How Logistic Regression Predicts Titanic Survival: A Step-by-Step R Guide

When the dependent variable is binary (“yes/no”), logistic regression (also called logit regression) can model the linear relationship between the probability of “yes” and the independent variables.

In this model, is the probability of “yes”, is the probability of “no”, and the relationship is expressed by the sigmoid function. The generalized linear model function glm() in R implements logistic regression and can fit various regression models.

The famous movie Titanic illustrates human choices before disaster, prioritizing women and children. The example uses real 1912 Titanic data with 11,309 passengers, including age, sex, passenger class, and survival status, sourced from the TitanicSurvival dataset in the carData package.

<code>library(carData)
logit.TS <- glm(survived ~ sex + age + factor(passengerClass), family = binomial, data = TitanicSurvival)
summary(logit.TS)
</code>

Result

<code>Call:
glm(formula = survived ~ sex + age + factor(passengerClass), 
    family = binomial, data = TitanicSurvival)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.6399  -0.6979  -0.4336   0.6688   2.3964  

Coefficients:
                     Estimate Std. Error z value Pr(>|z|)    
(Intercept)            3.522074   0.326702  10.781  < 2e-16 ***
sexmale               -2.497845   0.166037 -15.044  < 2e-16 ***
age                   -0.034393   0.006331  -5.433 5.56e-08 ***
factor(passengerClass)2nd -1.280570   0.225538  -5.678 1.36e-08 ***
factor(passengerClass)3rd -2.289661   0.225802 -10.140  < 2e-16 ***
---
Signif. codes:  ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 1414.62  on 1045  degrees of freedom
Residual deviance:  982.45  on 1041  degrees of freedom
  (263 observations deleted due to missingness)
AIC: 992.45

Number of Fisher Scoring iterations: 4
</code>

In this example, the generalized linear model formula is survived ~ sex + age + factor(passengerClass) , investigating the relationship between survival status and gender, age, and passenger class. Both survival and sex are binary variables, age ranges from 0 to 80, and class has three levels encoded as dummy variables. Using the binomial family yields a logit model appropriate for the binary outcome. After removing 263 rows with missing data, the results show that survival is highly significantly associated with gender, age, and class, reflecting a profound aspect of human behavior.

Source: Liu Hongde, Sun Xiao, Xie Jianming, Biological Data Analysis and Practice

Liu Hongde, Sun Xiao, Xie Jianming