Titanic Data Analysis

Packages

Loading necessary packages:

# A custom function for loading packages
# Source - https://github.com/MdAhsanulHimel/load_packages_R/blob/master/script.R
load_packages <- function(packages) {
  not_installed <- packages[!packages %in% rownames(installed.packages())]
  if(length(not_installed)>0){
    message("Installing packages:", paste(" ", not_installed))
    install.packages(not_installed, character.only = TRUE) |> suppressMessages()
  }
  lapply(X = packages, FUN = library, character.only = TRUE) |> invisible()
  message("Packages loaded:", paste(" ", packages))
}

load_packages("data.table")    # to import data
load_packages("dplyr")         # for data wrangling
load_packages("naniar")        # to visualize missing values
load_packages("table1")        # for pretty frequency table
load_packages("skimr")         # for summarizing data

Data

Using fread() to import the dataset since it is the fastestSee more:

data <- fread("train.csv", na.strings=c("",NA,"NULL"))
# na.strings=c("",NA,"NULL") from https://stackoverflow.com/a/24212891/13323413

Data dictionary:

Variable	Definition	Key
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

Explanatory Data Analysis

Structure of the data:

str(data)

## Classes 'data.table' and '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  NA "C85" NA "C123" ...
##  $ Embarked   : chr  "S" "C" "S" "S" ...
##  - attr(*, ".internal.selfref")=<externalptr>

Converting all character variables to factor:

data <- data %>% 
  mutate_if(is.character, as.factor)

Summary of the dataset:

summary(data)

##   PassengerId       Survived          Pclass     
##  Min.   :  1.0   Min.   :0.0000   Min.   :1.000  
##  1st Qu.:223.5   1st Qu.:0.0000   1st Qu.:2.000  
##  Median :446.0   Median :0.0000   Median :3.000  
##  Mean   :446.0   Mean   :0.3838   Mean   :2.309  
##  3rd Qu.:668.5   3rd Qu.:1.0000   3rd Qu.:3.000  
##  Max.   :891.0   Max.   :1.0000   Max.   :3.000  
##                                                  
##                                     Name         Sex           Age       
##  Abbing, Mr. Anthony                  :  1   female:314   Min.   : 0.42  
##  Abbott, Mr. Rossmore Edward          :  1   male  :577   1st Qu.:20.12  
##  Abbott, Mrs. Stanton (Rosa Hunt)     :  1                Median :28.00  
##  Abelson, Mr. Samuel                  :  1                Mean   :29.70  
##  Abelson, Mrs. Samuel (Hannah Wizosky):  1                3rd Qu.:38.00  
##  Adahl, Mr. Mauritz Nils Martin       :  1                Max.   :80.00  
##  (Other)                              :885                NA's   :177    
##      SibSp           Parch             Ticket         Fare       
##  Min.   :0.000   Min.   :0.0000   1601    :  7   Min.   :  0.00  
##  1st Qu.:0.000   1st Qu.:0.0000   347082  :  7   1st Qu.:  7.91  
##  Median :0.000   Median :0.0000   CA. 2343:  7   Median : 14.45  
##  Mean   :0.523   Mean   :0.3816   3101295 :  6   Mean   : 32.20  
##  3rd Qu.:1.000   3rd Qu.:0.0000   347088  :  6   3rd Qu.: 31.00  
##  Max.   :8.000   Max.   :6.0000   CA 2144 :  6   Max.   :512.33  
##                                   (Other) :852                   
##          Cabin     Embarked  
##  B96 B98    :  4   C   :168  
##  C23 C25 C27:  4   Q   : 77  
##  G6         :  4   S   :644  
##  C22 C26    :  3   NA's:  2  
##  D          :  3             
##  (Other)    :186             
##  NA's       :687

