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Questions tagged [correlation]

For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].

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What if correlation coefficient is much less whereas the p-values is much lesser than the our significance level?

I have a data between rating of the restaurant and the approximate price of food in the restaurant. After doing Hypothesis testing. The pearson correlation coefficient was found to be 0.33 whereas p ...
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is the correlation between two things separated by a comma a compact way of writing two statements?

I want to know if corr({a,b},c) = 0 is the same as saying that corr(a,c) = 0 corr(b,c) = 0 But that the first is just a short-hand way of writing it.
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How to create a covariance between two distributions?

I have two distributions $A$ and $B$ that are i.i.d. I want to create two distributions $A'$ and $B'$, that have the "same distribution" as $A$ and $B$ (meaning the same probability distribution ...
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Distribution/Variance of correlated squared normal random variables

If $X_{1}, X_{2}, \ldots, X_{N}$ are identically distributed normal random variables with mean $0$ and variance $\frac{(N+3)D\sigma^{2}}{N}$, then I want to calculate the distribution, or at least the ...
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setup time optimization using statistics

together I work at a manufacturer with numerous products. The diversity if variants is very high. For almost every product the machines have to be converted. There are essentially 3 characteristics, ...
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1answer
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How would one go about proving that two random variables are uncorrelated but not independent? [duplicate]

Suppose $\theta$ is a Uniform random variable on [0, 2$\pi$]. Let $X$ be $cos(\theta)$ and $Y$ be $sin(\theta)$. We have to show that $X$ and $Y$ are uncorrelated but not independent. My solution: $...
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51 views

Correlation between $X$ and $Y$ conditioned on $A\cup B$

Suppose $\theta \sim \text{Uniform}[0,2\pi]$, and $X=\cos(\theta)\,,\, Y=\sin(\theta)$. Let two events be defined by $A=\{X\geq 0\}\,,\, B=\{Y\geq 0\}$. I want to find the correlation coefficient ...
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What is a lag-based correlation?

could anyone please advise as to what a lag-based correlation is? Is this the same as a cross-lagged analysis? This type of analysis was recommended to me by a reviewer to elucidate the ...
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how to improve Normalized cross correlation

I used the Normal cross correlation (NCC) calculation to find an equation between two signals or images. now I'm trying to improve the calculations but have no idea. I just need a little improvement. ...
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1answer
18 views

Show $\left(X-m_{X}\right)-A\left(Y-m_{Y}\right)$ and $Y$ are Uncorrelated Given $AC_{Y}=C_{XY}$

I'm given the facts that $X$, $Y$ are jointly normal random vectors and the matrix $A$ solves $AC_{Y}=C_{XY}$, where $C_{Y}$ is the correlation matrix for $Y$ and $C_{XY}$ is the cross-correlation ...
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psd matrices associated with a family of partially recovering subsets of a given finite set

Initial remark : this question is motivated by this one : Show a specially defined matrix is positive definite. Let us take it from the beginning. Let $E_k \ (k=1\cdots n)$ be a sequence of $n$ ...
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1answer
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Autocorrelation and lags definition

I'm looking for a way to define lags in autocorrelation graphs / corellograms. I understand how to interpret such a graph but can't define a lag in a clear concise manner. Does a definition for this ...
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If $\frac{X_a}{X_a+Y_a}$ and $\frac{X_b}{X_b+Y_b}$ are correlated, what about $X_a+Y_a$ and $X_b+Y_b$

Suppose I have four normal random variables:$X_a$,$Y_a$,$X_b$,$Y_b$. $X_a$ and $Y_a$ follow bivariate normal, $X_b$ and $Y_b$ also follow bivariate normal. let $Z_a=\frac{X_a}{X_a+Y_a}$ , $Z_b=\...
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A question about stochastic processes

Imagine i have two stochastic processes.One is low frequency and the other is high frequency.Suppose i obtain 2 random variables X (low frequency process) and Y(high frequency process) from these ...
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Matrix square root of squared correlation matrix

Setup: Given $y \sim N(0,\Sigma)$, suppose we want to transform $y$ to a new space so entries have zero covariance. We can use the inverse square root and apply to transform $\tilde{y} = \Sigma^{-1/...
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Necessary conditions for defining correlation

Suppose I have a probability space on which I define the space of all random variables. On that given space I then define function F which takes two random variables as arguments and returns a real ...
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Correlation of complex random variables

If I have two complex standard normal variables vectors (10,1) $M_i$ and $N_i$ as below, $M_i = a_i+jb_i$ and $N_i = c_i +d_i, (1<i<10)$ How can I get correlation coefficients of these vectors?...
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Correlation is zero but with non-zero correlation coefficient

The correlation coefficient is given by $$\rho_{XY}=\frac{R_{XY}-\mu_X \, \mu_Y}{\sigma_X \, \sigma_Y}$$ If the product $\mu_X \, \mu_Y \neq 0$ and $\rho_{XY}\neq 0$, then we can have two cases: $...
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30 views

Can eigenvalues of a correlation matrix be negative?

