Statistical Modeling & Linear Regression
Relevant source files
The following files were used as context for generating this wiki page:
Introduction
The statistical modeling component of this project focuses on the ingestion, processing, and analysis of physiological data, such as cholesterol levels and body weight. It provides a framework for calculating central tendency, dispersion, and distribution skewness, which serve as foundational steps for more complex modeling tasks.
The system utilizes standard Python libraries including numpy and statistics to perform computations on datasets imported from flat text files. This module serves as a utility for descriptive statistics and preliminary data exploration.
Sources: hw1/p1.py:1-5, hw1/CHOLESTEROL.txt
Data Ingestion and Processing
The system employs a specific workflow for loading raw numerical data from external text files into memory. The process involves sanitizing input by stripping whitespace and handling non-numeric values through exception handling to ensure data integrity during computation.
This diagram illustrates the robust parsing logic used to transform text-based datasets into a format suitable for mathematical analysis.
Sources: hw1/p1.py:7-17
Data Sources
The modeling tools specifically target the following datasets:
| File | Description | Sample Data Points |
|---|---|---|
CHOLESTEROL.txt | Individual cholesterol measurements | 205, 166, 236... |
WEIGHT.txt | Individual weight measurements (kg) | 62, 51, 56... |
Sources: hw1/CHOLESTEROL.txt:1-28, hw1/WEIGHT.txt:1-12
Statistical Calculations
The core logic resides in the compute_file function, which aggregates various statistical metrics to describe the dataset's characteristics.
Metrics and Formulae
The system calculates several standard and custom statistical indicators:
| Metric | Implementation Method | Description |
|---|---|---|
| Mean | np.mean(data) | Arithmetic average |
| Median | np.median(data) | Middle value of sorted data |
| Mode | statistics.mode(data) | Most frequent value |
| Range | np.ptp(data) | Peak-to-peak difference (Max - Min) |
| Std Deviation | np.std(data) | Square root of variance |
| Variance | np.var(data) | Average of squared deviations |
Sources: hw1/p1.py:23-44
Higher-Order Coefficients
Beyond basic metrics, the system implements coefficients to determine distribution skewness and variability:
- First Coefficient of Variation (Pearson's Skewness):
Calculated as $3 \times \frac{(\text{mean} - \text{median})}{\text{std}}$.cv1 = 3*(mean - median) / std - Second Coefficient of Variation (Moment-based Skewness):
Calculated using the sum of cubed deviations from the mean divided by the count times the cubed standard deviation.cv2 = sum([(x - mean) ** 3 for x in data]) / (len(data) * std ** 3)
Sources: hw1/p1.py:46-51
Execution Flow
The following sequence diagram outlines the interaction between the file system, the parsing utility, and the statistical engine.
The sequence demonstrates the linear execution path from file identification to final coefficient output.
Sources: hw1/p1.py:19-53
Summary
The "Statistical Modeling & Linear Regression" module provides the project with essential tools for data quantification. By automating the extraction of central tendencies and skewness coefficients from CHOLESTEROL.txt and WEIGHT.txt, it establishes a reproducible pipeline for physiological data analysis.