Removing categorical variables that seem not useful and factorizing some numeric variables:

data2 <- data %>% 
  select(-c(PassengerId, Name, Ticket, Cabin)) %>% 
  mutate(Survived = factor(Survived, levels = c(0,1), labels = c("No", "Yes")),
         Pclass = factor(Pclass, levels = c(1,2,3), labels = c("1st", "2nd", "3rd")),
         Embarked = recode(Embarked, 
                           "C" = "Cherbourg", "Q" = "Queenstown", "S" = "Southampton"),
         Sex = recode(Sex, "female" = "Female", "male" = "Male"))

Summary of new dataset:

summary(data2)

##  Survived  Pclass        Sex           Age            SibSp      
##  No :549   1st:216   Female:314   Min.   : 0.42   Min.   :0.000  
##  Yes:342   2nd:184   Male  :577   1st Qu.:20.12   1st Qu.:0.000  
##            3rd:491                Median :28.00   Median :0.000  
##                                   Mean   :29.70   Mean   :0.523  
##                                   3rd Qu.:38.00   3rd Qu.:1.000  
##                                   Max.   :80.00   Max.   :8.000  
##                                   NA's   :177                    
##      Parch             Fare               Embarked  
##  Min.   :0.0000   Min.   :  0.00   Cherbourg  :168  
##  1st Qu.:0.0000   1st Qu.:  7.91   Queenstown : 77  
##  Median :0.0000   Median : 14.45   Southampton:644  
##  Mean   :0.3816   Mean   : 32.20   NA's       :  2  
##  3rd Qu.:0.0000   3rd Qu.: 31.00                    
##  Max.   :6.0000   Max.   :512.33                    
##

Detailed summary of the new dataset:

skim(data2) %>% yank("numeric")

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
Age	177	0.8	29.70	14.53	0.42	20.12	28.00	38	80.00	▂▇▅▂▁
SibSp	0	1.0	0.52	1.10	0.00	0.00	0.00	1	8.00	▇▁▁▁▁
Parch	0	1.0	0.38	0.81	0.00	0.00	0.00	0	6.00	▇▁▁▁▁
Fare	0	1.0	32.20	49.69	0.00	7.91	14.45	31	512.33	▇▁▁▁▁

skim(data2) %>% yank("factor")

Variable type: factor

skim_variable	n_missing	complete_rate	ordered	n_unique	top_counts
Survived	0	1	FALSE	2	No: 549, Yes: 342
Pclass	0	1	FALSE	3	3rd: 491, 1st: 216, 2nd: 184
Sex	0	1	FALSE	2	Mal: 577, Fem: 314
Embarked	2	1	FALSE	3	Sou: 644, Che: 168, Que: 77

Visualizing missing values:

gg_miss_var(data2)

Summary statistics by survival status:

# Defining custom function for continuous variable
my.render.cont <- function(x) {
    with(stats.apply.rounding(stats.default(x), digits=2),
         c("",
           "Mean (SD)"=sprintf("%s (&plusmn; %s)", MEAN, SD),
           "Min - Max"=sprintf("%s - %s", MIN, MAX)
           )
        )
}

# Defining custom function for categorical variable
my.render.cat <- function(x) { c("", 
    sapply(stats.default(x), function(y) with(y, sprintf("%d (%0.0f %%)", FREQ, PCT))))
}

# Perform ANOVA for continuous var. and Chi-square test for categorical var.
# https://github.com/benjaminrich/table1/issues/52#issuecomment-841916472
pvalue <- function(x, ...) {
  x <- x[-length(x)] # Remove "overall" group
  # Construct vectors of data y, and groups (strata) g
  y <- unlist(x)
  g <- factor(rep(1:length(x), times=sapply(x, length)))
  if (is.numeric(y)) {
    # For numeric variables, perform an ANOVA
    p <- summary(aov(y ~ g))[[1]][["Pr(>F)"]][1]
  } else {
    # For categorical variables, perform a chi-squared test of independence
    p <- chisq.test(table(y, g))$p.value
  }
  # Format the p-value, using an HTML entity for the less-than sign.
  # The initial empty string places the output on the line below the variable label.
  c("", sub("<", "&lt;", format.pval(p, digits=3, eps=0.0001)))
}

