# Questions tagged [correlation]

For questions about correlation of two random variables. Correlation is a statistical technique that can show whether and how strongly pairs of variables are related. Use it with [tag: random-variables] and [tag: probability].

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### Completing a positive semidefinite matrix; filling in the blanks

I have a (very) partially known correlation matrix. Is there an easy way to fill in the blanks and get a) the/a positive semidefinite matrix with the maximal sum of the covariances, and b) the/a ...
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### How does r and $r^{2}$ both describe the strength of correlations of variables? [closed]

I am currently going through Witte Statistics 11th edition and have come to an error in either the book or my understanding. Earlier in the book it says r gives the strength of correlations and $r^{2}$...
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### Is there a general method for generating correlated random variables from independent random variables?

For generating correlated normal random variables from independent normals, I know that you can use Cholesky/SVD. Is there a general method that applies for other random variables, e.g., uniformly ...
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Suppose $X, Y, Z$ have mean zero and variance $1$. The correlation between each pair of random variables is $\rho$. What is the range of $\rho$. I have solve this problem in several ways: (1) $$E[(X^... 0answers 14 views ### Prove the equations for variance over the conditional-expectation If a = \frac{cov(X,Y)}{var(Y)} and b = E(Y) - \frac{cov(X,Y)}{var(X)}\cdot E(X) prove the equation: \frac{var(E(Y|X))}{var(Y)} = (corr(X,Y))^2 For the general case of E(Y|X) prove: \frac{var(E(... 0answers 9 views ### Relationship between conditional probability and co-occurrence and cross correlation What is the relationship between conditional probability and co-occurrence and cross correlation? I have this example dataset of daily number of occurrences of events A and B: A alone = 100 B alone = ... 1answer 43 views ### Given the following joint density function; find the expectation of h(x,y)=2x+5y Let f(x,y) = c(2x+y) ; 0<x<2; and 0<y<3 and 0 otherwise Calculate: (i) Value of c (ii) Obtain Marginal PDF's of both X and Y (iii) find the expectation of h(x,y)=2x+5y... 0answers 12 views ### Is there a range or minimum value of correlation dimension to determine chaotic or not? I am trying to understand how to test if an observed time series is chaotic or not. Matlab's correlation dimension is one such test. However, reading the papers and the documentation it is not clear ... 0answers 22 views ### Finding the correlation function of the output process at zero and checking if it is WSS Assume two systems for which the following differential equations hold between their input and output signals.$$a \dfrac{dv(t)}{dt}+b v(t)=x(t)\dfrac{dy(t)}{dt}=v(t)u(t)$$Also, assume that the ... 1answer 27 views ### Two correlated AR(1) series [closed] I have two AR(1) series that are correlated.$$X_{t,1} = \rho_1X_{t-1,1} + e_{t,1}X_{t,2} = \rho_2X_{t-1,2} + e_{t,2}$$and corr(X_{t,1}, X_{t,2}) = \rho. I want to generate at each time t a ... 1answer 50 views ### Correlation between union of correlated Bernoulli processes Let X_{1,1},X_{1,2},X_{2,1},X_{2,2} be identically distributed r.v.s with distribution \sim Be(p) and equally par-wise correlated, with pair-wise Pearson correlation coefficient \rho, e.g. Corr[... 1answer 16 views ### Correlation between 2 independent Brownian motions I have been playing with some Brownian motion simulations (Euler scheme), when I discovered some strange behavior. When simulation 2 classical Brownian motions, the (Pearson) correlation between them ... 0answers 58 views ### Dudley's integral convergence for stationary gaussian process I am now studying "Gaussian processes" course at my university and i've faced a difficult problem for me: Imagine we have a Gaussian stationary process with expectation equal to zero, ... 1answer 15 views ### Is a pearson correlation matrix Symmetric Positive Definite? Let's suppose I have a table of size m x n. Is a correlation matrix SPD? Why / Why not? (By correlation matrix I mean a matrix M of size mxm where M(i,j) = Pearson correlation between i-th column and ... 2answers 31 views ### Probability that random set is in an up-set? Let X be a finite ground set and \mathcal{A}\subset \mathcal{P}(X) be an up-set. That is, a family of sets such that if A \in \mathcal{A} and A \subseteq B, then B\in \mathcal{A}. Now let ... 0answers 29 views ### Why is the scatter plot of two uncorrelated random variables in circle shape? I am trying to understand why the scatter plot of two random variables X_1 and X_2 is in a circle shape when corr(X,Y)=0. Is there any intuitive explanation for this? 0answers 15 views ### Consider n random variables with the same pairwise correlation \rho. What is the range of \rho? Correlation coefficient can be interpreted as the cosine of the angle, \theta between the centered random variables in a vector space. When \cos \theta = \rho = 1, we have \theta = 0. When \cos ... 0answers 24 views ### How good do two datasets agree? Short story: I have two vectors (random variables) A and B and want to compute how much they agree. Each entry is either 1 or 0. I would like to compare how often they agree to how often we would ... 1answer 14 views ### Why square of pearson correlation does not match with r2 score? As per link of correlation and R2 , it is mathematically shown that square of pearson correlation is equal to r2. However, I am trying to replicate these results with my data in python and I do not ... 2answers 65 views ### Correlation Coefficient of two Order Statistics [duplicate] My problem is exactly the same as asked in here with a change in the notation of the two order statistics. Reframing the question: If \left(X_1,X_2,…,X_n\right) are a random sample from Uniform(0,1)... 1answer 49 views ### If \mathbb{E}(X_n)=\mu and \mbox{var}(X_n)=\sigma^2, show that the correlation between X_n and X_m converges to 1 as m,n\rightarrow\infty. a) Let (X_n : n \ge 1) be a sequence of random variables which converges in mean square. Show that \mathbb{E}([X_n-X_m]^2)\rightarrow 0 as m,n\rightarrow \infty. b) If \mathbb{E}(X_n)=\mu and ... 0answers 21 views ### Why is there no change to the correlation coefficient and gradient? For the question below, I know there is no change to the Pearson product-moment correlation coefficient after the x values increase by 5 and the y values decrease by 4, and I know that the ... 1answer 27 views ### Correlation of IID normal RV's If we know that corr(X,Y)=\rho and Y,Z are independent and also X,Y,Z\sim N(0,1) then can we deduce anything about corr(X,Z)? 1answer 13 views ### How to calculate a sports team cohesion by how often a team plays together I’m not sure where to start with this so here goes: I’m researching cohesion within a team environment. Using soccer as an example. There are 20 teams in a league. Each team has a squad of 30 players ... 0answers 10 views ### Correlations estimator is invariant by space and location I need to check that Is invariant by space and location. Do not even know where or how to start exactly. 0answers 7 views ### Can correlation of two merged dataset be bigger than correlation of each? if I have data set (x1, y1) with 500 data points and correlation 0.05 and (x2,y2) with the same number of data points and correlation, can cor(x,y) = 0.1 where x and y are result of union of two ... 0answers 11 views ### Is it correct to compute the coefficient of correlation from fiducials/mean into Fisher's formalism A simple question : In a Fisher's formalism context, I have to know the correlation coefficient \rho_{xy} of 2 random variables X and Y. My code generates 5 values for \sigma_x and \sigma_y :... 0answers 13 views ### Sum of squares of errors identity through correlation coefficient Let X  and  Y  be random variables with standard deviations \sigma_X  and \sigma_Y. Consider the linear model Y_i=\beta_0+\beta_1 x_i +\epsilon_i where \epsilon~N(0,\sigma). If the ... 1answer 19 views ### Finding correlation between U and W Two investments X and Y give returns as follows (expectation and variance): E(X)=0.5,E(Y)=0.4 and V(X)=2, V(Y)=1. The correlation between X and Y is ρ (X,Y) = 0.6. (a) Find the ... 0answers 51 views ### Expression of multiple covariance terms in the Delta method for a 2D function I am looking for the expression of variance of a 2D function which is is actually f(x,y) =\dfrac{x}{y}. Let's do a Taylor expansion for the 2 function of 2 variables X and Y :$$ \begin{array}{c}...
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I have a set of test scores with X being test #1 and Y being test #2. After doing all the calculations to find the correlation I got .35 (which I know is correct). The question is what is the ...
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### Independence between $2$ Pearson Correlation Coefficients

