Titanic Data
Dijana K.
2025-02-24
# Import the titanic data
titanic_data <- read_csv("titanic_data.csv", col_names = TRUE)## Rows: 891 Columns: 12
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (5): Name, Sex, Ticket, Cabin, Embarked
## dbl (7): PassengerId, Survived, Pclass, Age, SibSp, Parch, Fare
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.Fare
# Compare the average difference in ticket price (Fare) between men and women (Sex)
avg_fare_sex <- titanic_data %>%
group_by(Sex) %>%
summarise(avg_fare = mean(Fare, na.rm = TRUE))
# Print the result
avg_fare_sex## # A tibble: 2 × 2
## Sex avg_fare
## <chr> <dbl>
## 1 female 44.5
## 2 male 25.5# Bar plot for average fare by sex
ggplot(avg_fare_sex, aes(x = Sex, y = avg_fare, fill = Sex)) +
geom_bar(stat = "identity") +
theme_minimal() +
labs(title = "Average Fare by Sex",
x = "Sex",
y = "Average Fare") +
scale_fill_brewer(palette = "Set2")
# Linear Regression of sex and fare
reg_fare_sex <- lm(formula = Fare ~ Sex, titanic_data)
summary(reg_fare_sex)##
## Call:
## lm(formula = Fare ~ Sex, data = titanic_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.73 -18.40 -16.76 2.70 486.81
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 44.480 2.759 16.122 < 2e-16 ***
## Sexmale -18.956 3.428 -5.529 4.23e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 48.89 on 889 degrees of freedom
## Multiple R-squared: 0.03325, Adjusted R-squared: 0.03216
## F-statistic: 30.57 on 1 and 889 DF, p-value: 4.231e-08# Compare the average difference in ticket price (Fare) between passenger classes (Pclass)
# Converting Pclass from numeric to factor
titanic_data$Pclass <- as.factor(titanic_data$Pclass)
avg_fare_pclass <- titanic_data %>%
group_by(Pclass) %>%
summarise(avg_fare = mean(Fare, na.rm = TRUE))
# Print the result
avg_fare_pclass## # A tibble: 3 × 2
## Pclass avg_fare
## <fct> <dbl>
## 1 1 84.2
## 2 2 20.7
## 3 3 13.7# Bar plot for average fare by passenger class
ggplot(avg_fare_pclass, aes(x = Pclass, y = avg_fare, fill = Pclass)) +
geom_bar(stat = "identity") +
theme_minimal() +
labs(title = "Average Fare by Passenger Class",
x = "Passenger Class",
y = "Average Fare") +
scale_fill_brewer(palette = "Set3")
# Linear Regression of passenger class and fare
reg_fare_pclass <- lm(formula = Fare ~ Pclass, titanic_data)
summary(reg_fare_pclass)##
## Call:
## lm(formula = Fare ~ Pclass, data = titanic_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -84.15 -6.93 -5.75 5.03 428.17
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 84.155 2.723 30.91 <2e-16 ***
## Pclass2 -63.493 4.014 -15.82 <2e-16 ***
## Pclass3 -70.479 3.267 -21.57 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 40.01 on 888 degrees of freedom
## Multiple R-squared: 0.3531, Adjusted R-squared: 0.3516
## F-statistic: 242.3 on 2 and 888 DF, p-value: < 2.2e-16# Compare the average difference in ticket price (Fare) between both Sex and Pclass
avg_fare_sex_pclass <- titanic_data %>%
group_by(Sex, Pclass) %>%
summarise(avg_fare = mean(Fare, na.rm = TRUE), .groups = "drop")
# Print the result
avg_fare_sex_pclass## # A tibble: 6 × 3
## Sex Pclass avg_fare
## <chr> <fct> <dbl>
## 1 female 1 106.
## 2 female 2 22.0
## 3 female 3 16.1
## 4 male 1 67.2
## 5 male 2 19.7
## 6 male 3 12.7# Bar plot for average fare by sex and passenger class
ggplot(avg_fare_sex_pclass, aes(x = Pclass, y = avg_fare, fill = Sex)) +
geom_bar(stat = "identity", position = "dodge") +
theme_minimal() +
labs(title = "Average Fare by Sex and Passenger Class",
x = "Passenger Class",
y = "Average Fare") +
scale_fill_brewer(palette = "Set2")
Based on the data, there is a notable difference in ticket prices between men and women on the Titanic. On average, women paid $44.48 for their tickets, while men paid $25.52. This is almost a $19 difference. The linear regression model for sex and fare shows a small p-value, suggesting that the difference is statistically significant. However, the multiple r-squared value of 0.03325 indicates that sex explains only 3.3% of the variation in ticket prices. This suggests that other factors likely played a much larger role in determining fares.