Can eigenvalues of a correlation matrix be negative? I am a bit confused because I know that a correlatin matrix $C$ is always positive semi-definite ie for all $v \in \mathbb R^n$ we have $v^T C v \...
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Calculate covariance given correlation, problem with percentages

The question is: find the covariance of ABC stock returns with the original portfolio returns. Pretty straightforward. However I get confused working between percentages and units. The ...
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Correlation of means or correlation of individual values

I have a data set of player performances and am looking to calculate some correlations of their stats with win percentage. Some players have multiple performances, is it valid for me to take the mean ...
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Construct Correlated Wiener Processes

Construction Hello.. I am trying to better understand how one can correlate independent Wiener processes given a correlation matrix. Please see the attached notes. This method uses the Cholesky ...
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Should we denoise a time series before calculating correlation?

While I understand the answer may depends on, say from method of denoising, to the information contained in the dataset. May I ask in general, does it make sense to denoise a time series before ...
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binary variables : bound on probability of $A=B$ given respective correlation with $C$

Let $(A,B,C)$ be three binary random variables, i.e., $(A,B,C)\in \{0,1\}^3$ Suppose pairwise correlations between $(A,C)$ and $(B,C)$ are respectively given by the following odds ratios $$ \frac{P[A=...
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1answer
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cross-correlation definition

If I understand correctly, wikipedia defines the cross-correlation of two signals (see here) as: $$ x \star y = \sum_{i=-\infty}^{\infty} x^\ast(i)y(n+i) $$ However, in some other sources, as matlab ...
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How many samples in a sequence do I need to evaluate to determine whether the Pearson correlation will be below a certain threshold?

I have two sequences $A$ and $B$ of equivalent length containing arbitrary numbers. I also have an arbitrary threshold value $T$ somewhere between -1 and 1, and know the means of both sequences. Now ...
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2answers
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Decomposing Sums of Random Variables

Suppose I have $M$ random variables, and a number of realizations of each variable. Each RV has the probability mass function: $$\rho_{X_i}(x) = \begin{cases} p_i, & x = 1\\ 1-p_i, & x = 0\\ 0,...
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1answer
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Correlation coefficient plus scaling and shifting

I am training a convolutional neural network with the Pearson correlation coefficient $\rho(a,b)$ where the error function $\epsilon$ is defined as $1-\rho$, for a given predicted output $a$ and a ...
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1answer
42 views

CDF of positively correlated Gaussians

Suppose $X,Y$ are two positively correlated Gaussians with zero mean and unit variance. Is it the case that for $a,b \in \mathbb{R}$, $$ \Pr[X \leq a, Y \leq b] \geq \Pr[X \leq a] \Pr[Y \leq b]? $$
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Population linear model

I have a dataset with 15 people. For each person I have the age and a blood measurement. The relation between the age and the blood measurement is linear. The plot between the two variables looks ...
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Calculation of expected value in terms ACF

How to find expexted value of system output in terms of transfer function with knowing expected value of input and autocorrelation function of input? I should find Expectation of $y(t)=\int x(t-\tau)...
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Cross-correlation of a deterministic signal and white Gaussian noise

I'm trying to describe the cross-correlation of a finite length input signal x[n] with the same signal corrupted by white Gaussian noise. If the signal would be infinitely long, the noise would be ...
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Normal Random Variables that all correlate with a single time series but not necessarily with each other

I have a sequence of normally distributed random variables. Let's call it $S_1$. I want to generate 4 more series, each of which has its own correlation with $S_1$ and its own variance. Let's call ...
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Bounds on the support of a correlation matrix' eigenvalue spectrum

