library(ggplot2)#  visualizations.
library(psych)# descriptive statistics functions.

## 
## Attaching package: 'psych'

## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha

library(dplyr)# For data manipulation and wrangling using the pipe operator %>%.

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

1 Load the Titanic Dataset

data <- read.csv("Titanic-Dataset.csv")

2 Explore the data

head(data)# It shows first 6 rows

##   PassengerId Survived Pclass
## 1           1        0      3
## 2           2        1      1
## 3           3        1      3
## 4           4        1      1
## 5           5        0      3
## 6           6        0      3
##                                                  Name    Sex Age SibSp Parch
## 1                             Braund, Mr. Owen Harris   male  22     1     0
## 2 Cumings, Mrs. John Bradley (Florence Briggs Thayer) female  38     1     0
## 3                              Heikkinen, Miss. Laina female  26     0     0
## 4        Futrelle, Mrs. Jacques Heath (Lily May Peel) female  35     1     0
## 5                            Allen, Mr. William Henry   male  35     0     0
## 6                                    Moran, Mr. James   male  28     0     0
##             Ticket    Fare   Cabin Embarked
## 1        A/5 21171  7.2500 Unknown        S
## 2         PC 17599 71.2833     C85        C
## 3 STON/O2. 3101282  7.9250 Unknown        S
## 4           113803 53.1000    C123        S
## 5           373450  8.0500 Unknown        S
## 6           330877  8.4583 Unknown        Q

describe(data)# it tells about about data

##             vars   n   mean     sd median trimmed    mad  min    max  range
## PassengerId    1 891 446.00 257.35 446.00  446.00 330.62 1.00 891.00 890.00
## Survived       2 891   0.38   0.49   0.00    0.35   0.00 0.00   1.00   1.00
## Pclass         3 891   2.31   0.84   3.00    2.39   0.00 1.00   3.00   2.00
## Name*          4 891 446.00 257.35 446.00  446.00 330.62 1.00 891.00 890.00
## Sex*           5 891   1.65   0.48   2.00    1.68   0.00 1.00   2.00   1.00
## Age            6 891  29.36  13.02  28.00   28.83   8.90 0.42  80.00  79.58
## SibSp          7 891   0.52   1.10   0.00    0.27   0.00 0.00   8.00   8.00
## Parch          8 891   0.38   0.81   0.00    0.18   0.00 0.00   6.00   6.00
## Ticket*        9 891 339.52 200.83 338.00  339.65 268.35 1.00 681.00 680.00
## Fare          10 891  32.20  49.69  14.45   21.38  10.24 0.00 512.33 512.33
## Cabin*        11 891 131.74  36.02 148.00  141.65   0.00 1.00 148.00 147.00
## Embarked*     12 891   2.54   0.79   3.00    2.67   0.00 1.00   3.00   2.00
##              skew kurtosis   se
## PassengerId  0.00    -1.20 8.62
## Survived     0.48    -1.77 0.02
## Pclass      -0.63    -1.28 0.03
## Name*        0.00    -1.20 8.62
## Sex*        -0.62    -1.62 0.02
## Age          0.51     0.97 0.44
## SibSp        3.68    17.73 0.04
## Parch        2.74     9.69 0.03
## Ticket*      0.00    -1.28 6.73
## Fare         4.77    33.12 1.66
## Cabin*      -2.16     3.38 1.21
## Embarked*   -1.26    -0.22 0.03

3 Structure of table

str(data)# View dataset structure

## '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 28 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  "Unknown" "C85" "Unknown" "C123" ...
##  $ Embarked   : chr  "S" "C" "S" "S" ...

