📊 Bayesian Multiparameter Model for Body Fat Prediction

This project implements a Multi-parameter Bayesian Linear Regression Model to predict human body fat percentage using two practical, low-cost physical indicators: body weight and abdomen circumference

Developed as part of the MDA3093 coursework.

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📌 Project Overview

• Domain: Biostatistics & Health Analytics
• Sample Size: 252 adult male subjects
• Target Variable ($Y$): Body Fat Percentage (estimated via underwater weighing)
• Predictors ($X$): Weight (lbs) and Abdomen Circumference (cm)
• Methodology: Normal-Inverse-Gamma (NIG) Conjugate Prior Model evaluated via R / MCMC simulation

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🎯 Objectives

1. Map Parameter Uncertainty: Estimate joint posterior distributions for regression coefficients ($\beta_0, \beta_1, \beta_2$) and residual variance ($\sigma^2$)
2. Quantify Effect Sizes: Evaluate the distinct contributions and credible intervals of weight vs. waist size
3. Automated Analysis: Execute analytical posterior updates and visualization dashboards using R

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🚀 Repository Contents

• Statistik Bayesian.pdf – Full project presentation/slides documenting the statistical theory and findings
• bodyfat.R – R script handling data preprocessing, matrix calculations, MCMC sampling, and 2x2 diagnostic plotting (posterior histograms and raw data regressions)

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📈 Key Findings

• Model Performance: Combining body weight and waist size explains roughly 72% of the variation in body fat percentage
• The "Weight Paradox": Once abdomen circumference is controlled for, overall weight exhibits a negative coefficient, indicating that heavier individuals with the same waist size carry more lean muscle mass rather than extra fat.