University Project: Predicting Titanic Survivors - INF30030 Report

This report presents an analysis of the Titanic disaster data to predict passenger survival probabilities. The study begins by defining business objectives and preparing the data, including handling categorical variables and calculating family size. Exploratory data analysis reveals key insights, such as the higher mortality rate among males and the impact of class and title on survival. Data sampling using a 70/30 train/test split is performed to build a logistic regression model. The model incorporates variables such as ticket class, sex, age, title, and family size. The results show statistically significant coefficients for all variables, with odds ratios indicating the influence of each factor on survival. Model validation using a ROC plot demonstrates the model's accuracy, with an AUC of 90.29%. The report concludes with model predictions and a discussion of the findings, highlighting the importance of gender, age, class, and family size in predicting survival. The analysis uses the R programming language and relevant statistical methods to provide a comprehensive understanding of the factors affecting survival during the Titanic disaster. The model achieves a sensitivity of 77.8% and specificity of 94.27%.

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TITANIC SURVIVAL ANALYTICS
Name
Course Number
Date
Faculty Name

Titanic Survival Analytics 2
Titanic Survivability Prediction
Introduction
The Titanic tragedy was one of the most devastating and deadliest events that ever
happened in modern history. Prediction models have been developed to estimate the probability
of survival among the passengers in the liner, in consideration to factors such as class, gender
and age among others. Lots of machine learning activities and predictive methods have been
tried to develop a model with the highest predictive power of survivability in the incident.
1. Defining Business Objectives
This paper is focused on developing a predictive model to predict the probability that an
individual would have survived the accident given different factors, which affected the victims
differently. The passenger liner was divided into 3 classes –first class being in the topmost,
second class in the middle and third class being at the bottom. This already shows that people in
the third class were more likely to die compared to the other classes. However, it is important to
prove this hypothesis, hence supporting our ideas and theories.
It has been documented that most people die because there were no enough lifesaving
jackets, which rendered most of the people who could have survived death. Due to theories of
nature, scarcity of the lifesaver jackets exposed men more compared to the other groups –
women and children. In addition, this effect would have been affected by levels of class. It would
be hypothesized that men in the first class were more romantic compared to those in second and
third classes. Therefore, the trends of survivability would vary between class for men and
women. In an ideal situation, men and women in the third class would have struggled in the
same manner to save their lives.
It is possible to predict their survivability based on the dynamic structure of the
catastrophe. As much as the survivability levels would have been due to chance, these dynamics
can explain to some level of confidence. Exploratory data analysis will be conducted to identify
the predictive variables for survivability. Therefore, a model will be developed to explain the
probability of survival using the provided variables explained in the metadata below.

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Methods
2. Preparing Data
Survival, ticket class and port of embarkation were recorded as categorical variables
using the factor() function for ease of analysis. Using the number of siblings and the number of
parents, family size was calculated. Also, a large family was defined as which has more than
three individuals. Extraction of individuals’ titles was done to generate other categorical
variables which would possibly contribute in the model development. For instance, men were
differentiated from male kids by extracting ‘Mr.’ titles. Subsets of the data were created to
effectively analyse the data for insights into the model development stage.
Table 1: Data dictionary
Variable Definition Key
survival Survival 0 = No, 1 = Yes
pclass Ticket class 1 = 1 st (Upper)
2 = 2 nd (Middle)
3 = 3 rd (Lower)
sex Sex 0 = females, 1= males
Age Age in years
sibsp Number of siblings/spouses aboard the Titanic
parch Number of parents/children aboard the Titanic
fare Passenger fare
embarked Port of Embarkation C = Cherbourg, Q =
Queenstown, S =
Southampton
3. Exploratory Data Analysis
According to our data set, 62.3% died and 37.7% survived. Among the males, 87.1% died
while 17.4% died among the females. On average, those who survived had paid double as much
fare as the survivors.

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According to the figure below, a higher proportion of males died as compared to the
females. More males in the middle and lower classes died as compared to those in the upper
class. Amongst the females, the survival rate among those in the lower class was smaller
compared to those in the upper and middle-class category (Jordan and Kleinberg, 2006).
Figure 1: Distribution of survival by gender and ticket class
As shown in the figure below, few passengers who had “miss” and “Mrs” titles died in
upper class compared to middle and lower class categories.

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Figure 2: Survival distribution by title and ticket class
On average, the survivors had larger families. Some extreme values are observed,
indicating that few individuals had more than family members on board.
Figure 3: Survival by family size

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More male died in all the classes than females and the proportions of females who died in the
three class reduce significantly from third class to first class.
4. Data Sampling
Using the caret’s package function, createDataPartition (), the train and test datasets were
created a 70 to 30 ratio respectively.
set.seed(999)
train.samples <- createDataPartition(y = TitanicData$Survived, p = .70,list =
FALSE)
train <- TitanicData[train.samples, ]
test <- TitanicData[-train.samples, ]
5. The Logistic Model
According to the data exploration performed in this paper, the best model includes ticket
class, sex, age, passengers with “Mr.” initials and family size. The model output is shown in the
table below.
## glm(formula = Survived ~ Pclass + Sex + Age + Mr + Family.size,
## family = "binomial", data = train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4310 -0.5103 -0.3149 0.5270 2.6117
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.615628 0.527027 8.758 < 2e-16 ***
## PclassMiddle -1.559324 0.317087 -4.918 8.76e-07 ***
## PclassLower -2.433104 0.317273 -7.669 1.74e-14 ***
## Sexmale -2.337843 0.388411 -6.019 1.76e-09 ***
## Age -0.033125 0.008768 -3.778 0.000158 ***
## Mr -1.509350 0.403529 -3.740 0.000184 ***
## Family.size -0.221536 0.081176 -2.729 0.006351 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 987.05 on 731 degrees of freedom
## Residual deviance: 550.91 on 725 degrees of freedom
## (185 observations deleted due to missingness)
## AIC: 564.91