# first column for total and next columns for stratified data by Survived variable
strata <- c(split(data2, data2$Survived), list(Total=data2)) 
# Labeling to make the table readable
labels <- list(variables=list(Age = "Age",
                              Sex = "Sex",
                              Pclass = "Passenger Class",
                              Fare = "Fare",
                              SibSp = "Number of Siblings / Spouses",
                              Parch = "Number of Parents / Children",
                              Embarked = "Port of Embarkation"),
               groups=list("Survived", "", "")
               )
table1(strata, labels, 
       groupspan=c(2, 1, 1),
       topclass="Rtable1-grid",
       render.continuous=my.render.cont, 
       render.categorical=my.render.cat,
       extra.col=list(`P value`=pvalue), 
       extra.col.pos=4  # adding p-value column at the end
       )

	Survived
	No (N=549)	Yes (N=342)	Total (N=891)	P value
Age
Mean (SD)	31 (± 14)	28 (± 15)	30 (± 15)	0.0391
Min - Max	1.0 - 74	0.42 - 80	0.42 - 80
Missing	125 (22.8%)	52 (15.2%)	177 (19.9%)
Sex
Female	81 (15 %)	233 (68 %)	314 (35 %)	<1e-04
Male	468 (85 %)	109 (32 %)	577 (65 %)
Passenger Class
1st	80 (15 %)	136 (40 %)	216 (24 %)	<1e-04
2nd	97 (18 %)	87 (25 %)	184 (21 %)
3rd	372 (68 %)	119 (35 %)	491 (55 %)
Fare
Mean (SD)	22 (± 31)	48 (± 67)	32 (± 50)	<1e-04
Min - Max	0 - 260	0 - 510	0 - 510
Number of Siblings / Spouses
Mean (SD)	0.55 (± 1.3)	0.47 (± 0.71)	0.52 (± 1.1)	0.292
Min - Max	0 - 8.0	0 - 4.0	0 - 8.0
Number of Parents / Children
Mean (SD)	0.33 (± 0.82)	0.46 (± 0.77)	0.38 (± 0.81)	0.0148
Min - Max	0 - 6.0	0 - 5.0	0 - 6.0
Port of Embarkation
Cherbourg	75 (14 %)	93 (27 %)	168 (19 %)	<1e-04
Queenstown	47 (9 %)	30 (9 %)	77 (9 %)
Southampton	427 (78 %)	217 (63 %)	644 (72 %)
Missing	0 (0%)	2 (0.6%)	2 (0.2%)

It can be seen that all the variables except SibSp have significant association at 5% level with Survived.

Note: ANOVA was performed on continuous variables and Chi-square test was performed on categorical variables.

Replacing missing age values for each group in Survived by their median age (since median is not influenced by extreme observations) and removing the two passengers whose Embarked information is missing:

# https://www.codingprof.com/3-ways-to-replace-missing-values-with-the-median-per-group-in-r/
data3 <- data2 %>%
  filter(!is.na(Embarked)) %>% 
  group_by(Survived) %>% 
  mutate(Age = ifelse(is.na(Age), floor(median(Age, na.rm = TRUE)), Age))

Detailed summary of the new dataset:

table1(c(split(data3, data3$Survived), list(Total=data3)), 
       labels, 
       groupspan=c(2, 1, 1),
       topclass="Rtable1-grid",
       render.continuous=my.render.cont, 
       render.categorical=my.render.cat,
       extra.col=list(`P value`=pvalue), 
       extra.col.pos=4  # adding p-value column at the end
       )

