All Questions
36 questions
0
votes
0
answers
11
views
How to use ICC with given data
I have data with columns like this:
ENTITY Avg_Score_1 N_obs_1 Avg_Score_2 N_obs_2
With sample values:
001 | 0.997 | 900 | 1.13 | 905
002 | 0.890 | 250 | 0.96 | 251
For about 1000 unique ENTITY values,...
Jbell
0
votes
0
answers
30
views
Equivalence between two expressions for autocorrelation
Have that
$$
\text{Corr}(X_t,X_{t+h}) = \frac{\text{Cov}(X_t,X_{t+h})}{\sqrt{\text{Var}(X_t)\text{Var}(X_{t+h})}}
$$
and
$$
\rho(h) = \frac{\gamma_X(h)}{\gamma_X(0)}.
$$
Those are both ways to express ...
- 207
0
votes
0
answers
33
views
Deriving a standard deviation of a random variable using correlated other random variables
Consider three random variables: $$u_1, u_2, u_3 \;\; with \;\; E[u_j]=0 \;\; and\;\; Var[u_j]=\sigma^2_j\;\;for\;\;j=1,2,3$$
Here, we know the values $\sigma_1,\;\sigma_2$ and $\rho_{13},\;\rho_{23}$...
- 441
1
vote
0
answers
98
views
When would correlation between two variables not exist?
If we have two random variables $X$ and $Y$, then $\text{corr}(X,Y)=\dfrac{
\text{cov}(X,Y)
}{
\sqrt{
\text{var}(X)\text{var}(Y)
}
}$.
This correlation will not be defined if either variable has an ...
- 67.1k
0
votes
2
answers
186
views
How do I calculate the weighted variance, $\sigma^2$, of a set of $N$ random variables considering their correlation $\rho$? [duplicate]
In a finance textbook of mine, there is an equation for calculating the variance $\sigma^2$ of a portfolio of two risky assets (i.e. random variables) $X$ and $Y$ by considering the correlation $\rho$ ...
2
votes
1
answer
355
views
R function to compute variance of average of correlated random variables
I want to calculate the variance of the average of n correlated variables. I found a formula for that in Borenstein et al. (2009) Introduction to Meta-Analysis.
$$\operatorname{Var}\left(\frac{1}{m}\...
- 151
3
votes
1
answer
78
views
Let $X, Y$ be independent RVs given the variances and no means what is correlation coefficient of $X$ and $Z=2X+Y$?
Let $X, Y$ be independent RV given the variance and no means what is correlation coefficient of $X$ and $Z=2X+Y$?
Given $var(X)=3, var(Y)=4$ and $\mathbf{E}[X]$ and $\mathbf{E}[Y]$ are not known, let $...
- 730
2
votes
1
answer
196
views
Variance of the Product of Correlated Random Variables?
I would like to multiply two correlated random variables, but I'm getting a negative variance. Please point out where I'm wrong.
Variable1 and ...
- 23
5
votes
2
answers
1k
views
Finding correlation coefficient of $X$ and $XY$
Let $X$ and $Y$ be independent random variables with nonzero variances. I'm looking to find the correlation coefficient $\rho$ of $Z=XY$ and $X$ in terms of the means and variances of $X$ and $Y$, i.e....
- 221
1
vote
0
answers
1k
views
How do you interpret generalized variance?
Per Wiki, generalized variance is the determinant of a covariance matrix: https://en.wikipedia.org/wiki/Generalized_variance
I have heard that if the determinant is small, there is strong correlation ...
- 3,263
1
vote
0
answers
67
views
What is the difference between covariance and correlation? [closed]
I am analysing stock returns and whether they move in the same or opposite directions across different regions, investment styles or company sizes.
Which of the covariance or the correlation gives ...
- 29
0
votes
0
answers
29
views
Can I determine what the correlation matrix is if I have regression coefficients and standard errors?
