For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].

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1answer
27 views

Distinction between correlation coefficient and coefficient of determination

In my stats class, I am learning about correlation coefficient and coefficient of determination. I dont understand what the difference is between them. there are $r,\,$ $r^2$ and $R^2$. $r^2$ and ...
1
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1answer
17 views

Correlation between a random variable and its rank

Let $X_1,\ldots,X_n$ be a random sample from $U(0,1)$ and $X_{(1)}<\ldots<X_{(n)}$ be the corresponding order statistics. Define, $$ R(X_1) = r\quad \text{if}\quad X_{(r)} = X_1;\quad r = ...
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2answers
38 views

Generate two negatively correlated data in excel

Let's say that we have two prices that are negatively correlated to each other, for instance we have price $p_1$ and we want to generate negatively correlated price $p_2$ with the following ...
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0answers
29 views

Determining whether or not random variables are correlated

I'm working on the following problem: Consider random variables $X$ and $Y$ such that exactly one of them is equal to $0$. The other then takes the value $1$ or $-1$ with equal probability ...
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0answers
8 views

zipf and lognormal with a particular correlation

I have been struggling on how to generate a correlated zipf and lognormal distribution. I want to generate a set of data ,say,$(X,Y)$,where $X$ is the popularity of file described by ...
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1answer
19 views

Assess two matrixes overlapping

I have two binary matrixes, of the same size (e.j. 5000x5000). Those matrixes represent the same area, divided in cells of the same size. Each cell of one matrix can be true or false, meaning some ...
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0answers
12 views

Calculating the coefficient of concordance for vague data

I'm trying to adapt a formula that calculates the coefficient of concordance for vague data. The paper that describes it is here ...
2
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1answer
37 views

Necessary sufficient condition for correlation between last 2 out of 3 normal random variables.

Consider $X,Y,Z$ all standard normal random variables. Now I also want to have some correlation between them. Lets denote these $\rho_{XY},\rho_{YZ}$ and $\rho_{XZ}$. Surely I cannot choose them ...
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2answers
63 views

question about correlation of variables

Here is an interview question I had and cannot figure out how to solve it. Any hint? Let $X$, $Y$, $Z$ be 3 random variables such that $\mathsf{Corr}(X, Y)=0.9$ and $\mathsf{Corr}(Y, Z)=0.8$. What ...
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0answers
31 views

What do the eigenvalues of a correlation matrix represent?

I was wondering if there was any special meaning to the eigenvalues/eigenvectors of a correlation matrix. I get what they mean in a covariance matrix, and how that relates to PCA, though. Can you do ...
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0answers
35 views

Meaning of horizontal bar in old formula (paranthesis?)

When reading an old paper from 1921* I find formulas like: $\rho + \frac{\rho(1- \rho^2)}{2\overline{n - 1}} \big( 1+ \frac{9 - 14\rho^2}{6\overline{n-1}} \big)$ which is said to be the median of ...
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1answer
33 views

Correlation between $X\cdot W$ and $Z$ ($Z$ and $W$ are independent)

I have quite a tricky question about correlation. Suppose that there are three random variables $X$, $W$ and $Z$. $X$ and $W$ are correlated and $X$ and $Z$ are also correlated. But, $W$ and $Z$ are ...
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1answer
18 views

Why is $Y$ and linear function of $X$ if the correlation equals $+1$ or $-1$?

Just looking for a proof of $\operatorname{Cor}(X,Y) = \begin{cases} +1 & \text{if } a>0, \\ -1 & \text{if } a<0, \end{cases}$ where $X$ and $Y$ are random variables such that $Y=aX+b$ ...
2
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1answer
27 views

Calculate $P[A,B,C]$ from $P[A,B]$ and $P[B,C]$

I have 3 (not independent) events $A, B, C$ and I know everything about how any two of them correlate. For example, I know: $$ P[A], P[B], P[C], P[A,B], P[A,C], P[B,C], P[A|B], P[A|C], P[B|C], ...
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0answers
28 views

Implementing Normalized Cross-Correlation using FFT - How to?

Is there any way to calculate the normalized cross correlation between 2 signals by using the FFT? (I managed to implement it already for standard cross correlation equation). Thanks in advance,
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0answers
17 views

Modelling Correlation between CAC and DAX index

I am working on the implementation of a Garch-copula model ("Patton" approach who did it on exchange rate) to model the correlation between these two index. It is implemented now. Basically, you first ...
1
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2answers
22 views

Let $X = -10Y + 10$. Let $r_1$ be the correlation between $X$ and $Z$ and $r_2$ be the correlation between $Y$ and $Z$.

