.567, adj=0.041, (0 split)
##       embarked_c < 0.5      to the left,  agree=0.555, adj=0.014, (0 split)
##
## Node number 4: 451 observations,    complexity param=0.008049242
##   predicted class=0  expected loss=0.1596452  P(node) =0.513083
##     class counts:   379    72
##    probabilities: 0.840 0.160
##   left son=8 (430 obs) right son=9 (21 obs)
##   Primary splits:
##       age        < 9.5      to the right, improve=4.4139660, (0 missing)
##       parch      < 0.5      to the left,  improve=0.9013663, (0 missing)
##       embarked_c < 0.5      to the left,  improve=0.7373491, (0 missing)
##       fare       < 51.6979  to the left,  improve=0.6388989, (0 missing)
##       sibsp      < 3.5      to the right, improve=0.3591483, (0 missing)
##   Surrogate splits:
##       sibsp < 2.5      to the left,  agree=0.956, adj=0.048, (0 split)
##
## Node number 5: 107 observations,    complexity param=0.008049242
##   predicted class=0  expected loss=0.3738318  P(node) =0.1217292
##     class counts:    67    40
##    probabilities: 0.626 0.374
##   left son=10 (104 obs) right son=11 (3 obs)
##   Primary splits:
##       age        < 15       to the right, improve=2.4203810, (0 missing)
##       embarked_c < 0.5      to the left,  improve=2.3709840, (0 missing)
##       embarked_s < 0.5      to the right, improve=2.0337560, (0 missing)
##       parch      < 1.5      to the left,  improve=1.0909330, (0 missing)
##       fare       < 109.8916 to the left,  improve=0.8876608, (0 missing)
##
## Node number 6: 145 observations,    complexity param=0.02272727
##   predicted class=1  expected loss=0.4896552  P(node) =0.1649602
##     class counts:    71    74
##    probabilities: 0.490 0.510
##   left son=12 (20 obs) right son=13 (125 obs)
##   Primary splits:
##       fare       < 23.35    to the right, improve=7.812966, (0 missing)
##       embarked_s < 0.5      to the right, improve=3.617690, (0 missing)
##       embarked_c < 0.5      to the left,  improve=3.407144, (0 missing)
##       parch      < 1.5      to the right, improve=2.780228, (0 missing)
##       sibsp      < 2.5      to the right, improve=2.232369, (0 missing)
##   Surrogate splits:
##       sibsp < 2.5      to the right, agree=0.897, adj=0.25, (0 split)
##       parch < 1.5      to the right, agree=0.897, adj=0.25, (0 split)
##
## Node number 7: 176 observations
##   predicted class=1  expected loss=0.05681818  P(node) =0.2002275
##     class counts:    10   166
##    probabilities: 0.057 0.943
##
## Node number 8: 430 observations
##   predicted class=0  expected loss=0.144186  P(node) =0.4891923
##     class counts:   368    62
##    probabilities: 0.856 0.144
##
## Node number 9: 21 observations,    complexity param=0.008049242
##   predicted class=0  expected loss=0.4761905  P(node) =0.02389078
##     class counts:    11    10
##    probabilities: 0.524 0.476
##   left son=18 (11 obs) right son=19 (10 obs)
##   Primary splits:
##       sibsp      < 2.5      to the right, improve=6.8580090, (0 missing)
##       pclass     splits as  -RL,          improve=3.6011900, (0 missing)
##       fare       < 19.9125  to the right, improve=2.1428570, (0 missing)
##       embarked_s < 0.5      to the left,  improve=1.0011900, (0 missing)
##       age        < 7.5      to the left,  improve=0.7408964, (0 missing)
##   Surrogate splits:
##       fare       < 19.9125  to the right, agree=0.810, adj=0.6, (0 split)
##       pclass     splits as  -RL,          agree=0.762, adj=0.5, (0 split)
##       age        < 5.5      to the left,  agree=0.619, adj=0.2, (0 split)
##       parch      < 1.5      to the right, agree=0.619, adj=0.2, (0 split)
##       embarked_c < 0.5      to the left,  agree=0.619, adj=0.2, (0 split)
##
## Node number 10: 104 observations,    complexity param=0.008049242
##   predicted class=0  expected loss=0.3557692  P(node) =0.1183163
##     class counts:    67    37
##    probabilities: 0.644 0.356
##   left son=20 (67 obs) right son=21 (37 obs)
##   Primary splits:
##       embarked_c < 0.5      to the left,  improve=1.9627100, (0 missing)
##       embarked_s < 0.5      to the right, improve=1.6651020, (0 missing)
##       fare       < 58.575   to the right, improve=1.2640680, (0 missing)
##       age        < 49.5     to the right, improve=0.7287281, (0 missing)
##       sibsp      < 0.5      to the left,  improve=0.2355769, (0 missing)
##   Surrogate splits:
##       embarked_s < 0.5      to the right, agree=0.990, adj=0.973, (0 split)
##       fare       < 53.99795 to the left,  agree=0.692, adj=0.135, (0 split)
##       age        < 50.5     to the left,  agree=0.663, adj=0.054, (0 split)
##
## Node number 11: 3 observations
##   predicted class=1  expected loss=0  P(node) =0.003412969
##     class counts:     0     3
##    probabilities: 0.000 1.000
##
## Node number 12: 20 observations
##   predicted class=0  expected loss=0.1  P(node) =0.02275313
##     class counts:    18     2
##    probabilities: 0.900 0.100