4 Summary of table

summary(data)# Summary statistics

##   PassengerId       Survived          Pclass          Name          
##  Min.   :  1.0   Min.   :0.0000   Min.   :1.000   Length:891        
##  1st Qu.:223.5   1st Qu.:0.0000   1st Qu.:2.000   Class :character  
##  Median :446.0   Median :0.0000   Median :3.000   Mode  :character  
##  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                     
##      Sex                 Age            SibSp           Parch       
##  Length:891         Min.   : 0.42   Min.   :0.000   Min.   :0.0000  
##  Class :character   1st Qu.:22.00   1st Qu.:0.000   1st Qu.:0.0000  
##  Mode  :character   Median :28.00   Median :0.000   Median :0.0000  
##                     Mean   :29.36   Mean   :0.523   Mean   :0.3816  
##                     3rd Qu.:35.00   3rd Qu.:1.000   3rd Qu.:0.0000  
##                     Max.   :80.00   Max.   :8.000   Max.   :6.0000  
##     Ticket               Fare           Cabin             Embarked        
##  Length:891         Min.   :  0.00   Length:891         Length:891        
##  Class :character   1st Qu.:  7.91   Class :character   Class :character  
##  Mode  :character   Median : 14.45   Mode  :character   Mode  :character  
##                     Mean   : 32.20                                        
##                     3rd Qu.: 31.00                                        
##                     Max.   :512.33

5 Dimension of table: It check how many rows and column

dim(data) # It gives how many rows and column

## [1] 891  12

6 Checking missing values`

colSums(is.na(data))   # count of NA values per column

## PassengerId    Survived      Pclass        Name         Sex         Age 
##           0           0           0           0           0           0 
##       SibSp       Parch      Ticket        Fare       Cabin    Embarked 
##           0           0           0           0           0           0

anyNA(data)            # quick check if any NA exists

## [1] FALSE

7 How many passengers survived vs. died?

table(data$Survived)                        # count survived vs died

## 
##   0   1 
## 549 342

#Survival Proportions by Gender and class (using prop.table()

prop.table(table(data$Sex, data$Survived),1) # survival rate by gender, this gives percentage

##         
##                  0         1
##   female 0.2579618 0.7420382
##   male   0.8110919 0.1889081

prop.table(table(data$Pclass, data$Survived),1) # survival rate by class

##    
##             0         1
##   1 0.3703704 0.6296296
##   2 0.5271739 0.4728261
##   3 0.7576375 0.2423625

8 Distribution of fare

mean(data$Fare, na.rm = TRUE) # average fare

## [1] 32.20421

median(data$Fare, na.rm = TRUE) #median fare

## [1] 14.4542

range(data$Fare, na.rm = TRUE)# min and max fare

## [1]   0.0000 512.3292

9 Arrange: Sort passengers by Age (descending)

head(data %>%
  arrange(desc(Age)) %>%
  select(Name, Age, Survived, Pclass))

##                                   Name  Age Survived Pclass
## 1 Barkworth, Mr. Algernon Henry Wilson 80.0        1      1
## 2                  Svensson, Mr. Johan 74.0        0      3
## 3            Goldschmidt, Mr. George B 71.0        0      1
## 4              Artagaveytia, Mr. Ramon 71.0        0      1
## 5                 Connors, Mr. Patrick 70.5        0      3
## 6          Mitchell, Mr. Henry Michael 70.0        0      2

10 Aggregate analysis Average Age by Passenger Class

aggregate(Age ~ Pclass, data = data, FUN = mean, na.rm = TRUE) #average age by class.

##   Pclass      Age
## 1      1 36.81213
## 2      2 29.76538
## 3      3 25.93263

11 Group by Summarize: Group by Passenger Class

data %>%
  group_by(Pclass) %>%
  summarise(
    avg_Age     = mean(Age, na.rm = TRUE),
    avg_Fare    = mean(Fare, na.rm = TRUE),
    survival_rate = mean(as.numeric(Survived) - 1, na.rm = TRUE)
  )

## # A tibble: 3 × 4
##   Pclass avg_Age avg_Fare survival_rate
##    <int>   <dbl>    <dbl>         <dbl>
## 1      1    36.8     84.2        -0.370
## 2      2    29.8     20.7        -0.527
## 3      3    25.9     13.7        -0.758

12 Find Class with Highest Survival Rate

data %>%
  group_by(Pclass) %>%
  summarise(survival_rate = mean(as.numeric(Survived) - 1, na.rm = TRUE)) %>%
  arrange(desc(survival_rate)) %>%
  slice(1)

## # A tibble: 1 × 2
##   Pclass survival_rate
##    <int>         <dbl>
## 1      1        -0.370

13 Categorize Age into Child, Adult, Senior

data <- data %>%
  mutate(age_category = ifelse(Age >= 60, "Senior",
                        ifelse(Age < 18, "Child", "Adult")))

head(data[, c("Name", "Age", "age_category")])

