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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How to prove this relation for Kendall's distribution function (or Kendall's measure)

Kendall Distribution Function (Nelsen, 2006, p. 163) Or Kendall Measure (Salvadori et al., 2007, p. 148) Or Kendall Function (Joe, 2014, pp. 419–422) is the cumulative distribution function (CDF) of ...
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What is the expectation of $R^2$ for for iid $y, x_1, ... x_k \sim N(0,1)$

$Y, X_1, ...., X_k$ are all iid $N(0,1)$ with $n$ samples. I can't make any progress on this problem... I don't even know an approximation but from simulation it seems to be $k/n$. What is the ...
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Formula for jointly correlated variables

I've always seen the following expression for normal correlated variables which is considered quite basic: $$A=\rho Z+\sqrt{1-\rho^2}\epsilon$$ I understand that it follows ...
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Proportion of variance in a linear regression model with a covaring predictor

Given a model: \begin{align}Y_{i}=Z_{i}*\beta * X_{i} + Z_{i}\tag{Eq. 1}&\end{align} I am interested in a closed formula for the proportion of variance explained by the predictor variable $X$, ...
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Correlation vs Regression for a simple task

Hello everyone and thank you for taking the time with my issue! I want to apologize in advance if my question would've fit better on stack exchange, but I decided that the question is more related to ...
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Why is the autocorrelation of an uncorrelated random noise process the dirac delta distribution?

I am reading Stochastic Methods by Gardiner and in the beginning of chapter 4 he motivates the rigorous interpretation of a Stochastic Differential equation by describing the properties of a "...
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Which Test to Find a Correlation Between Two Selections.

I have a dataset of about 22 000 items, from which two processes have selected a small subset. I want to know if there is a correlation between the two selections, and I wonder which statistical test ...
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Using Orthogonal Decomposition of Bivariate Normally Distributed X,Y Reveals Different Result Than Calculating Variance Directly

This is the exercise description: 6.5.4. Suppose X and Y are standard normal variables. Find an expression for P(X + 2Y ≤ 3) in terms of the standard normal distribution function Φ, (a) in case X and ...
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Understanding correlation in the context of a time series, simulation and brownian motion

I have the doubt of calulating and meaning of correlation. I know it is from my incapacity to grasp a concept, specially regarding time series but would appreciate any comments on it. I think I ...
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What is the intuitive difference between covariance and the product of the standard deviations of bivariate data?

Can someone help me understand what the difference is—intuitively—between these concepts? Here's how I currently think of these things. The covariance, represented by: ... is essentially a mean area, ...
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