	Survived
	No (N=549)	Yes (N=340)	Total (N=889)	P value
Age
Mean (SD)	30 (± 13)	28 (± 14)	29 (± 13)	0.0374
Min - Max	1.0 - 74	0.42 - 80	0.42 - 80
Sex
Female	81 (15 %)	231 (68 %)	312 (35 %)	<1e-04
Male	468 (85 %)	109 (32 %)	577 (65 %)
Passenger Class
1st	80 (15 %)	134 (39 %)	214 (24 %)	<1e-04
2nd	97 (18 %)	87 (26 %)	184 (21 %)
3rd	372 (68 %)	119 (35 %)	491 (55 %)
Fare
Mean (SD)	22 (± 31)	48 (± 67)	32 (± 50)	<1e-04
Min - Max	0 - 260	0 - 510	0 - 510
Number of Siblings / Spouses
Mean (SD)	0.55 (± 1.3)	0.48 (± 0.71)	0.52 (± 1.1)	0.311
Min - Max	0 - 8.0	0 - 4.0	0 - 8.0
Number of Parents / Children
Mean (SD)	0.33 (± 0.82)	0.47 (± 0.77)	0.38 (± 0.81)	0.0131
Min - Max	0 - 6.0	0 - 5.0	0 - 6.0
Port of Embarkation
Cherbourg	75 (14 %)	93 (27 %)	168 (19 %)	<1e-04
Queenstown	47 (9 %)	30 (9 %)	77 (9 %)
Southampton	427 (78 %)	217 (64 %)	644 (72 %)

Training and Test Set

Creating train and test datasets on 80:20 ratio:

set.seed(0)  # setting seed for reproducibility
train_ids <- sample(seq_len(nrow(data3)), size = floor(0.80*nrow(data3)))
train <- data3[train_ids, ]
test <- data3[-train_ids, ]

Logistic Regression

logistic_model <- glm(Survived ~ .,
                      data = train,
                      family = binomial(link = 'logit'))
epiDisplay::logistic.display(logistic_model, simplified = TRUE)

##  
##                             OR  lower95ci upper95ci     Pr(>|Z|)
## Pclass2nd           0.45170433 0.23754842 0.8589272 1.536125e-02
## Pclass3rd           0.12932715 0.06837099 0.2446288 3.184129e-10
## SexMale             0.06876174 0.04428593 0.1067647 8.704131e-33
## Age                 0.95788282 0.94113165 0.9749321 1.749924e-06
## SibSp               0.70934024 0.55797593 0.9017657 5.042322e-03
## Parch               0.93038895 0.71881270 1.2042408 5.836084e-01
## Fare                1.00103972 0.99625625 1.0058462 6.706813e-01
## EmbarkedQueenstown  0.72329095 0.31703384 1.6501387 4.414296e-01
## EmbarkedSouthampton 0.52142803 0.31146111 0.8729411 1.325589e-02

# Step wise regression with backward direction
summary(step(logistic_model, direction="backward"))

## Start:  AIC=650.33
## Survived ~ Pclass + Sex + Age + SibSp + Parch + Fare + Embarked
## 
##            Df Deviance    AIC
## - Fare      1   630.51 648.51
## - Parch     1   630.63 648.63
## <none>          630.33 650.33
## - Embarked  2   636.74 652.74
## - SibSp     1   639.80 657.80
## - Age       1   655.40 673.40
## - Pclass    2   677.43 693.43
## - Sex       1   808.21 826.21
## 
## Step:  AIC=648.51
## Survived ~ Pclass + Sex + Age + SibSp + Parch + Embarked
## 
##            Df Deviance    AIC
## - Parch     1   630.74 646.74
## <none>          630.51 648.51
## - Embarked  2   637.47 651.47
## - SibSp     1   639.80 655.80
## - Age       1   656.08 672.08
## - Pclass    2   699.52 713.52
## - Sex       1   809.59 825.59
## 
## Step:  AIC=646.74
## Survived ~ Pclass + Sex + Age + SibSp + Embarked
## 
##            Df Deviance    AIC
## <none>          630.74 646.74
## - Embarked  2   637.68 649.68
## - SibSp     1   642.33 656.33
## - Age       1   656.21 670.21
## - Pclass    2   699.92 711.92
## - Sex       1   816.35 830.35