##                                                  Name Age age_category
## 1                             Braund, Mr. Owen Harris  22        Adult
## 2 Cumings, Mrs. John Bradley (Florence Briggs Thayer)  38        Adult
## 3                              Heikkinen, Miss. Laina  26        Adult
## 4        Futrelle, Mrs. Jacques Heath (Lily May Peel)  35        Adult
## 5                            Allen, Mr. William Henry  35        Adult
## 6                                    Moran, Mr. James  28        Adult

14 Group by Sex + Summarise

data %>%
  group_by(Sex) %>%
  summarise(
    avg_Age = mean(Age, na.rm = TRUE),
    survival_rate = mean(as.numeric(Survived) - 1, na.rm = TRUE)
  )

## # A tibble: 2 × 3
##   Sex    avg_Age survival_rate
##   <chr>    <dbl>         <dbl>
## 1 female    27.9        -0.258
## 2 male      30.1        -0.811

15 Correlation Between Fare and Class: Check correlation and visualize.

# Select only numeric columns
numeric_data <- data[, c("Age","Fare","Pclass","SibSp","Parch")]

# Correlation matrix
cor_matrix <- cor(numeric_data, use="complete.obs")

# Print
print(cor_matrix)

##                Age        Fare      Pclass       SibSp       Parch
## Age     1.00000000  0.09668842 -0.33989833 -0.23329633 -0.17248195
## Fare    0.09668842  1.00000000 -0.54949962  0.15965104  0.21622494
## Pclass -0.33989833 -0.54949962  1.00000000  0.08308136  0.01844267
## SibSp  -0.23329633  0.15965104  0.08308136  1.00000000  0.41483770
## Parch  -0.17248195  0.21622494  0.01844267  0.41483770  1.00000000

15.1 Visualization of correlation

library(reshape2)

ggplot(melt(cor_matrix), aes(x=Var1, y=Var2, fill=value)) +
  geom_tile(color="white") +
  geom_text(aes(label=round(value,2)), color="black") +
  scale_fill_gradient(low="lightblue", high="darkblue") +
  labs(title="Correlation Heatmap of Titanic Variables")

16 grouped bar chart Visualization: show how Survival varied across Passenger Class

ggplot(data, aes(x = factor(Pclass), fill = factor(Survived))) +
  geom_bar(position = "dodge") +
  labs(title = "Survival by Passenger Class", x = "Class", y = "Count", fill = "Survived")

17 grouped bar chart Visualization: Highlights the difference between male and female survival rates

ggplot(data, aes(x = Sex, fill = factor(Survived))) +
  geom_bar(position = "dodge") +
  labs(title = "Survival by Gender", x = "Gender", y = "Count", fill = "Survived")

18 Boxplot: Shows age distribution among survivors and non‑survivors

boxplot(Age ~ Survived, data=data,
        main="Age Distribution by Survival",
        xlab="Survived (0=No, 1=Yes)", ylab="Age",
        col=c("lightcoral","lightgreen"))

19 Stacked Bar Chart: Survival by Class and Gender

ggplot(data, aes(x=factor(Pclass), fill=factor(Survived))) +
  geom_bar(position="stack") +
  facet_wrap(~Sex) +
  labs(title="Stacked Survival by Class and Gender", x="Class", y="Count", fill="Survived")

20 Line plot(Average Age by Passenger Class):Displays how average age changes across classes.

avg_age <- aggregate(Age ~ Pclass, data = data, FUN = mean, na.rm = TRUE)

ggplot(avg_age, aes(x = Pclass, y = Age)) +
  geom_line(group = 1, color = "darkred") +
  geom_point(size = 3, color = "black") +
  labs(title = "Average Age by Passenger Class", x = "Class", y = "Average Age")

21 Scatter plot (Age vs Fare):Shows relationship between age, fare, and survival status

ggplot(data, aes(x = Age, y = Fare, color = factor(Survived))) +
  geom_point(alpha = 0.6) +
  labs(title = "Age vs Fare Colored by Survival", x = "Age", y = "Fare", color = "Survived")

22 Histogram (Age distribution of passengers):Displays how passenger ages were spread out

ggplot(data, aes(x = Age)) +
  geom_histogram(binwidth = 5, fill = "skyblue", color = "black") +
  labs(title = "Age Distribution of Titanic Passengers",
       x = "Age",
       y = "Frequency")

