Editing Pearson correlation coefficient (section)

===Weighted correlation coefficient===
Suppose observations to be correlated have differing degrees of importance that can be expressed with a weight vector ''w''. To calculate the correlation between vectors ''x'' and ''y'' with the weight vector ''w'' (all of length&nbsp;''n''),<ref>{{cite web|url=http://sci.tech-archive.net/Archive/sci.stat.math/2006-02/msg00171.html|title=Re: Compute a weighted correlation|website=sci.tech-archive.net}}</ref><ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/20846-weighted-correlation-matrix|title=Weighted Correlation Matrix – File Exchange – MATLAB Central}}</ref>

* Weighted mean: <math display="block">\operatorname{m}(x; w) = \frac{\sum_i w_i x_i}{\sum_i w_i}.</math>
* Weighted covariance <math display="block">\operatorname{cov}(x,y;w) = \frac{\sum_i w_i \cdot (x_i - \operatorname{m}(x; w)) (y_i - \operatorname{m}(y; w))}{\sum_i w_i }.</math>
* Weighted correlation <math display="block">\operatorname{corr}(x,y;w) = \frac{\operatorname{cov}(x,y;w)}{\sqrt{\operatorname{cov}(x,x;w) \operatorname{cov}(y,y;w)}}.</math>