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##
OR 2.5 % 97.5 %
## (Intercept) 101.05126328 37.12359554 293.8110424
## PclassMiddle 0.21027808 0.11159168 0.3876449
## PclassLower 0.08776403 0.04631873 0.1610626
## Sexmale 0.09653569 0.04421031 0.2039411
## Age 0.96741808 0.95063377 0.9839373
## Mr 0.22105368 0.10026833 0.4913842
## Family.size 0.80128703 0.68099737 0.9369452
All the variables included in the model are statistically significant with 95% confidence level
(Elliott and Woodward, 2007; McCluskey and Lalkhen, 2007; Ledolter, 2013).
The table above includes exponents of the coefficient in the model, which indicate that all
the predictor variables were associated with lower odds of survival. Individuals in the middle
class were less likely to survive by 21.03% compared to those in the first class keeping the other
factors constant. Similarly, those in the lower class were less likely to survive by 91% compared
to those in the upper-class category. Male individuals in the passenger liner were less likely to
survive by approximately 90%, by controlling for the other variables in the model. Increasing
age by 1 year reduces the odds of surviving by around approximately 3%. Males with “Mr.”
initials in their names were less likely to survive by approximately 78% after controlling for the
other variables in the model. Finally, increasing family size by one member led to approximately
20% reduced chance of survival (Hosmer, Lemeshow and Sturdivant, 2013; Ledolter, 2013).

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6. Model Validation
Figure 4: Model ROC plot
According to the ROC plot shown above, the best threshold to be used in the prediction
will be 0.54. The area under the curve is approximately 90.29%, showing that the model is very
good.
7. Model Prediction
table(test$Pred_Survived)
##
## Pred_Died Pred_Survived
## 209 105
prop.table(table(test$Pred_Survived))
##
## Pred_Died Pred_Survived
## 0.6656051 0.3343949
table(test$Pred_Survived, test$Sex)
##
## female male
## Pred_Died 7 202
## Pred_Survived 101 4
prop.table(table(test$Pred_Survived, test$Sex),2)

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##
## female male
## Pred_Died 0.06481481 0.98058252
## Pred_Survived 0.93518519 0.01941748
table(test$Pred_Survived, test$Pclass)
##
## Upper Middle Lower
## Pred_Died 37 52 120
## Pred_Survived 41 31 33
table(test$Pred_Survived, test$Survived)
##
## Died Survived
## Pred_Died 181 28
## Pred_Survived 11 94
prop.table(table(test$Pred_Survived, test$Survived), 2)
##
## Died Survived
## Pred_Died 0.94270833 0.22950820
## Pred_Survived 0.05729167 0.77049180
33.63% (112) were predicted to have survived in the test dataset and 66.37% (221) to
have died. Of those who survived, 16% (18) were men and 84% (94) were women. 15% of the
survivors were from the third class, 26.6% from second class and 56.25% from first class
(Michael, 2001; Sainani, 2013).
Conclusion
In conclusion, gender, age, ticket class, family size and having a “Mr” initial effectively
predicts the probability of survival using the Titanic data set. The model's overall accuracy is
90.29%, indicating that it can accurately classify survival and deaths 90% of the times per 100
persons. According to the ROC curve, we can conclude that the best threshold to predict survival
is around 0.54. Using this threshold, the model has a sensitivity of 77.8% and specificity of
94.27%.

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References
Elliott, A. C. and Woodward, W. a. (2007) ‘Analysis of Categorical Data’, Statistical Analysis
Quick Reference Guidebook, pp. 113–150. doi: 10.1007/SpringerReference_60770.
Hosmer, D., Lemeshow, S. and Sturdivant, R. X. (2013) ‘Model-Building Strategies and
Methods for Logistic Regression’, in Applied Logistic Regression, pp. 89–151. doi:
10.1002/0471722146.ch4.
Jordan, M. and Kleinberg, J. (2006) ‘Information Science and Statistics’, Pattern Recognition,
4(356), pp. 791–799. doi: 10.1641/B580519.
Ledolter, J. (2013) Data Mining and Business Analytics with R, Data Mining and Business
Analytics with R. doi: 10.1002/9781118596289.
McCluskey, A. and Lalkhen, A. G. (2007) ‘Statistics III: Probability and statistical tests’,
Continuing Education in Anaesthesia, Critical Care and Pain, 7(5), pp. 167–170. doi:
10.1093/bjaceaccp/mkm028.
Michael, R. S. (2001) ‘Crosstabulation and Chi-square’, Indiana University Retrieved, pp. 1–8.
Sainani, K. L. (2013) ‘Understanding linear regression’, PM and R, 5(12), pp. 1063–1068. doi:
10.1016/j.pmrj.2013.10.002.