23 Heatmap: Correlation among numeric variables.

library(reshape2)
corr <- cor(data[,c("Age","Fare","Pclass")], use="complete.obs")
ggplot(melt(corr), aes(Var1, Var2, fill=value)) +
  geom_tile()

24 Logistic regression model: Logistic regression shows that sex and class are strong predictors, while age and fare have weaker effects. Coefficients quantify the odds of survival.

model <- glm(Survived ~ Pclass + Sex + Age + Fare,
             data=data, family="binomial")
summary(model)

## 
## Call:
## glm(formula = Survived ~ Pclass + Sex + Age + Fare, family = "binomial", 
##     data = data)
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  4.6553374  0.5085945   9.153  < 2e-16 ***
## Pclass      -1.1529180  0.1355637  -8.505  < 2e-16 ***
## Sexmale     -2.6072959  0.1872514 -13.924  < 2e-16 ***
## Age         -0.0331244  0.0073991  -4.477 7.58e-06 ***
## Fare         0.0005922  0.0020347   0.291    0.771    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1186.7  on 890  degrees of freedom
## Residual deviance:  805.5  on 886  degrees of freedom
## AIC: 815.5
## 
## Number of Fisher Scoring iterations: 5

25 Visualization of logistic regression model

# Create predicted probabilities
data$PredictedProb <- predict(model, type="response")

# Plot Age vs Predicted Probability
ggplot(data, aes(x=Age, y=PredictedProb, color=Sex)) +
  geom_point(alpha=0.5) +
  geom_smooth(method="loess", se=FALSE) +
  labs(title="Logistic Regression: Survival Probability by Age",
       x="Age", y="Predicted Probability of Survival")

## `geom_smooth()` using formula = 'y ~ x'

26 Linear Regression: Regression line shows weak correlation — age does not strongly predict fare. This confirms fare was more tied to class than age.

# Simple linear regression
lm_simple <- lm(Fare ~ Age, data=data)
summary(lm_simple)

## 
## Call:
## lm(formula = Fare ~ Age, data = data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -40.90 -23.53 -16.88   1.46 478.04 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  21.3686     4.0919   5.222  2.2e-07 ***
## Age           0.3690     0.1274   2.896  0.00387 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 49.49 on 889 degrees of freedom
## Multiple R-squared:  0.009349,   Adjusted R-squared:  0.008234 
## F-statistic: 8.389 on 1 and 889 DF,  p-value: 0.003867

# Visualization
ggplot(data, aes(x=Age, y=Fare)) +
  geom_point(alpha=0.6, color="blue") +
  geom_smooth(method="lm", se=FALSE, color="red") +
  labs(title="Linear Regression: Fare vs Age",
       x="Age", y="Fare")

## `geom_smooth()` using formula = 'y ~ x'

27 Multiple linear Regression: Adding predictors (age, class, family size) improves prediction. The actual vs. predicted plot shows model fit.

# Multiple linear regression
lm_multi <- lm(Fare ~ Age + Pclass + SibSp + Parch, data=data)
summary(lm_multi)

## 
## Call:
## lm(formula = Fare ~ Age + Pclass + SibSp + Parch, data = data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -70.35 -20.53   3.92   6.53 443.07 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 108.9972     6.1697  17.667  < 2e-16 ***
## Age          -0.1552     0.1115  -1.393    0.164    
## Pclass      -34.3020     1.6876 -20.326  < 2e-16 ***
## SibSp         5.8190     1.3433   4.332 1.65e-05 ***
## Parch        10.2516     1.8159   5.645 2.22e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 39.54 on 886 degrees of freedom
## Multiple R-squared:  0.3698, Adjusted R-squared:  0.3669 
## F-statistic:   130 on 4 and 886 DF,  p-value: < 2.2e-16

# Visualization: predicted vs actual
data$PredictedFare <- predict(lm_multi, data)

ggplot(data, aes(x=Fare, y=PredictedFare)) +
  geom_point(alpha=0.6, color="darkgreen") +
  geom_abline(intercept=0, slope=1, color="red") +
  labs(title="Multiple Linear Regression: Actual vs Predicted Fare",
       x="Actual Fare", y="Predicted Fare")

