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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21 views

What is the intuition behind a Frobenius norm?

I am reading up on how to find the closest correlation matrix and they approach it by minimizing a weighted Frobenius norm. Now I am trying to understand the intuition as to why they use this. Let's ...
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33 views

Why does the cross-correlation of a sine wave with white noise also show harmonic properties?

If we find the cross-correlation of a sine wave with a white noise process, why does the resulting signal also show harmonic properties with the same frequency as the input sine wave? I would have ...
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Error of prediction from the required line of regression

The error of prediction of x from the required line of regression is $n\sigma^2_x(1-\rho^2)$ This is given in my reference without any further explanation. What does this realy mean and how do we ...
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find the correlation coefficient of two random variables after the same function transformation

we have two random variables: U1 and U2 follow uniform distribution between 0 and 1: U1 ~ U(0,1), U2 ~ U(0,1) and correlation: corr(U1,U2) = ρ covariance : cov(U1,U2) = corr(U1,U2)/12 Then we do ...
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13 views

Correlation between a linear function of a matrix and a concave function of the matrix

Suppose we have two functions, $f,g:\sf{R}^{n \times n} \to \sf R$, i.e. a mapping between matrices of dimension of $n$ times $n$ and a real number. Here we can assume that the matrices are symmetric ...
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joint pdf and solve correlation

Click here please I don't know how to solve this problem. How can I get correlation of X and Y?
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30 views

When mean corrected matrix $X_c = UΛV^T$, how to use this singular value decomposition to prove its three spatial properties?

We use the singular value decomposition on a mean corrected data matrix. $X_c = \begin{bmatrix}(x_1-x̄)^T\\(x_2-x̄)^T\\⋮\\(x_n-x̄)^T\end{bmatrix} = UΛV^T$, Let $\sqrt{n-1}U = (\dfrac{x_c\hat{e_1}}{\...
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Eigen Vector Method Vs Correlation-Free Coordinates Transformation Method

It is fair to say that eigen-vector problem transforms the original problem to uncorrelated state. According to the following, figure the transformation to new coordinates system is done using sines ...
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How to quantify group-level significance of circular-linear association?

I am working on an analysis of EEG recorded during task performance, and I am interested in how the power and phase of ongoing oscillations are related to stimulus qualities. Within each subject, I ...
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12 views

How to determine if variables have significant impact on binary outcome?

I have the following dataset with discrete, boolean, and categorical variables : ...
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5 views

Difference Between Two Methods of Calculating Spearman's Rank-Order Correlation

According to this site, there are two methods to calculate Spearman's correlation depending on whether: (1) your data does not have tied ranks or (2) your data has tied ranks. The formula for when ...
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40 views

RVs that are uncorrelated but not independent

Given that $X\sim N(0,1)$, $Z\sim Unif(\{\pm 1\})$, and $Y=XZ$. $Z$ is independent of $X$. After calculation we found that $Y\sim N(0,1)$. Show that X and Y are uncorrelated but not independent. I ...
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Calculate the Probability of 2 Negatively Correlated Outcomes

How does one calculate the probabilities of 2 outcomes that are negatively correlated (A happens and B happens, A happens and B doesn't happen, B happens and A doesn't happen, neither A or B happen)? ...
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33 views

problem finding the Variance of dependent variables using covariance and correlation

Hello I have been trying to figure out this question for a few hours and I am very stuck and don't know how to progress but I am pretty sure I am wrong and would greatly appreciate some help. $X$~$N(\...
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What does the multiplication mean in this context?

I am trying to understand the intuition behind using multiplication, especially for the context of calculating things like the covariance, correlation, R-squared, etc. for example, I know that, in ...
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Finding autocorrelation of a random process.

The autocorrelation of a random process $X(t)$ is given by \begin{align} R_{XX}(t_1,t_2) = \langle X(t_1) X(t_2) \rangle = \lim_{N\rightarrow \infty} \frac{1}{N} \sum_{i=1}^N X^{(i)}(t_1) X^{(i)}(t_2),...
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Auto correlation of a cosine signal

I have to find the autocorrelation of $ x(t) = A cos ( 2\pi f_0 t) $ , and I know from theory that I should calculate $ lim_{x \rightarrow \infty } \frac{A^{2}}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} ...
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How can I evaluate the arg min/argmin of a sequence in Simulink/real-time?

