Correlation

Creator
Creator
Seonglae ChoSeonglae Cho
Created
Created
2021 May 31 5:44
Editor
Edited
Edited
2025 Apr 27 13:2

Normalized
Covariance
, measures linear correlation

The correlation coefficient, Pearson product-moment correlation coefficient, PPMCC, Bivariate correlation, Pearson's r
Since variance is non-negative, correlation bounds to -1 to 1 ()
Correlation does not imply
Casuality
such as spurious correlation. Uncorrelated This means that there is no linear relationship.

Difference with
Convolution
is flip

Uncorrelated does not imply independence. However, if two random variables X and Y are
Normal distribution
uncorrelated, then they are
Pairwise Independence
. Since zero correlation makes
Covariance Matrix
and thus inverse of covariance matrix become diagonal. The joint PDF simplifies to the product of two independent normal distributions which satisfies
Pairwise Independence
.
The correlation between an
Even function
and the original variable is zero. (Integral cancels out) Naturally, even powers also exhibit this property.
Other Correlations
 
notion image
 
 
 
 
 

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