## 
## Call:
## glm(formula = Survived ~ Pclass + Sex + Age + SibSp + Embarked, 
##     family = binomial(link = "logit"), data = train)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.5572  -0.6246  -0.4001   0.6419   2.4871  
## 
## Coefficients:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          4.338160   0.466434   9.301  < 2e-16 ***
## Pclass2nd           -0.854608   0.297963  -2.868  0.00413 ** 
## Pclass3rd           -2.119471   0.279486  -7.583 3.36e-14 ***
## SexMale             -2.656733   0.218390 -12.165  < 2e-16 ***
## Age                 -0.043180   0.008969  -4.814 1.48e-06 ***
## SibSp               -0.355654   0.116927  -3.042  0.00235 ** 
## EmbarkedQueenstown  -0.312078   0.416582  -0.749  0.45377    
## EmbarkedSouthampton -0.665305   0.259314  -2.566  0.01030 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 942.14  on 710  degrees of freedom
## Residual deviance: 630.74  on 703  degrees of freedom
## AIC: 646.74
## 
## Number of Fisher Scoring iterations: 5

---
title: "Titanic Data Analysis"
author: 'MD AHSANUL ISLAM'
date: "Last updated on `r format(Sys.Date(), '%d %B, %Y')`"
output:
  rmdformats::readthedown:
    self_contained: true
    lightbox: true
    code_download: true
    code_folding: show
---

```{css, echo=FALSE}
body{
  font-family: "Arial";
  font-size: 11pt;
}
```

```{r, include=FALSE, class.source = 'fold-show'}
# class.source = 'fold-hide'
knitr::opts_chunk$set(
  comment = "##", prompt = F, message = F, warning = F
)
```

## Packages

Loading necessary packages:
```{r, class.source = 'fold-hide'}
# A custom function for loading packages
# Source - https://github.com/MdAhsanulHimel/load_packages_R/blob/master/script.R
load_packages <- function(packages) {
  not_installed <- packages[!packages %in% rownames(installed.packages())]
  if(length(not_installed)>0){
    message("Installing packages:", paste(" ", not_installed))
    install.packages(not_installed, character.only = TRUE) |> suppressMessages()
  }
  lapply(X = packages, FUN = library, character.only = TRUE) |> invisible()
  message("Packages loaded:", paste(" ", packages))
}
```

```{r}
load_packages("data.table")    # to import data
load_packages("dplyr")         # for data wrangling
load_packages("naniar")        # to visualize missing values
load_packages("table1")        # for pretty frequency table
load_packages("skimr")         # for summarizing data
```

---

## Data 

Using fread() to import the dataset since it is the fastest[See more](https://www.r-bloggers.com/2021/04/10-tips-and-tricks-for-data-scientists-vol-6/):
```{r}
data <- fread("train.csv", na.strings=c("",NA,"NULL"))
# na.strings=c("",NA,"NULL") from https://stackoverflow.com/a/24212891/13323413
```


Data dictionary:   

| Variable |                 Definition                 |                       Key                      |
|:---------|:-------------------------------------------|:-----------------------------------------------|
| 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 |

---

## Explanatory Data Analysis

Structure of the data:
```{r}
str(data)
```

Converting all character variables to factor:
```{r}
data <- data %>% 
  mutate_if(is.character, as.factor)
```

Summary of the dataset:
```{r}
summary(data) 
```

Removing categorical variables that seem not useful and factorizing some numeric variables:
```{r}
data2 <- data %>% 
  select(-c(PassengerId, Name, Ticket, Cabin)) %>% 
  mutate(Survived = factor(Survived, levels = c(0,1), labels = c("No", "Yes")),
         Pclass = factor(Pclass, levels = c(1,2,3), labels = c("1st", "2nd", "3rd")),
         Embarked = recode(Embarked, 
                           "C" = "Cherbourg", "Q" = "Queenstown", "S" = "Southampton"),
         Sex = recode(Sex, "female" = "Female", "male" = "Male"))
```

Summary of new dataset: 
```{r}
summary(data2)
```

Detailed summary of the new dataset:
```{r}
skim(data2) %>% yank("numeric")
skim(data2) %>% yank("factor")
```