Let $X = -10Y + 10$. Let $r_1$ be the correlation between $X$ and $Z$ and $r_2$ be the correlation between $Y$ and $Z$. Then, which of the following is the best answer? $r_1 = r_2$. $r_1 = 10r_2$ ...
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2answers
62 views

Covariance/Correlation Proof

I'm having a little problem with a statistics problem I am working on. I'm not really sure where to start to prove the two statements. Any help would be greatly appreciated. Let $x$ and $y$ be ...
1
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1answer
48 views

The mathematics of Correlation is not equal to Causation

In statistics, it is a common practice to say that "correlation does not mean causation", and mostly the proof for this is given by examples. While that is good for the intuition, it's not rigorous. ...
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0answers
30 views

Proof that space of correlation matrices is compact

An $n\times n$ real symmetric matrix is a correlation matrix, if it is positive-semidefinite and all its diagonal entries equal 1. According to most references it is easy to see that the space of ...
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0answers
25 views

Combined Effect size

Is there a way to calculate the effect size between more than 2 components? For example, if i know the effect size of variable A on C and I also know the effect size of variable B on C, is there a ...
0
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1answer
25 views

How can I solve $\phi_1$ and $\phi_2$?

Let be $$\rho(1)=\frac{\phi_1}{1-\phi_2}, \rho(2)=\frac{\phi_1^2+\phi_2(1-\phi_1)}{1-\phi_2}$$ How can I solve $\phi_1,\phi_2$? My idea: $\rho(1)=\frac{\phi_1}{1-\phi_2}\Leftrightarrow ...
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0answers
20 views

Relationship/correlation between data - does it exist?

Data I refer to in this question Some analysis has been conducted for my business by an external company. The data, as it stands, only really tells part of the story and doesn't provide any real ...
0
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1answer
23 views

Can I get $\mathrm{Cov}(X_1, X_2)$ in this case?

I know the values of: $\mathrm{Cov}(X_1,Z_1)=M_1$, $\mathrm{Cov}(X_1,Z_2)=M_1*A$, $\mathrm{Cov}(X_2,Z_1)=M_2*B$, $\mathrm{Cov}(X_2,Z_2)=M_2$ Is it possible to get the value of ...
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0answers
10 views

Bounded Stochastic discrete process

I just came across this stochastic process (link): $dY_t = (a-bY_t)dt + c \sqrt{Y_t(1-Y_t)}dW_t$, where $dW_t$ is a Wiener Process. According to the author under certain conditions this process is ...
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0answers
15 views

Problems about Farlie-Morgenstern family of bivariate CDFs

Hi I am trying to solve the following problem: Let $F_X:\mathbb{R}\to[0,1]$ and $F_Y:\mathbb{R}\to[0,1]$ be unnivariate Cumulative Distribution Functions (CDFs) and suppose $-1\le\alpha\le 1$. Define ...
1
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1answer
29 views

Correlation of three values

I have a data set that considers three values, $x,y,z$. And I have three questions: What's the relationship between $x$ and $y$? What's the relationship between $z$ and $y$? What's the relationship ...
0
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1answer
37 views

Why is autocorrelation used without normalization in signal processing field?

According to the wikipedia(Link), autocorrelation has two definition. Oh my god! In statistics, the definition of the autocorrelation between times $s$ and $t$ is like the following: $$\displaystyle ...
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1answer
35 views

Orthogonality of Two Signals.

My last question's link: Reconciling different definitions of orthogonality However, I failed to understand why they are equivalent. If $f$ and $g$ are real, \begin{align} ...
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0answers
26 views

How to calculate the correlation between two ratings

Suppose x and z are two persons who rate a classical piece of music y on a five point scale. x rates y $3$ out of $5$ z also rates y $3$ out of $5$ I need to know how much the ratings of x ...
0
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1answer
48 views

Reconciling different definitions of orthogonality

I want to establish about orthogonality in my mind. I knew the orthogonality of two functions $f$ and $g$ in interval T like the following: $$ \int_{<T>}f(t)g^*(t)~dt=0 \tag{1} $$ where $$ ...
0
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1answer
19 views

Correlate normal shocks

I am trying to generate some random standard normal variables and correlate them In particular I want: $$ \bf Y \sim \mathcal N(0, \Sigma) $$ where $\textbf{Y} = (Y_1,\dots,Y_n)$ is the vector I ...
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0answers
39 views

Correlation between $X$ and $Y$ where $X$,$Y$ are from i.i.d. standard normals and $X+Y > 0$?

Suppose $Z = X + Y$, where $X$ and $Y$ are independent standard normal random variables. If we generate plenty of $(X,Y)$ pairs and only keep the ones where $Z>0$, what's the correlation between ...
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1answer
23 views

What is the correlation between the pairwise differences of 2 bivariate normal random variables? [closed]

Given (X,Y) bivariate normal, $U = \frac{X_i - X_j}{\sqrt2\sigma_x}$ and similarly $V = \frac{Y_i - Y_j}{\sqrt2\sigma_y}$ for any two independent pairs $(X_i, Y_i)$ and $(X_j, Y_j)$. Why is this true ...
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1answer
24 views

Sum of two standard variables with joint bivariate distribution?