The data also highlights significant differences in ticket prices based on passenger class. On average, passengers in class 1 paid $84.15 for their tickets, passengers in class 2 paid $20.66, and passengers in class 3 paid $13.68. Passengers in class 2 and 3 paid considerably less than those in class 1. The linear regression model for passenger class and fare shows small p-values for both class 2 and 3, indicating that the differences in fares across passenger classes are statistically significant. The multiple r-squared value of 0.351 suggests that passenger class accounts for 35.3% of the variation in ticket prices. This is a much higher proportion compared to sex, meaning that the passenger class had a greater impact on ticket prices than sex of the passenger.
Survival
# Compare the average survival chance (Survived) between men and women (Sex)
avg_survival_sex <- titanic_data %>%
group_by(Sex) %>%
summarise(avg_survival = mean(Survived, na.rm = TRUE))
# Print the result
avg_survival_sex## # A tibble: 2 × 2
## Sex avg_survival
## <chr> <dbl>
## 1 female 0.742
## 2 male 0.189# Bar plot for survival chance by sex
ggplot(avg_survival_sex, aes(x = Sex, y = avg_survival, fill = Sex)) +
geom_bar(stat = "identity") +
theme_minimal() +
labs(title = "Average Survival Rate by Sex", y = "Average Survival Rate", x = "Sex") +
scale_fill_brewer(palette = "Set2")
# Linear Regression of sex and survival chance
reg3 <- lm(formula = Survived ~ Sex, titanic_data)
summary(reg3)##
## Call:
## lm(formula = Survived ~ Sex, data = titanic_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7420 -0.1889 -0.1889 0.2580 0.8111
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.74204 0.02307 32.17 <2e-16 ***
## Sexmale -0.55313 0.02866 -19.30 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4087 on 889 degrees of freedom
## Multiple R-squared: 0.2952, Adjusted R-squared: 0.2944
## F-statistic: 372.4 on 1 and 889 DF, p-value: < 2.2e-16# Compare the average survival chance (Survived) between passenger class (Pclass)
avg_survival_pclass <- titanic_data %>%
group_by(Pclass) %>%
summarise(avg_survival = mean(Survived, na.rm = TRUE))
# Print the result
avg_survival_pclass## # A tibble: 3 × 2
## Pclass avg_survival
## <fct> <dbl>
## 1 1 0.630
## 2 2 0.473
## 3 3 0.242# Bar plot for survival chance by passenger class
ggplot(avg_survival_pclass, aes(x = Pclass, y = avg_survival, fill = Pclass)) +
geom_bar(stat = "identity") +
theme_minimal() +
labs(title = "Average Survival Rate by Passenger Class",
x = "Passenger Class",
y = "Average Survival Rate") +
scale_fill_brewer(palette = "Set3")
# Linear Regression of passenger class and survival chance
reg4 <- lm(formula = Survived ~ Pclass, titanic_data)
summary(reg4)##
## Call:
## lm(formula = Survived ~ Pclass, data = titanic_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6296 -0.2424 -0.2424 0.3704 0.7576
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.62963 0.03117 20.198 < 2e-16 ***
## Pclass2 -0.15680 0.04596 -3.412 0.000675 ***
## Pclass3 -0.38727 0.03741 -10.353 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4582 on 888 degrees of freedom
## Multiple R-squared: 0.1155, Adjusted R-squared: 0.1135
## F-statistic: 57.96 on 2 and 888 DF, p-value: < 2.2e-16# Compare the average difference in survival chance (Survived) between both Sex and Pclass
avg_survival_sex_pclass <- titanic_data %>%
group_by(Sex, Pclass) %>%
summarise(avg_survival = mean(Survived, na.rm = TRUE), .groups = "drop")
# Print the result
avg_survival_sex_pclass## # A tibble: 6 × 3
## Sex Pclass avg_survival
## <chr> <fct> <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# Bar plot for survival chance by sex and passenger class
ggplot(avg_survival_sex_pclass, aes(x = Pclass, y = avg_survival, fill = Sex)) +
geom_bar(stat = "identity", position = "dodge") +
theme_minimal() +
labs(title = "Average Survival by Sex and Passenger Class",
x = "Passenger Class",
y = "Average Survival") +
scale_fill_brewer(palette = "Set2")
This data reveals a significant difference in survival rates on the Titanic between men and women. On average, the survival rate for women was 74.2%, compared to just 18.9% for men. This means that women were over 55% more likely to survive. The linear regression model for sex and survival shows a small p-value, suggesting that this difference is statistically significant. The multiple r-squared value of 0.2952 indicates that sex explains about 29.5% of the variation in survival probability.
The data also shows varying survival rates based on passenger class. On average, passengers in class 1 had a survival rate of about 63%, those in class 2 had a survival rate of 47.3%, and passengers in class 3 had the lowest survival rate at 24.2%. The linear regression model for passenger class and survival shows small p-values for both class 2 and 3, indicating that the differences in survival rates across these classes are statistically significant. The multiple r-squared value of 0.1155 suggests that passenger class accounts for 11.55% of the variation in survival rates. This indicates that sex had a greater impact on survival rates than passenger class did. Overall, this data highlights a significant gender and socio-economic divide on the Titanic.