I am wondering whether someone could give me some hints on how to evaluate/implement the math function arg min/argmin in Simulink. Let's say that I have the following expression $$ \hat{y_{16}}:\...
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Shall Box-Jenkins function return 1 for tau=1? Why an implementation returns some error?

I have the following 50 samples time-series: ...
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Is it needed to normalize time series to calculate correlation?

Let $x$ and $y$ be two time series and I would like to analyse if they are correlated or not. So far I have found that the following formula can be used to determine the correlation. $$corr(x,y) = \...
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How can I compute the correlation coefficient iteratively?

I'd like to compute the Pearson Correlation Coefficient (PCC) on-line i.e, deriving the PCC for n samples, then updating it with observation n+1.
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28 views

What is correct ranking for Spearman Correlation?

In order to calculate Spearman Correlation Coefficient, the data should be ranked. However, many people do this in different way. Some sort them like an increasing sequence (i.e the smallest number ...
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Sample correlation coefficient of i.i.d Cauchy variables

Let $X_1,X_2, \dots, X_n, \dots$ be i.i.d Cauchy random variables, and let $Y_1,\dots, Y_n,\dots$ be i.i.d Cauchy random variables independent of the $X_i$'s. Let $\rho_n$ be the sample correlation ...
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Relation between correlation and the inner product

I saw in several places in the numerical linear algebra that the inner product is interpreted as the correlation. However, I don't see why they do it. Please, can you explain to me what is the ...
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14 views

How to generate two dimension normal distribution with given parameters?

I want to generate a two dimensional normal distribution, given two variance number and correlation coefficent.
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20 views

Differentiability and Continuity in Exponential-Gauss Covariance Functions

Updated: In the Exponential-Gauss covariance function: $$ R(\theta_k;d_{ij}^k)=\exp(-\theta_k|d_{ij}^k|^h) $$ where $0<h \leq 2$, what can we say about differentiability and continuity of this ...
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Correlation of Parameters

I have six parameters and I want to do correlation analysis between this 6 parameters.In general, the result I want to achieve should be as follows.I find this formula but I do not understand how to ...
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Confusion regarding number of pairs (N) when calculating P-value from Pearson (R) calculator

I am doing a little education research at my school and am trying to analyze the data using the Pearson (R) calculator. I am looking for a (negative) correlation between the length of the assignment ...
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What does $cov(x_1,x_2) >> 0, cov(y_1, y_2) >> 0$ and $cov(x_1+y_1, x_2+y_2) = 0$ tell us about $x_1, x_2, y_1, y_2$?

I was posed this problem where we know: $$ cov(x_1,x_2) >> 0 \\ cov(y_1, y_2) >> 0 \\ cov(x_1+y_1, x_2+y_2) = 0 \\ $$ What does this tell us about the structure of $x_1, x_2, y_1, y_2$? ...
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Estimating correlation

Say I have a mathematical model specified by: $X_i = r_i S + \sqrt{(1-r_i^2)} \epsilon_i$ where $S$ is random variable distributed as $N(0,1)$, where $\epsilon_i$ is random variable distributed as ...
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38 views

Meaning of $\lor$ and $\land$ [duplicate]

What is the meaning of $\lor$ and $\land$ in the following function:$$\phi(x):= (x\land1)\lor(-1)$$ To give a little context, this should be a bounded transformation to bound a correlation estimator ...
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19 views

Weighted sum of two normally distributed random variables incorporating correlation

I am currently looking into a financial model that has two random variables which are normally distributed. $X \sim N(0,1)$ $Y \sim N(0,1)$ The aim of the model is to create a third variable $Z$ ...
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How to calculate the autocorrelation function

I tried to do it but I obtain parts like: $$\int _{-\infty }^{\infty }cos\left[2\left(nw_0+\theta \right)\right]dn$$, that I supposed it has no sense because $$cos[2(nw_0+\theta)]$$ is oscillant...
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Correlation of multiple variables.

I'm struggling with severe skin allergy. This is not a question about medical advice. I'm under a constant care of a certified doctor, but we're at loss, so I'm diversifying our investigation :) I ...
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61 views

Does zero correlation imply mean independence in at least one direction?