I have a covariance matrix $V=(v_{ij})$ and construct a correlation matrix $C$ with entries $c_{ij}=\frac{v_{ij}}{\sqrt{v_{ii}v_{jj}}}$. The matrices $V$ and $C$ are positive definite, so I know that ...
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Bivariate density with uniform marginals

I kindly ask for your help to solve this problem. Consider two standard uniform random variables $X_1,X_2\sim U[0,1]^2$. Then, the questions are: 1) is it possible to find the explicit form of joint ...
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correlation between two variables with different ranges

I have two variables $A$ and $B$, where A is between range $[1, \infty)$ and B range is $[0,1]$. Does that affect the correlation results? I used the Pearson correlation now. Any idea can help me on ...
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longitudinal study with repeated measures

I have a data-set which is collected using two devices (A and B) to measure the same variable, for 10 participants during 5 different types of activities . Each activity goes for 15 minutes and there ...
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Spearman's Correlation Coefficient for Bivariate Normal Distribution

Referring to the answer here https://stats.stackexchange.com/a/66617 It is written that $\rho_s(X_1,X_2) = \rho(F_1(X_1),F_2(X_2))$ My Questions are :- Is that forumla correct? Because I am not ...
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1answer
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Confidence interval of Pearson’s correlation seems too tight for low N

Say we have a matrix M where each column is a book, each row is a user, and cells are ratings - cells may be empty (not rated), or have values from 1 (didn’t like the book) to 5 (loved the book). If ...
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1answer
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Compute the correlation coefficient $r(X_{(1)},X_{(3)})$ .

I got this problem where: The random variables $X_1, X_2,$ and $X_3$ are independent and $Exp(1)-$ distributed. Compute the correlation coefficient $r(X_{(1)},X_{(3)})$ . I know through research ...
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1answer
27 views

Relationship between different types of correlation coefficients

Let, $r_{1(2.34...p)}$ = Correlation between $x_1$ and $x_{2.34...p}$. The latter being the residuals after regressing $x_2$ on $x_3 , x_4 ....x_p$. $r_{1.234..p}$ = Multiple correlation coefficient ...
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Testing cross-covariance in the residuals of a VAR(p) model

Suppose I have a vector autoregressive model of order $p$: $$y_t = c + A_1 y_{t-1} + ... + A_p y_{t-p} + u_t$$, where $y_t$ is a $K\times 1$ vector and $A_i$ are $K\times K$ matrices. We assume the ...
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Prove a time series to be NOT identically independent distributed

I am trying to prove that this time series (given that $X_{t}$ and $M_{t}$ are iid and independent of each other) $$ Y_{t} = X_{t}(1-X_{t-1})M_{t} $$ is not i.i.d, so my understanding is that I need ...
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Covariance of assets with different probabilities for each scenario.

There are three assets given and for each asset there are three scenarios with their respective probabilities. Asset 1: $$\begin{array}{c|c|c|} & \text{Return} & \text{Probability} \\ \...
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Ordinal scrambling quantification upon placing and retrieving labeled spheres to and from a cylindrical container.

Trying to derive a formula to quantify the degree to which objects in an original order are scrambled upon some amount of repeated random handling. Say there are $n$ spheres labeled with labels $1$ ...
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What is the name of this Correlation matrix?

$ \left[ {\begin{array}{cc} 1 & p & p^{2} & ... & p^{n}\\ p & 1 & p & ... & p^{n-1}\\ p^{2}&p&1&...&p^{n-2}\\ ...\\ p^n&p^{n-1}&...&...
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Does a square root matrix of a circulant correlation matrix with positive entries also have all positive entries?

I have a circulant correlation matrix that has only positive entries. (Because it is a correlation matrix, it is symmetric with diagonal entries of 1.) I am wondering about the entries of the square ...
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Bound for type of correlation measure

Assume you have a finite, discrete probability distribution for a joint random variable and such that $P(X=i,Y=j) = p_{i,j}$ for $i \in \{1, \dots, |X|\},j \in \{1, \dots, |Y|\}$. The marginal ...
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Cross correlation coefficient for 2 matrices (two 2d arrays)

I'm trying to manually calculate cross correlation coefficient for 2 matrices. But I'm not sure how to apply the formula and how it works. Here are my example matrices: Matrix 1 Matrix 2 Any help ...
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Correlation between 2 signals of uneven dimensions

As a part of my work, I am trying to correlate the audio signal in a video with the pixels of each frame. The steps I follow are: 1] Audio sampling rate and frame rate of the video are known. So, ...