Let $X_1$ and $X_2$ have standard normal distribution and let $(X_1,X_2)$ have a joint bivariate distribution. Can anyone explain why: $X_1+X_2=\sqrt{2+2\rho}Z$ where $Z\sim N(0,1)$ and $\rho$ is the ...
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2answers
33 views

Is there any difference between Correlation and Correlation coefficient?

I learnt in probability theorem class that correlation coefficient is $$ \rho=\frac{\sigma_{XY}}{\sigma_X \sigma_Y}=\frac{E\left[(X-\mu_X)(Y-\mu_Y)\right]}{\sigma_X \sigma_Y} $$ However, my ...
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2answers
29 views

How does Variance become an Autocorrelation Function?

"For a Gaussian stochastic process $X=\{X(t)|-\infty<t<\infty\}$ with mean function $\mu(t)=0$ for all $t$, its autocorrelation function is $$ E(X(t)\cdot X(s))=R(h)=\max(0,1-|h|), h=t-s. $$ ...
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1answer
35 views

Relation between correlation and regression

Let $y\in \mathbb{R}$ be a random variable. Let $y$ be expressed as a linear combination of $x_i$ $i=1,2,\cdots,n$, as follows \begin{equation} y = \sum\limits_{i=1}^nw_ix_i + \epsilon \end{equation} ...
3
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0answers
147 views

Can't find the relationship between two columns of numbers. Please Help [closed]

I cannot find the relationship between these two columns...other than I know that they both increase or decrease in value at the same time. I'm not a math person, but I would appreciate any help ...
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0answers
37 views

Autocorrelation function of a Wiener process & Poisson process.

Can anyone possibly explain step 3 and 4 in this solution?
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3answers
78 views

Correlation between $(X+Y)^2$ and $X$

Good evening everybody! I am totally puzzled about how to solve this problem. We are given the random variables $X$ and $Y$, both of which are independent and uniformly distributed on $[0,1]$. Then ...
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2answers
53 views

Autocorrelation function of integral of cont. white noise

Let $W(t)$ be continuous time white noise, that is, a wide-sense stationary (WSS) zero-mean Gaussian process with autocorrelation function $R_W (\tau) = σ^2\delta(\tau)$. Calculate the auto ...
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1answer
23 views

Need Help explaining this equation for the correlation coefficient

As I am not a math geek so I have problem comprehending this equation: equation for the correlation coefficient Its basically the formula used in the CORREL functon in Microsoft Excel and I am ...
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0answers
35 views

Why is the length of a BAPS (binary almost perfect sequence) a multiple of 4?

a BAPS is a binary sequence of length $n$ with an almost perfect autocorrelation: $$ A(\tau)=\left\{\begin{matrix} n & \tau=0 \\ k & \tau= {n \over 2} \\ 0 & else \end{matrix}\right. $$ ...
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0answers
16 views

Measuring correlation of two time series

I have two sets of annual time series (employment growth from 2 different sources), which I display by using index. I would like to measure somehow whether series 1 (which are more timely) can be used ...
3
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0answers
97 views

Minimum and maximum bound on mean of product of three pairwise uncorrelated random variables

There are three pairwise uncorrelated random variables $X, Y, Z$ $$E(X) = E(Y) = E(Z) = 0$$ $$E(X^2) = E(Y^2) = E(Z^2) = \sigma^2$$ How we could find minimum and maximum bound on $E(XYZ)$? I ...
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0answers
20 views

Show covariance matrix must have condition number larger than correlation matrix

The inverse of covariance matrix can be used to find the conditional independencies among variables. This inverse is more sensitive to changes then the correlation matrix. As a result two samples with ...
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0answers
20 views

General correlation between function with itself and other input data

I've collected data for a function F = f(g(x)), for different function shapes g(x). The goal is to predict values of ...
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1answer
36 views

Correlation Coefficient

I am trying to understand the following equation for Correlation Coefficient: $r = \frac{\sum_{i=1}^{n}(x_i-\bar x)(y_i-\bar y)}{\sqrt(\sum_{i=1}^{n}(x_i - \bar x)^2\sum_{i=1}^{n}(y_i-y)^2)}$ ...
0
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1answer
30 views

calculate mean of two variables given two regression equations

Given these 2 regression equations how do I compute mean and find $r_{XY}$. $X=-0.4Y+6.4$ $Y=-0.6X+4.6$ when I rearranged the equations, I solved for $X$ and $Y$ hence $X=6$, $Y=1$ How do I get ...