28 Analysis

# Survival rate by Gender and Class
analysis <- data %>%
  group_by(Sex, Pclass) %>%
  summarise(survival_rate = mean(Survived, na.rm = TRUE))

## `summarise()` has regrouped the output.
## ℹ Summaries were computed grouped by Sex and Pclass.
## ℹ Output is grouped by Sex.
## ℹ Use `summarise(.groups = "drop_last")` to silence this message.
## ℹ Use `summarise(.by = c(Sex, Pclass))` for per-operation grouping
##   (`?dplyr::dplyr_by`) instead.

analysis

## # A tibble: 6 × 3
## # Groups:   Sex [2]
##   Sex    Pclass survival_rate
##   <chr>   <int>         <dbl>
## 1 female      1         0.968
## 2 female      2         0.921
## 3 female      3         0.5  
## 4 male        1         0.369
## 5 male        2         0.157
## 6 male        3         0.135

29 Model cleaning (Logistic Regression)

# Data cleaning (IMPORTANT)
data$Survived <- as.numeric(as.character(data$Survived))
data$Sex <- as.factor(data$Sex)
data$Age[is.na(data$Age)] <- mean(data$Age, na.rm = TRUE)

30 Model Training

# Train model
model <- glm(Survived ~ Pclass + Sex + Age + Fare,
             data = data,
             family = "binomial")

summary(model)

## 
## Call:
## glm(formula = Survived ~ Pclass + Sex + Age + Fare, family = "binomial", 
##     data = data)
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  4.6553374  0.5085945   9.153  < 2e-16 ***
## Pclass      -1.1529180  0.1355637  -8.505  < 2e-16 ***
## Sexmale     -2.6072959  0.1872514 -13.924  < 2e-16 ***
## Age         -0.0331244  0.0073991  -4.477 7.58e-06 ***
## Fare         0.0005922  0.0020347   0.291    0.771    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1186.7  on 890  degrees of freedom
## Residual deviance:  805.5  on 886  degrees of freedom
## AIC: 815.5
## 
## Number of Fisher Scoring iterations: 5

31 Predict for a NEW passenger

# New passenger data
new_passenger <- data.frame(
  Pclass = 1,
  Sex = "female",
  Age = 25,
  Fare = 100
)

# Predict probability
prob <- predict(model, newdata = new_passenger, type = "response")

prob

##         1 
## 0.9389764

ifelse(prob > 0.5, "Survived", "Not Survived")  # convert survival prediction

##          1 
## "Survived"

Titanic Dataset

Madhu

r Sys.Date()

1 Load the Titanic Dataset

2 Explore the data

3 Structure of table

4 Summary of table

5 Dimension of table: It check how many rows and column

6 Checking missing values`

7 How many passengers survived vs. died?

8 Distribution of fare

9 Arrange: Sort passengers by Age (descending)

10 Aggregate analysis Average Age by Passenger Class

11 Group by Summarize: Group by Passenger Class

12 Find Class with Highest Survival Rate

13 Categorize Age into Child, Adult, Senior

14 Group by Sex + Summarise

15 Correlation Between Fare and Class: Check correlation and visualize.

15.1 Visualization of correlation

16 grouped bar chart Visualization: show how Survival varied across Passenger Class

17 grouped bar chart Visualization: Highlights the difference between male and female survival rates

18 Boxplot: Shows age distribution among survivors and non‑survivors

19 Stacked Bar Chart: Survival by Class and Gender

20 Line plot(Average Age by Passenger Class):Displays how average age changes across classes.

21 Scatter plot (Age vs Fare):Shows relationship between age, fare, and survival status

22 Histogram (Age distribution of passengers):Displays how passenger ages were spread out

23 Heatmap: Correlation among numeric variables.

24 Logistic regression model: Logistic regression shows that sex and class are strong predictors, while age and fare have weaker effects. Coefficients quantify the odds of survival.

25 Visualization of logistic regression model

26 Linear Regression: Regression line shows weak correlation — age does not strongly predict fare. This confirms fare was more tied to class than age.

27 Multiple linear Regression: Adding predictors (age, class, family size) improves prediction. The actual vs. predicted plot shows model fit.

28 Analysis

29 Model cleaning (Logistic Regression)

30 Model Training

31 Predict for a NEW passenger