# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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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$\rho \in (0,1)... 1answer 25 views ### Proving that two RVs are uncorrelated (See also related question here) Let$\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)... 0answers 15 views ### 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: $$\phi_{hh} = corr(X_t-\hat X_t, X_{t+h} - \hat X_{t+h}) =corr(X_t, X_{t+h}|... 1answer 21 views ### Marginal Density Correlation I was given a function f(x,y)=1120x^{3}y^{3} for 0\leq x, 0\leq y, and x+y \leq 1 I went ahead and calculated the marginal PDF's for X and Y f_{X}(x) = \int_{-\infty}^{\infty} f_{x,y}(x,y)... 0answers 13 views ### How to assign single numeric value to a time series data, which denotes trend in a time-series data? I am working with time-series data and I need to determine whether data is upward sloping or downward sloping. The value of 1 would indicate data is upward sloping and the value of -1 would indicate ... 2answers 36 views ### Pearson's correlation formula - intuition behind the definition of the formula.$$ 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 ... 0answers 16 views ### 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,...
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 ...