I am trying to reverse engineer a manuscript and was wondering if I can get a correlation matrix or the covariance-variance matrix from values reported in a paper. Can I use the reported regression ...
- 662
6
votes
2
answers
3k
views
Linear Mixed Effects Model Variances
Consider the following model:
\begin{equation}
Y_i = X_i\beta + Z_ib_i + \varepsilon_i,
\end{equation}
where $b_i \sim N(0, D)$, and $\varepsilon_i \sim N(0, R_i(\gamma))$.
The variance of $Y_i$ ...
- 843
1
vote
1
answer
415
views
Variance of X-Y and X-Z when Z and Y are correlated
I have a hard time solving the following issue, so hopefully someone is willing to help. I believe I am almost there but just missing a single step.
There are three random variables $X$, $Y$, and $Z$ ...
- 371
3
votes
1
answer
457
views
Minimum variance of the mean for $n$ correlated random variables
If $X_1,\cdots,X_n$ all have the same variance equal to 1, then $0\leq \mbox{Var}[\bar{X}]\leq 1$ where $\bar{X}=(X_1 + \cdots + X_n)/n$. The upper bound is attained if $\mbox{Cov}[X_k,X_l]=1$ for all ...
4
votes
2
answers
985
views
Intuitive understanding of variance of sum vs variance of difference
$\newcommand{\Var}{\operatorname{Var}}\newcommand{Cov}{\operatorname{Cov}}$Mathematically,
$\Var(X + Y) = \Var(X) + \Var(Y) + 2\Cov(X,Y)$ and
$\Var(X - Y) = \Var(X) + \Var(Y) - 2\Cov(X,Y)$
This ...
- 529
2
votes
2
answers
428
views
Outlier and correlation
Hi, I have a question.
The scatter plot doesn't show any type of correlation and there is an outlier.
If the outlier was to be removed, would the correlation:
Increase dramatically
Increase ...
- 21
0
votes
0
answers
87
views
What is the covariance between X and Y, when $Y>0$ if $X<0$ and $Y<0$ if $X>0$?
Let $X$ and $Y$ be two random variables, and $Y>0$ when $X<0$ and $Y<0$ when $X>0$, but can we conclude Cov$(X,Y)<0$?
If the question only states $Y>0$ when $X<0$, then the ...
- 567
6
votes
1
answer
3k
views
Why would we ever use Covariance over Correlation and Variance over Standard Deviation?
I am unable to understand the practical use of Covariance and Variance.
In my understanding, Covariance and Correlation are both measures of how one variable changes with respect to another. The only ...
- 163
0
votes
1
answer
284
views
Given the variance of sum and difference of two identically distributed random variables, how can I calculate the correlation of the variables?
Suppose $X$ and $Y$ are two identically distributed random variables such that:
\begin{eqnarray*}
\sigma^2_{X+Y} = a \, (a \in \mathbb{R}) \\
\sigma^2_{X-Y} = b \, (b \in \mathbb{R})
\end{eqnarray*}
...
- 3
1
vote
1
answer
101
views
Correlation.. covariance.. I am so lost
This monday I'll take my exam in Investment analyses. My teacher usually gives a matrix with covariances and beta's, which makes it easy to find Expected return/ Variance. He just posted some exam ...
0
votes
1
answer
278
views
Variance of a difference variable
I have a question I'm quite struggling with.
$\newcommand{\Var}{{\rm Var}} \newcommand{\Cov}{{\rm Cov}}$
Let's say I have variable $x_1$, and I know that $x_2=x_1+d$, with $d$ being a random variable ...
- 11
12
votes
1
answer
3k
views
Understanding $\operatorname{Cov}(X,X) = \operatorname{Var}(X)$ intuitively
I just saw this question and the wonderful accepted answer in this forum. I was then triggered to try understanding intuitively why division of $S_xS_y$ is normalizing the covariance:
$$\frac{\...
