Correlation

Creator
Creator
Seonglae ChoSeonglae Cho
Created
Created
2021 May 31 5:44
Editor
Edited
Edited
2024 Nov 12 11:59

Normalized
Covariance
, measures linear correlation

The correlation coefficient, Pearson product-moment correlation coefficient, PPMCC, Bivariate correlation, Pearson's r
Correlation does not imply causation such as spurious correlation.
Since variance is non-negative, correlation bounds to -1 to 1 ()
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.
Correlations
 
notion image
 
 
 
 

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