Visualizing missing values:
```{r}
gg_miss_var(data2)
```

Summary statistics by survival status:
```{r, class.source = 'fold-hide'}
# Defining custom function for continuous variable
my.render.cont <- function(x) {
    with(stats.apply.rounding(stats.default(x), digits=2),
         c("",
           "Mean (SD)"=sprintf("%s (&plusmn; %s)", MEAN, SD),
           "Min - Max"=sprintf("%s - %s", MIN, MAX)
           )
        )
}

# Defining custom function for categorical variable
my.render.cat <- function(x) { c("", 
    sapply(stats.default(x), function(y) with(y, sprintf("%d (%0.0f %%)", FREQ, PCT))))
}

# Perform ANOVA for continuous var. and Chi-square test for categorical var.
# https://github.com/benjaminrich/table1/issues/52#issuecomment-841916472
pvalue <- function(x, ...) {
  x <- x[-length(x)] # Remove "overall" group
  # Construct vectors of data y, and groups (strata) g
  y <- unlist(x)
  g <- factor(rep(1:length(x), times=sapply(x, length)))
  if (is.numeric(y)) {
    # For numeric variables, perform an ANOVA
    p <- summary(aov(y ~ g))[[1]][["Pr(>F)"]][1]
  } else {
    # For categorical variables, perform a chi-squared test of independence
    p <- chisq.test(table(y, g))$p.value
  }
  # Format the p-value, using an HTML entity for the less-than sign.
  # The initial empty string places the output on the line below the variable label.
  c("", sub("<", "&lt;", format.pval(p, digits=3, eps=0.0001)))
}
```

```{r}
# first column for total and next columns for stratified data by Survived variable
strata <- c(split(data2, data2$Survived), list(Total=data2)) 
# Labeling to make the table readable
labels <- list(variables=list(Age = "Age",
                              Sex = "Sex",
                              Pclass = "Passenger Class",
                              Fare = "Fare",
                              SibSp = "Number of Siblings / Spouses",
                              Parch = "Number of Parents / Children",
                              Embarked = "Port of Embarkation"),
               groups=list("Survived", "", "")
               )
table1(strata, labels, 
       groupspan=c(2, 1, 1),
       topclass="Rtable1-grid",
       render.continuous=my.render.cont, 
       render.categorical=my.render.cat,
       extra.col=list(`P value`=pvalue), 
       extra.col.pos=4  # adding p-value column at the end
       )
```


It can be seen that all the variables except `SibSp` have significant association at 5% level with `Survived`.

Note: ANOVA was performed on continuous variables and Chi-square test was performed on categorical variables.

Replacing missing age values for each group in Survived by their median age (since median is not influenced by extreme observations) and removing the two passengers whose Embarked information is missing:
```{r}
# https://www.codingprof.com/3-ways-to-replace-missing-values-with-the-median-per-group-in-r/
data3 <- data2 %>%
  filter(!is.na(Embarked)) %>% 
  group_by(Survived) %>% 
  mutate(Age = ifelse(is.na(Age), floor(median(Age, na.rm = TRUE)), Age))
```

Detailed summary of the new dataset:
```{r}
table1(c(split(data3, data3$Survived), list(Total=data3)), 
       labels, 
       groupspan=c(2, 1, 1),
       topclass="Rtable1-grid",
       render.continuous=my.render.cont, 
       render.categorical=my.render.cat,
       extra.col=list(`P value`=pvalue), 
       extra.col.pos=4  # adding p-value column at the end
       )
```

---

## Training and Test Set

Creating train and test datasets on 80:20 ratio:
```{r}
set.seed(0)  # setting seed for reproducibility
train_ids <- sample(seq_len(nrow(data3)), size = floor(0.80*nrow(data3)))
train <- data3[train_ids, ]
test <- data3[-train_ids, ]
```

---

## Logistic Regression

```{r}
logistic_model <- glm(Survived ~ .,
                      data = train,
                      family = binomial(link = 'logit'))
epiDisplay::logistic.display(logistic_model, simplified = TRUE)

# Step wise regression with backward direction
summary(step(logistic_model, direction="backward"))
```




