# 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.

1,769 questions
Filter by
Sorted by
Tagged with
29 views

1 vote
25 views

### Relation between first three moments of distribution

Consider a random variable $X$ with distribution described by the first three moments: $$\mathbb{E}(X) = \mu$$ $$\mathbb{E}(X-\mu)^2 = \sigma^2$$ $$\mathbb{E}(X-\mu)^3 = \gamma$$ Is there a nontrivial ...
• 252
29 views

• 857
48 views

### Path analysis with perfect fit

I'm trying to determine if I can display two regression models and the covariance between the dependent variables in one unified model using path analysis with lavaan in R. In the following (scaled) ...
19 views

### Using bootstrap to estimate covariance of mean estimators from two distinct (dependant) populations

Given two samples : an i.i.d. $n_u$-sample $(u_{j})_{1 \leq j \leq n_u}$ and an i.i.d. $n_v$-sample $(v_{i})_{1 \leq i \leq n_v}$. Note : The populations of the two samples are disjoint (let's say we ...
13 views

### Alternative method to deriving autocorrelation function of stationary AR(2) process [duplicate]

I have read this question/answer: Autocorrelation of a stationary AR(2) process How can we derive this using Expectation. Let $Y_t = \phi_0 +\phi_1 Y_{t-1} + \phi_2 Y_{t-2}+\epsilon_t$ I found the ...
13 views

15 views

33 views

### Prove that the equality holds [closed]

How to prove that for any random variables $X$, $Y$ and $Z$ with finite variances, we have $Cov(X,Y)=E(Cov(X,Y|Z))+Cov(E(X|Z),E(Y|Z))$?
315 views

### Imaginary numbers in PCA output

Using PCA manually on correlation matrix, I'm getting imaginary numbers in both eigenvalues and eigenvectors. Is this expected behavior? I understand that when interpreting a matrix as a linear ...
• 3,404
### If $A^2$, and $B^2$ are DEPENDENT random variables, will $A$, and $B$ be necessarily DEPENDENT too?
I know that if $A$, and $B$ are independent, the independence is preserved for $A^c$, and $B^c$, where $c$ is a constant. I am wondering if the same applies to the case where the random variables are ...