Ch.03 Mini Project 01 — Multivariate Statistics Explorer¶

Concept: Location statistics matrix, dispersion statistics matrix, covariance matrix, and Pearson correlation matrix for multivariate data.

What it does¶

Given any CSV file (or the built-in Friends dataset), the project computes and prints four multivariate summary tables:

Location matrix — min, Q1, median, mean, mode, Q3, max for every numeric column
Dispersion matrix — amplitude, IQR, MAD, std dev, variance for every numeric column
Covariance matrix — sample covariance for every pair of numeric columns
Pearson correlation matrix — scale-independent linear correlation for every pair

Expected output (Friends dataset)¶

The printed correlation matrix should show: - Weight / Height: r = 0.94 (very strong positive) - All diagonal entries: 1.00

Files¶

File	Language	Description
`multivariate_statistics.py`	Python 3	Pure stdlib; beginner-friendly step-by-step
`multivariate_statistics.R`	R	Base R only; uses `apply()`, `cov()`, `cor()`

Usage¶

Python¶

# Built-in demo (Friends dataset)
python multivariate_statistics.py

# From a CSV file
python multivariate_statistics.py data.csv

No external dependencies — pure Python 3 standard library.

R¶

source("multivariate_statistics.R")

Base R only — no packages needed.

Key Concepts from Ch.03 Applied¶

Concept	Where it appears
Location statistics matrix	`print_location_matrix()`
Dispersion statistics matrix	`print_dispersion_matrix()`
Sample covariance	`compute_covariance_matrix()`
Pearson correlation	`compute_correlation_matrix()`
Symmetric matrices	Diagonal = 1 (correlation); symmetric off-diagonal

Formulas Used¶

Covariance:   cov(X,Y) = (1/(n-1)) * sum[ (xi - x_bar)(yi - y_bar) ]
Pearson r:    r(X,Y)   = cov(X,Y) / (std(X) * std(Y))
MAD:          median( |xi - median(X)| )
IQR:          Q3 - Q1
Amplitude:    max - min