PRB-25

Correlation

Pearson rho.

Reading speed

GoverningCorrelation

Governing equation

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

$cov \in \left[-20, 20\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

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

$cov \in \left[-20, 20\right]$

$cov = -20$ $rho = -1.667$

Along the curve

②

Domain of the variable — blue

cov_{\min} = -20,\quad cov_{\max} = 20

$cov \in \left[-20, 20\right]$

$cov = -20$ $cov = -20$

Along the curve

③

Response curve — green

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

$cov \in \left[-20, 20\right]$

$cov = -20$ $rho = -1.667$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}rho}{\mathrm{d}cov}

$cov \in \left[-20, 20\right]$

$cov = -19.75$ $rho^{\prime} = 0.083$

Along the curve

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