Any example of two random variables $X$ and $Y$ with correlation $\rho(X,Y)=0$ seems to satisfy that either $X$ is mean independent of $Y$, $\mathbb{E}[Y\mid X]=E[Y]$, or vice versa, $\mathbb{E}[X\mid ...
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41 views

Correlation Function of Squared Standard Wiener Process

I'm trying to find the mean and correlation functions of $ X_t:=W_t^2 $, where $W_t$ is a standard Wiener process ($\sigma=1,E\{W_t^2\}=t$ for $t\geq 0$). Unless I'm missing something large here, the ...
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25 views

Need help for an explanation for correlation coefficient.

Let $X$ and $Y$ be two (continuous) random variables with the joint p.d.f $$f(x,y)=\dfrac{1}{4ah};\quad\text{for }-a+bx<y<a+bx,-h<x<h,\\ \text{and } f(x,y)=0;\quad\text{elsewhere. }$$ ...
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How (or which) filter methods we can use to check if thete is no direct relationship between features and target

one approach of feature selection is filter method. In this method we check 2 things: relation between feature i and target. we want to preserve only features that influence the target relation ...
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When to use continuity correction in estimating Kendall's tau correlation.

I understand that continuity correction is used when a discrete distribution (e.g. binomial distribution) is approximated by a continuous distribution (e.g. Normal approximation). I am using Kendall’s ...
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Attainable correlation bounds of two log-normal random variables

McNeill et al. (2015) mention that the attainable correlation for two lognormal random variables are not between 1 and -1 as they are not of the same type. Now I was wondering since the minimum ...
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27 views

How to find the coefficient of correlation

This question was appeared in my practice test last week and i was bit confused about it, how to approach this question as a whole. Q. If a linear relation $𝑎𝑋 + 𝑏𝑌 + 𝑐 = 0$ exists between the ...
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Three markov tree to represent the dependence mixture

I am having the following problem: Consider variables $X_1, X_2, X_3$ with joint normal distribution with standard normal margins which are equicorrelated (all correlations are equal to$\rho \in (0,1)...
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25 views

Proving that two RVs are uncorrelated

(See also related question here) Let $\omega\in (0,1]$ be represented in binary as $\omega=0.d_1(\omega)d_2(\omega)\cdots$ where each $d_i(\omega)$ is either $0$ or $1$ (a tail of zeros is prohibited)...
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PACF of stationary process with Gaussian distribution?

According to these slides (page 24) a WSS process with Gaussian distribution has a PACF which is a conditional correlation: $$\phi_{hh} = corr(X_t-\hat X_t, X_{t+h} - \hat X_{t+h}) =corr(X_t, X_{t+h}|...
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21 views

Marginal Density Correlation

I was given a function $f(x,y)=1120x^{3}y^{3}$ for $0\leq x, 0\leq y, $ and $ x+y \leq 1$ I went ahead and calculated the marginal PDF's for X and Y $f_{X}(x) = \int_{-\infty}^{\infty} f_{x,y}(x,y)$...
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How to assign single numeric value to a time series data, which denotes trend in a time-series data?

I am working with time-series data and I need to determine whether data is upward sloping or downward sloping. The value of 1 would indicate data is upward sloping and the value of -1 would indicate ...
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36 views

Pearson's correlation formula - intuition behind the definition of the formula.

$$ r = \frac{ \sum z_x z_y }{n-1}\,, $$ where $$z_x = \frac{x_i - \bar{x}}{\sigma_x}$$ and $$z_y = \frac{y_i - \bar{y}}{\sigma_y}$$ I came across the above formula for correlation when reading a ...
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Cumulant of sum of correlated random variables?

Let $X,Y$ be two random variables. We denote by $[X^k]$ and $[Y^k]$ the $k$'th order cumulants of $X$ and $Y$, respectively. I'm interested in computing the $k$'th order cumulant of $Z = X+Y$. If $X,...
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39 views

Homework Problem: Finding the Covariance and the correlation

I have an idea on how to start the problem and that's with finding the expectation of X and Y and then apply the formula of Covariance but I'm not sure since it is a biased coin. Any help would be ...
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1answer
44 views

Find the correlation Corr[X,Y] from the joint pdf

The joint pdf is as follows: $f(x,y) = 5040x^3y^5$ ($0≤x, 0≤y, x+y≤1$) I have worked out: $f_{X}(x)=840x^3(1-x)^6$ for ($0≤x≤1$) $f_{Y}(y)=1260(1-y)^4y^5$ for ($0≤y≤1$) However, when working out ...

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