##
## Node number 13: 125 observations,    complexity param=0.009943182
##   predicted class=1  expected loss=0.424  P(node) =0.1422071
##     class counts:    53    72
##    probabilities: 0.424 0.576
##   left son=26 (97 obs) right son=27 (28 obs)
##   Primary splits:
##       fare       < 15.3729  to the left,  improve=2.1848660, (0 missing)
##       embarked_c < 0.5      to the left,  improve=2.0420970, (0 missing)
##       age        < 29.535   to the right, improve=1.9308760, (0 missing)
##       embarked_s < 0.5      to the right, improve=1.1204990, (0 missing)
##       parch      < 0.5      to the left,  improve=0.2686984, (0 missing)
##   Surrogate splits:
##       parch < 2.5      to the left,  agree=0.792, adj=0.071, (0 split)
##       age   < 8.5      to the right, agree=0.784, adj=0.036, (0 split)
##       sibsp < 1.5      to the left,  agree=0.784, adj=0.036, (0 split)
##
## Node number 18: 11 observations
##   predicted class=0  expected loss=0.09090909  P(node) =0.01251422
##     class counts:    10     1
##    probabilities: 0.909 0.091
##
## Node number 19: 10 observations
##   predicted class=1  expected loss=0.1  P(node) =0.01137656
##     class counts:     1     9
##    probabilities: 0.100 0.900
##
## Node number 20: 67 observations
##   predicted class=0  expected loss=0.2835821  P(node) =0.07622298
##     class counts:    48    19
##    probabilities: 0.716 0.284
##
## Node number 21: 37 observations,    complexity param=0.008049242
##   predicted class=0  expected loss=0.4864865  P(node) =0.04209329
##     class counts:    19    18
##    probabilities: 0.514 0.486
##   left son=42 (17 obs) right son=43 (20 obs)
##   Primary splits:
##       fare  < 58.575   to the right, improve=2.327663000, (0 missing)
##       age   < 49.5     to the right, improve=1.430542000, (0 missing)
##       sibsp < 0.5      to the left,  improve=0.008225617, (0 missing)
##       parch < 0.5      to the left,  improve=0.003727866, (0 missing)
##   Surrogate splits:
##       parch < 0.5      to the right, agree=0.757, adj=0.471, (0 split)
##       sibsp < 0.5      to the right, agree=0.703, adj=0.353, (0 split)
##       age   < 32.25    to the right, agree=0.649, adj=0.235, (0 split)
##
## Node number 26: 97 observations,    complexity param=0.009943182
##   predicted class=1  expected loss=0.4742268  P(node) =0.1103527
##     class counts:    46    51
##    probabilities: 0.474 0.526
##   left son=52 (53 obs) right son=53 (44 obs)
##   Primary splits:
##       age        < 23.5     to the right, improve=1.9697620, (0 missing)
##       fare       < 7.26665  to the right, improve=1.6568480, (0 missing)
##       embarked_c < 0.5      to the left,  improve=0.8326725, (0 missing)
##       parch      < 1.5      to the right, improve=0.4736981, (0 missing)
##       embarked_s < 0.5      to the right, improve=0.2722423, (0 missing)
##   Surrogate splits:
##       fare       < 7.9771   to the left,  agree=0.608, adj=0.136, (0 split)
##       sibsp      < 0.5      to the left,  agree=0.588, adj=0.091, (0 split)
##       parch      < 0.5      to the left,  agree=0.577, adj=0.068, (0 split)
##       embarked_s < 0.5      to the left,  agree=0.577, adj=0.068, (0 split)
##       embarked_c < 0.5      to the left,  agree=0.557, adj=0.023, (0 split)
##
## Node number 27: 28 observations
##   predicted class=1  expected loss=0.25  P(node) =0.03185438
##     class counts:     7    21
##    probabilities: 0.250 0.750
##
## Node number 42: 17 observations
##   predicted class=0  expected loss=0.2941176  P(node) =0.01934016
##     class counts:    12     5
##    probabilities: 0.706 0.294
##
## Node number 43: 20 observations
##   predicted class=1  expected loss=0.35  P(node) =0.02275313
##     class counts:     7    13
##    probabilities: 0.350 0.650
##
## Node number 52: 53 observations,    complexity param=0.009943182
##   predicted class=0  expected loss=0.4339623  P(node) =0.06029579
##     class counts:    30    23
##    probabilities: 0.566 0.434
##   left son=104 (49 obs) right son=105 (4 obs)
##   Primary splits:
##       fare       < 7.3896   to the right, improve=2.7724300, (0 missing)
##       embarked_s < 0.5      to the right, improve=0.8883106, (0 missing)
##       sibsp      < 0.5      to the right, improve=0.6377358, (0 missing)
##       parch      < 0.5      to the right, improve=0.6377358, (0 missing)
##       age        < 29.535   to the right, improve=0.4237008, (0 missing)
##
## Node number 53: 44 observations
##   predicted class=1  expected loss=0.3636364  P(node) =0.05005688
##     class counts:    16    28
##    probabilities: 0.364 0.636
##
## Node number 104: 49 observations
##   predicted class=0  expected loss=0.3877551  P(node) =0.05574516
##     class counts:    30    19
##    probabilities: 0.612 0.388
##
## Node number 105: 4 observations
##   predicted class=1  expected loss=0  P(node) =0.004550626
##     class counts:     0     4
##    probabilities: 0.000 1.000``````

