# 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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### Sampling from a Poisson distribution

I am currently working on a thesis for my final year and am stuck with a problem involving the poisson process. I was wondering if someone could help me with it. I am trying to simulate a one ...
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### If a correlation matrix is a band matrix with value 1 on the band, is this equivalent to correlation matrix with all 1?

Say I have a stationary sequence ${x_1,x_2,\cdots,x_n}$ and if two elements of the sequence are less than or $m$ apart from each other, we say they are correlated. This is called an m-dependent ...
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### Time series analysis on ACF and PACF plots

So I have a non stationary time series that is hourly, daily and monthly recorded for a year and I have the ACF and PACF plots for the serie. ACF and PACF I applied the the Ljung-Box test and for ...
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### If there is a high correlation between two variables, should we expect the high linear regression coefficient? [closed]

I have a data set with multiple features, let suppose $x_1,x_2,x_3,x_4$ and my dependent variable is $y$, when I compute the correlation matrix for $y,x_1,x_2,x_3,x_4$ then imagine the correlation ...
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### "Leave-on-out Correlation" between Matrices

I'd like to enforce a special constraint in my optimization problem. The solution to my problem is a set of matrices $Q_1, ..., Q_N \in \mathbb{R}^{G \times K}$ and I'd like to make sure that: For ...
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### Practical correlation metric for a large number of vectors

I am dealing with a timeseries consisting of input flow sampled every 5 minutes over 441 days. My aim is to find any possible correlation from data coming from: The same day of the week The same ...
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### Autocorrelation of a random process

Let X be a random process. X(t) = A*Cos(wt+θ) ; where A and w are constants. The only random thing is θ. Lets say θ has a probability density function, f(θ)= 1/2pi for 0<θ<2pi and zero elsewhere....
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### Can the chi-square statistic in Kruskal-Wallis test be compared to determine the most appropriate to distinguish the groups?

I have a dataframe in R which format is similar as follows: v1 v2 v3 group 1 3.5 100 a 3 5 200 a 10 5.5 150 b 8 7.5 210 b 4 4.5 300 c 9 2.5 200 c ... My ...
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### Maximum number of random variables to make pairwise correlation coefficient less than C

Assuming N random variables $X_1, X_2, ..., X_N$, each has $m$ samples, (e.g. $m=3$). what is the maximum N such that all pairwise sample correlation coefficients $\rho_{X_i, X_j}$ are less than some ...
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### Hypothesis testing on sample mean when observation are correlated

How can I test whether the mean of a sample is significantly larger than the population mean, when observations are not independent, but the exact correlation matrix is known? I have a variable $X$ ...
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### Let $X,Y,Z$ be three random variables such that the correlation coefficients $\rho_{XY}=0.2, \rho_{YZ}=0.2$, what values can $\rho_{XZ}$ take?

Let $(X,Y,Z)^T$ be jointly normal variable with zero mean such that the correlation coefficients $\rho_{XY}=0.2, \rho_{YZ}=0.2$, what values can $\rho_{XZ}$ take? Prove that there exists a ...
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### Can I subtract a correlation factor from another correlation factor to remove noise?

I’m trying to understand how spending on digital advertising affects things like first installs of a product. I have many channels where spending has occurred, but all with wildly different amounts. ...
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### Intuition of R-squared in a quantile

I assume, R-squared (correlation of determination) can be used as a measure of the goodness-of-fit in a quantile plot (QQ-plot). In a QQ-plot we measure between empirical quantiles (the ranked sample) ...
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### time-shifted signals correlation

imagine you have the 2 following signals: s=[0,0,0,1,1,1,0,0,0,3,3,3,0,0,0] p=[1,1,1] The correlations for each shift (considering only lags for which the shifted ...
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### How general is this property about correlation and the sum of two normal RVs?

Edited to make this more concrete: Given a random vector $(X_1,X_2)$ that is jointly normal with means / sd's $\mu_1,\mu_2, \sigma_1,\sigma_2$ and correlation $\rho$, the sum of $S=X_1+X_2$ is ...
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### Auto correlation

Consider the signal x(t)=u(t) where u(t)=1(t≥0), i.e. the Heaviside function. Find the signal y(t)=x(t)∗x(−t) My attempt: y(t)=x(t)∗x(−t) =u(t)∗u(−t) =∫∞−∞[u(τ)][u(−t+τ)] dτ since u(τ) exists from 0 ...
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### Maximal Correlation of two random variables

I am trying to wrap my head around one problem that involves two identically distributed random variables $X$ and $Y$ with distribution $Bernoulli(p)$ assuming that $P(X=Y=1)=\theta$. It then asks a ...
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### Intraclass correlation: Separating intra-rater variability from inter-examination variability.

I have a question regarding Intra-class correlation. Suppose we have 2 MRI-scans (2 trials) made on each of $n$ subjects (on the same MRI-scanner). All MRI-scans are analyzed by the same rater. The ...
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### Is there a matrix algebra equivalent of finding the cross correlation between two vectors?

To calculate the cross correlation of two vectors we slide the vectors over each other multiply the corresponding elements and sum them. This is an example for two length 8 vectors giving a length 15 ...
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### Indepedent copy of Bivariate Normal

In this question, Correlated joint normal distribution: calculating a probability Most upvoted answer obtained independent copy using this equation, $\pmatrix{U\\V}=\Sigma^{-1/2} \pmatrix{X\\Y}$. I ...
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### correlation and covariance of two random variables

I have two continuous random variable X and Y. In U- shape region we have $P_{XY}(X,Y)=\frac{1}{12}$ in other regions we have $P_{XY}(X,Y)=0$. How the correlation and covariance of these two variable ...
1 vote
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### Based on multiple daily weather observations, how can I calculate the "most similar" day to any other given day?

This is definitely a case of "not even sure how to ask the question," but I am wondering if there is math available to solve a problem I have. I have several years of daily weather ...
1 vote
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### Inequality of fourier transform for $L^2$ functions

Suppose $f,g$ are $L^2$ functions over $\mathbb R$ such that $\|f\|^2\ge \|g\|^2$ and for any $y\in \mathbb R$, $$\int_{\mathbb R} f(x) \overline{g(x-y)} dx = 0.$$ If $F,G$ are their respective ...
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### Correlations in implementations of random unitary channels

A random unitary channel (RUC) acting on a quantum system $S$ is any completely positive and trace preserving (CPTP) linear map $\mathcal{E}$ that can be expressed as \begin{align} \mathcal{E}(\...
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### Uniform lower bound of the inner product of two positively correlated random variables

Suppose $W$ is a mean-zero random variable with unit variance, i.e., $E(W)=0,Var(W)=1$. Let $g(\cdot)$ be a non-constant increacing function such that $g(W)$ has zero mean and variance $\epsilon>0$,...
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Suppose $\bar{U}$ and $\bar{V}$ are sample means from a highly correlated or highly dependent random process (e.g., waiting times from a queueing process) That is, let  \bar{U} = \frac{1}{n}\left(...