Mathematical Modeling Competition Topic - Wine Quality Evaluation

The 2012 National College Mathematical Modeling Competition presented an intriguing challenge: how to evaluate wine quality effectively? To address this problem, we need to investigate wine composition data and perform various statistical analyses. The provided materials include wine composition data (Excel format) and pre-packaged MATLAB functions for statistical processing that can be implemented directly. The statistical programs encompass: - Data preprocessing: Functions for data cleaning, noise removal, and normalization to ensure data accuracy and consistency - Grey prediction: Implementation of grey system theory for forecasting unknown data points using GM(1,1) modeling - Grey relational analysis: Calculation of relational degrees between different indicators to comprehensively evaluate wine quality - Fuzzy comprehensive evaluation with entropy weight method: Algorithm that determines indicator weights through entropy calculations for more precise quality assessment - Principal component analysis (PCA): Dimensionality reduction technique to identify key factors influencing wine quality - Systematic clustering: Hierarchical clustering methods to group similar wines based on composition characteristics - Multiple linear regression: Statistical modeling to predict relationships between wine quality and compositional factors These methodologies and their corresponding code implementations enable researchers to better understand wine quality characteristics, facilitating more accurate evaluation and comparison processes. The MATLAB functions are optimized for efficiency and include proper error handling for robust data analysis.