CP is the complexity parameter. It prevents overfitting and controls the size of the tree. To get added into a node, a variable has to be having CP less than 0.008 or else tree building will not continue.

``print(fit)``
``````## n= 879
##
## node), split, n, loss, yval, (yprob)
##       * denotes terminal node
##
##   1) root 879 352 0 (0.59954494 0.40045506)
##     2) female< 0.5 558 112 0 (0.79928315 0.20071685)   ##       4) pclass=2,3 451  72 0 (0.84035477 0.15964523)   ##         8) age>=9.5 430  62 0 (0.85581395 0.14418605) *
##         9) age< 9.5 21  10 0 (0.52380952 0.47619048)   ##          18) sibsp>=2.5 11   1 0 (0.90909091 0.09090909) *
##          19) sibsp< 2.5 10   1 1 (0.10000000 0.90000000) * ##       5) pclass=1 107  40 0 (0.62616822 0.37383178)   ##        10) age>=15 104  37 0 (0.64423077 0.35576923)
##          20) embarked_c< 0.5 67  19 0 (0.71641791 0.28358209) * ##          21) embarked_c>=0.5 37  18 0 (0.51351351 0.48648649)
##            42) fare>=58.575 17   5 0 (0.70588235 0.29411765) *
##            43) fare< 58.575 20   7 1 (0.35000000 0.65000000) *
##        11) age< 15 3   0 1 (0.00000000 1.00000000) * ##     3) female>=0.5 321  81 1 (0.25233645 0.74766355)
##       6) pclass=3 145  71 1 (0.48965517 0.51034483)
##        12) fare>=23.35 20   2 0 (0.90000000 0.10000000) *
##        13) fare< 23.35 125  53 1 (0.42400000 0.57600000)
##          26) fare< 15.3729 97  46 1 (0.47422680 0.52577320)   ##            52) age>=23.5 53  23 0 (0.56603774 0.43396226)
##             104) fare>=7.3896 49  19 0 (0.61224490 0.38775510) *
##             105) fare< 7.3896 4   0 1 (0.00000000 1.00000000) *
##            53) age< 23.5 44  16 1 (0.36363636 0.63636364) * ##          27) fare>=15.3729 28   7 1 (0.25000000 0.75000000) *
##       7) pclass=1,2 176  10 1 (0.05681818 0.94318182) *``````
``prp(fit)``

There are 6 leaf nodes representing class 0 and 7 leaf nodes representing class 1. Now, let’s plot CP values.

``plotcp(fit)``

``printcp(fit)``
``````##
## Classification tree:
## rpart(formula = survived ~ ., data = trainSplit, method = "class",
##     control = rpart.control(minsplit = 10, cp = 0.008))
##
## Variables actually used in tree construction:
## [1] age        embarked_c fare       female     pclass     sibsp
##
## Root node error: 352/879 = 0.40046
##
## n= 879
##
##          CP nsplit rel error  xerror     xstd
## 1 0.4517045      0   1.00000 1.00000 0.041270
## 2 0.0227273      1   0.54830 0.54830 0.034866
## 3 0.0099432      3   0.50284 0.52841 0.034402
## 4 0.0080492      6   0.47159 0.55398 0.034995
## 5 0.0080000     12   0.42330 0.55114 0.034931``````

Now, let’s do the predictions.

``````predictTrain = predict(fit, trainSplit, type="class")
table(predictTrain, trainSplit\$survived)``````
``````##
## predictTrain   0   1
##            0 486 108
##            1  41 244``````

Thus, Accuracy for training dataset = 730/879 = 83.05%.

``````predictTest = predict(fit, testSplit, type = "class")
table(predictTest, testSplit\$survived)``````
``````##
## predictTest   0   1
##           0 223  44
##           1  26  85``````

Thus, Accuracy for test dataset = 308/378 = 81.48%. As compared to the logistic regression, which gives the accuracy of 80% on the training dataset and 78.83% on test dataset, decision tree gives the accuracy of 83.05% on the training dataset and 81.5% on the test dataset.