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Post by Karel on Jun 5, 2016 13:09:33 GMT
Apparently it is a deep statistical truth that highly correlated quantities increase the variance.
I don't get why. Can anyone explain? Thanks!
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Post by NullModel on Jun 5, 2016 14:15:56 GMT
This is my uneducated guess, deduced after some googling, so take it all with a grain of salt or salt mine: # 1. Correlation between two standardized variables X and Y is defined as = covariance(X,Y)/(Standard Deviation(X)*Standard Deviation(Y)). So reducing the covariance will reduce the correlation, and an increase in covariance exhibit an increase in correlation. # 2. In general, the variance of a sum of correlated variables can be given by their sum of covariances. They write about it here: en.wikipedia.org/wiki/Variance#Sum_of_correlated_variables So, if your variables are strongly correlated, they will show more covariance, which increases the variance of the sum. ~ Alex |
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