Titanic
2024-08-21
The data-set
Data Dictionary
Variable
survival: Survival 0 = No, 1 = Yes
pclass: Ticket class 1 = 1st, 2 = 2nd, 3 = 3rd
sex: Sex
Age: Age in years
sibsp: # of siblings / spouses aboard the Titanic
parch: # of parents / children aboard the Titanic
ticket: Ticket number
fare: Passenger fare
cabin :Cabin number
embarked: Port of Embarkation C = Cherbourg, Q = Queenstown, S = Southampton
pclass: A proxy for socio-economic status (SES)
1st = Upper 2nd = Middle 3rd = Lower
age: Age is fractional if less than 1. If the age is estimated, is it in the form of xx.5
sibsp: The dataset defines family relations in this way…
Sibling = brother, sister, stepbrother, stepsister
Spouse = husband, wife (mistresses and fiancés were ignored)
parch: The dataset defines family relations in this way…
Parent = mother, father
Child = daughter, son, stepdaughter, stepson
Some children travelled only with a nanny, therefore parch=0 for them.
TRAIN DATA
Dimension of the data-set
[1] 891 12Variables in the data-set
'data.frame': 891 obs. of 12 variables:
$ PassengerId: int 1 2 3 4 5 6 7 8 9 10 ...
$ Survived : int 0 1 1 1 0 0 0 0 1 1 ...
$ Pclass : int 3 1 3 1 3 3 1 3 3 2 ...
$ Name : chr "Braund, Mr. Owen Harris" "Cumings, Mrs. John Bradley (Florence Briggs Thayer)" "Heikkinen, Miss. Laina" "Futrelle, Mrs. Jacques Heath (Lily May Peel)" ...
$ Sex : chr "male" "female" "female" "female" ...
$ Age : num 22 38 26 35 35 NA 54 2 27 14 ...
$ SibSp : int 1 1 0 1 0 0 0 3 0 1 ...
$ Parch : int 0 0 0 0 0 0 0 1 2 0 ...
$ Ticket : chr "A/5 21171" "PC 17599" "STON/O2. 3101282" "113803" ...
$ Fare : num 7.25 71.28 7.92 53.1 8.05 ...
$ Cabin : chr "" "C85" "" "C123" ...
$ Embarked : chr "S" "C" "S" "S" ...Column Names
[1] "PassengerId" "Survived" "Pclass" "Name" "Sex"
[6] "Age" "SibSp" "Parch" "Ticket" "Fare"
[11] "Cabin" "Embarked" We remove the 1st,4th,9th and 11th column from the data-set
We replace the NA values in the Age column with the mean of that column and convert the character variables into factor variables.
In the dataset, we remove the empty cells from the ‘Embark’ column
PLOTS
## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
Since our response variable is binary, taking only the values 0 and 1, we use a logistic regression model.
Call:
glm(formula = Survived ~ Pclass + Sex + Age + SibSp + Parch +
Fare + Embarked, family = "binomial", data = ndata)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 4.102784 0.476303 8.614 < 2e-16 ***
Pclass2 -0.924047 0.297882 -3.102 0.00192 **
Pclass3 -2.149626 0.297749 -7.220 5.21e-13 ***
Sexmale -2.709611 0.201336 -13.458 < 2e-16 ***
Age -0.039320 0.007888 -4.984 6.21e-07 ***
SibSp -0.322143 0.109545 -2.941 0.00327 **
Parch -0.095061 0.119028 -0.799 0.42450
Fare 0.002261 0.002462 0.918 0.35842
EmbarkedQ -0.029839 0.381534 -0.078 0.93766
EmbarkedS -0.445754 0.239730 -1.859 0.06297 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1182.82 on 888 degrees of freedom
Residual deviance: 783.74 on 879 degrees of freedom
AIC: 803.74
Number of Fisher Scoring iterations: 5We can see that ‘Pclass2’, ‘Pclass3’, ‘SexMale’, ‘Age’, and ‘SibSp’ are statistically significant, as their p-values are less than 0.05.
To improve the fit of our model we use AIC backward method.
Backward elimination based on the Akaike Information Criterion(AIC)
Start: AIC=803.74
Survived ~ Pclass + Sex + Age + SibSp + Parch + Fare + Embarked
Df Deviance AIC
- Parch 1 784.38 802.38
- Fare 1 784.65 802.65
<none> 783.74 803.74
- Embarked 2 788.16 804.16
- SibSp 1 793.85 811.85
- Age 1 810.58 828.58
- Pclass 2 843.57 859.57
- Sex 1 1010.80 1028.80
Step: AIC=802.38
Survived ~ Pclass + Sex + Age + SibSp + Fare + Embarked
Df Deviance AIC
- Fare 1 785.03 801.03
<none> 784.38 802.38
- Embarked 2 789.08 803.08
- SibSp 1 797.02 813.02
- Age 1 811.03 827.03
- Pclass 2 847.53 861.53
- Sex 1 1016.06 1032.06
Step: AIC=801.03
Survived ~ Pclass + Sex + Age + SibSp + Embarked
Df Deviance AIC
<none> 785.03 801.03
- Embarked 2 790.30 802.30
- SibSp 1 797.02 811.02
- Age 1 812.43 826.43
- Pclass 2 882.25 894.25
- Sex 1 1022.23 1036.23We have selected the variables ‘Embarked’, ‘SibSp’, ‘Age’, ‘Pclass’, and ‘Sex’ for our regression model.
Half-Normal Probability (hnp) Plot
Loading required package: MASSBinomial model 
Most of the residuals fall within these confidence bands, suggesting that the model is capturing the majority of the variability in the data accurately.
Residual vs Fitted Plot
Receiver Operator Characteristic (ROC) Curve and Area Under the Curve (AUC)
Loading required package: lattice
The model’s AUC is 0.8567, indicating good predictive performance.