PRB-25

Correlation

Pearson rho.

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GoverningCorrelation

Governing equation

\\rho=\\mathrm{cov}/(\\sigma_x\\sigma_y)

where

cov: cov (—)
sx: sx (—)
sy: sy (—)
rho: Correlation (—)

Lecture brief

Historical brief

Bernoulli trials, Poisson, Gauss, Bayes and Shannon entropy turned chance into a calculus of belief and noise. The lab computes likelihood, interval and information in SI-free counts. This sheet (PRB-25 — Correlation) is the form associated with Correlation. Working symbols: $cov$ , $sx$ , $sy$ $\rightarrow$ $rho$ . Pearson rho. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

rho

from

cov

sx

sy

in Probability & statistics via

\\rho=\\mathrm{cov}/(\\sigma_x\\sigma_y)

Pearson rho. Use it when a real probability & statistics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

cov = 2.000\,\mathrm{—}

sx = 3.000\,\mathrm{—}

sy = 4.000\,\mathrm{—}

, the governing relation

\\rho=\\mathrm{cov}/(\\sigma_x\\sigma_y)

yields

rho = 0.167\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

cov cov2 —sx sx3 —sy sy4 —

Outputs

Correlation rho0.167 —

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Pearson rho. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube