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Titanic Fare Prediction: Linear Regression Analysis

Project Overview

This project explores linear regression techniques to predict Titanic passenger fares using various features from the dataset. The analysis compares multiple regression approaches and feature combinations to identify the most effective predictive model.

Dataset

  • Source: Titanic passenger data
  • Target Variable: Fare (ticket price in dollars)
  • Features Explored: Age, family size, passenger class, survival status

Methodology

Feature Engineering

  • Created pclass_survival feature combining passenger class and survival status
  • Tested four feature combinations:
  • Case 1: Age only
  • Case 2: Family size only
  • Case 3: Age + family size
  • Case 4: Pclass_survival + family size (best performing)

Models Tested

  1. Linear Regression (baseline)
  2. Ridge Regression (L2 regularization)
  3. Elastic Net (L1 + L2 regularization)
  4. Polynomial Regression (degree 3 and 7)

Key Findings

Best Model Performance

  • Polynomial Regression (degree=3) achieved the best results:
  • R²: 0.425
  • RMSE: $28.84
  • MAE: $15.58

Feature Importance

  • pclass_survival was the most predictive feature, capturing the relationship between passenger class, survival rates, and ticket prices
  • Adding family_size improved model performance
  • Age alone was a poor predictor (R² = 0.003)

Model Complexity Insights

  • Polynomial features significantly improved predictions by capturing nonlinear relationships
  • Regularization (Ridge, Elastic Net) provided minimal benefit, suggesting models weren't overfitting
  • Higher-order polynomials (degree=7) showed no improvement over cubic (degree=3)

Challenges

  • Fare prediction remained moderately difficult (best R² = 0.425), with 57.5% of variance unexplained
  • High variation in fares within the same passenger class
  • Outliers (luxury tickets $150-$260) were consistently underpredicted
  • Missing pricing factors: cabin location, embarkation port, purchase timing

Technologies Used

  • Python
  • pandas, numpy
  • scikit-learn
  • matplotlib

Conclusions

The nonlinear relationship between passenger class, survival, family size, and fare requires polynomial regression for adequate modeling. While the polynomial model performed well, substantial fare variation remains unexplained, suggesting additional features would be needed for more accurate predictions.