# Questions tagged [covariance]

Covariance is a quantity used to measure the strength and direction of the linear relationship between two variables. The covariance is unscaled, & thus often difficult to interpret; when scaled by the variables' SDs, it becomes Pearson's correlation coefficient.

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### Weighted least squares estimator variance using noisy weights

I have a linear system with uncorrelated, heteroscedastic noise, $Y \propto \mathcal{N}(Xβ,Σ)$ where $Σ$ is a diagonal matrix with elements $σ_{ii}^2$. The MLE is given by weighted least squares (WLS) ...
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### Is there anything interesting to be taken from the fact that $E[(X-E[X])(Y-E[X])] = E[(X-E[X])(Y-E[Y])]$?

While playing around with the formula for covariance, I discovered something I wasn't expecting. Replacing the $E[Y]$ in the definition of covariance with an $E[X]$ appears to simplify back down to ...
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### Weighted average of covariance matrixes

My issue is as follows: In my model there are 4 different states, which each have a calculated probability of happening. I also have calculated covariance matrixes for my variables in each of these ...
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### What affects correlation in this situation?

Suppose a dataset I with 20 samples pairs of x and y collected from 20 different farms in State A. Another dataset II with 20 samples pairs of x and y collected from 20 different farms in State A, B, ...
$\newcommand{\e}{\operatorname E}$"Obviously" if $g$ is a weakly increasing function and $X$ and $g(X)$ are both random variables with finite variance, then the covariance (and hence the ...