Suppose that $X_1, X_2, Y$ are three scalar Gaussian distributed variables. Suppose we know that $X_1$ independent from $X_2$. However, $X_1, Y$ could be correlated. Similarly, $X_2, Y$ could be ...
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### Covariance/Correlations between circular and linear random variables?

Assume that I have $N$ samples $(x_1,\theta_1),...,(x_N,\theta_N)$ from two scalar random variables $X$ and $\Theta$, where $X$ is defined on a linear space, and $\Theta$ is defined on a circular ...
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### Squared of series containing delta function

In spectral density theorem we often found spectral density in a form of series with delta function $$J(\omega)=\sum_{k=0}^\infty \frac{c_k^2}{m_k \omega_k}\delta(\omega-\omega_k)$$ If I want to ...
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### Real-world example where two positively correlated pairs (X, Y ) and (Y, Z) of random variables give a negative correlation for (X,Z).

Let X, Y and Z be random variables with finite means and finite variances. Suppose that the correlations ρ(X, Y ) and ρ(Y, Z) have unspecified positive values. Then without additional information on ...
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### Calculate $\text{Cov}(\, \, \mid X\mid \, \, , \, \, \mid Y\mid \, \, )$ where $X$ and $Y$ are jointly normal

Let two random variables $X$ and $Y$ are jointly normal as follows: \begin{eqnarray} \left( \begin{array}{c} X \\ Y \end{array} \right) \sim \text{Normal} \left( \left( \begin{array}{c} \mu_x \\ \...
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### Normally distributed and uncorrelated does not imply independent wiki page

In https://en.wikipedia.org/wiki/Normally_distributed_and_uncorrelated_does_not_imply_independent, it states To say that the pair $(X,Y)$ of random variables has a bivariate normal distribution means ...
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### Wiener-Khinchin theorem and fluctuations in flicker noise

Suppose that we have a flicker noise process, that takes values $d(t)\in\{-1,+1\}$. We discretize time into $t\in[0,dt,2dt,\ldots, (N-1)dt]$, and $dt = T/N$ with $T$ being the total length of the '...