# 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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### Correlation of multivariate distributions without "slope"

Wikipedia has this image showing different correlations: It says: The correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (...
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### Demonstration and Interpretation between a Fisher matrix and its dual space which is covariance matrix

I have a simple (maybe not) issue about the interpretation of the link between Fisher information matrix and its inverse which is the covariance matrix. How to formulate that a line of Covariance ...
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### covariance of lognormal random variables

I am trying to find the variance of b*log(x+y) - log(x), where x and y are independent and identically distributed lognormal random variables, the range for log(x) and log(y) is negative infinity to ...
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### Cross-covariance in context of Andrews plot

As shown in this Cross-Validated post Close curves on an Andrews plot I don't understand how, in the accepted answer, the cross-covariance can be defined as, $$\int_{-\pi}^{\pi}f_xf_ydt$$ Considering ...
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### ANOVA or ANCOVA? I have a control variable

In my study, I am analyzing 4 groups, as it is a 2 (primed or not primed) × 2 (high efficacy or low efficacy) experimental design. I am planning on using ANOVA between-subject analyses to test for ...
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### Is there any way of simplifying the covariance of a function of a random variable and a random variable?

For example, if we had random variables $X$ and $Y$ and we know that $corr(X,Y)=\rho$, how would you solve for $Cov(e^X,Y)$?
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I have a collection of data of numerical ratings of comments from threads on a website. I want to determine how strongly these ratings are correlated with other comments within the same thread. More ...
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### Justifying the choice of covariance function

For a Gaussian process I run I have chosen to use the Matern52 covariance function, as from research this is practical to use for physical data as it does not overally smooth the function. However is ...
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### When to add covariances of mediators [SEM]

I have just created my first mediation model using sem() with the lavaan package in R. I am using a bootstrapping with 5000 resamples and BCA to calculate the confidence intervals at a 0.9 level. Now, ...
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### Confusion on calculating Mahalanobis distance

I am slightly confused as to how you calculate Mahalanobis distance given a set of data. I have tried asking my tutor for help but he does not seem interested in helping what so ever and I am ...
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### mean and covarince matrix of AR(1) [closed]

assume I have a price data called pt, I fitted AR(1) model p_t= alpha + beta pt_1 + e_t , ...
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### What is the analog of precision matrix for cross-covariance matrices?

For a covariance matrix, I am aware of the precision matrix, the covariance matrix inverse. What's the analog for that for a cross covariance matrix, i.e. $E[XY^{\top}]-E[X]E[Y^{\top}]$ for two random ...
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### Definition of autocorrelation?

EDIT: Apparently I was not thorough enough in my search for previous questions on this topic. This is pretty much the same question, and has been answered: Auto-correlation vs Auto-covariance The ...
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