- 223
1
vote
0
answers
44
views
Expected value of a semi-partial correlation
Say I have 4 random variables. $X^{(1)}$ and $X^{(2)}$ are jointly multivariate normal with mean 0 and covariance $\Sigma_X$, and $Y^{(1)}$ and $Y^{(2)}$ are jointly multivariate normal with mean 0 ...
- 7,752
8
votes
1
answer
10k
views
What's the relationship between covariance, shared variance, and common variance?
I've generally assumed that shared variance and common variance were the same thing. However, here it is written that "Common variance is the realm of total collinearity. On the other hand, the term "...
2
votes
0
answers
450
views
Covariance between ordinal variable and discrete variable
I have two variables $y$ and $p$. Since $p$ is a discrete variable (numeric vector) and $y$ is an ordinal variable (total time watching TV).
...
- 1,623
2
votes
0
answers
91
views
How to calculate correlation between two MLEs?
Let's say I have a dataset: $X_1, \ldots, X_n$ that follows some distribution $F(\theta)$. Assume that the MLE for $\theta$ does not have a closed form, so we must find it using numerical methods (...
- 21
6
votes
1
answer
5k
views
What can be inferred from "covariance matrix of residuals" and "correlation matrix of residuals" after VAR?
I have this VAR:
summary(VAR(V6CADModelSt45obs1D.df[,c(5,3,2,6,1,4)], p=5, type="none", ic="SC"))
The following is the result of this VAR:
<...
- 549
8
votes
3
answers
13k
views
Covariance greater than Variance?
It is straightforward to verify that for two random variables $X$ and $Y$ with variances $\sigma^2_X \neq \sigma^2_Y$, we have that
$$\Big|{\rm Cov}(X, Y)\Big| \leq \max\{\sigma^2_X,\, \sigma^2_Y\}$$
...
0
votes
2
answers
151
views
Understanding COVARIANCE when using same scale
Assuming that an experiment has 3 variables.
Time, Temperature inside, Temperature outside.
Also, considering that both the temperatures are measured using the same scale say Degree Celsius.
If the ...
- 121
1
vote
3
answers
1k
views
Correlation coefficient: If $\rho = 0$, then $r$ is normally distributed with mean 0. Why?
From this source, the estimation of the coefficient of correlation is
$$r = \frac{\Sigma (X_i-E[X])(Y_i-E[Y])}{\sqrt { \Sigma (X_i-E[X])^2 \Sigma (Y_i - E[Y])^2}}$$
If the coefficient correlation is ...
- 5,182
1
vote
0
answers
185
views
Standard Error of a linear regression
As defined here, the estimation of the coefficient of correlation is
$$r = \frac{\Sigma (X_i-E[X])(Y_i-E[Y])}{\sqrt { \Sigma (X_i-E[X])^2 \Sigma (Y_i - E[Y])^2}}$$
and the standard error of $r$ is
$...
- 5,182
9
votes
1
answer
4k
views
Why does $r^2$ between two variables represent proportion of shared variance?
Firstly, I appreciate that discussions about $r^2$ generally provoke explanations about $R^2$ (i.e., the coefficient of determination in regression). The problem I'm seeking to answer is generalizing ...
- 759
5
votes
1
answer
622
views
If three random variables have the same variance, what will the co-variances look like?
I'm curious to know, if three random variables have the same variance, what will the co-variances look like? Can somebody help me to figure it out?
- 2,743
2
votes
0
answers
94
views
Finding correlation coefficient
if I have A and B with the following known variables:
with $E[A]$, $E[B]$ , $\sigma_{A}$ , $\sigma_B$
and correlation coefficient: $\rho_{AB}$ (assign numbers if you like)
Say: $C=0.6A+0.4B$
Then ...
- 21
10
votes
2
answers
37k
views
Covariance of a variable and a linear combination of other variables
Let $X,A,B,C,D$ be time-series variables and the covariance between any two pairs of these are known.
Suppose we want to find $\textrm{cov}(X,aA + bB + cC + dD)$, where $a,b,c,d$ are constants.
Is ...
user14281