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

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32 views

Correlation between properties

I have a table in a database where each record includes the ID of a person and the ID of a property of that person. Each person may have more than one property. Which is the statistical instrument ...
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1answer
257 views

Related rates, where do I start?

A revolving searchlight, which is $100$ m from the nearest point on a straight highway, casts a horizontal beam along a highway. The beam leaves the spotlight at an angle of $\frac{π}{16}$ rad and ...
2
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0answers
35 views

Finding correlations between many unknown functions.

Given an arbitrarily large number of black-box functions of one variable, is it possible to produce expressions that approximate their relationships to each other over their shared domain? Is it ...
2
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2answers
1k views

help understanding step in derivation of correlation coefficient

I'm looking to understand the starred step in the derivation below (also, if someone could help with the LaTex alignment, I'd appreciate it). The regression line is $y= b_0 + b_1 x$, where $b_0$ and ...
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0answers
109 views

Correlation function of Brownian motion. What am I doing wrong?

Can anyone tell me where I am going wrong here? (I am leaving out any random fluctuation forcings, because I don't think they are relevant to my problem.) 1: $\displaystyle \frac{dv(t)}{dt}=-\eta ...
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0answers
79 views

Calculation of conditional joint probability given certain conditionals for data which aren't independent

The context of this problem is the estimation of the distribution of a parameter $v$ given sets of data $A$ and $B$, where $A$ and $B$ are not independent. Suppose I know $P(v | A)$ and $P(v | B)$. ...
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1answer
96 views

correlation of product with its normally distributed factors

If x and y are normally dist. with standard deviation of 10%, and they are independent, then their product X.Y is 71% correlated with Y (or X). I can show this empirically, but how to I prove it in ...
0
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2answers
203 views

Trying to understand correlation and independence geometrically

I am trying to understand correlation and independence of two random variables geometrically, but found it difficult to grasp the intuition and to explain it rigorously. First, given two uniformly ...
2
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0answers
62 views

Dimension free Concentration bounds for Martingales

Consider the following random process which is defined on $n$ numbers $0\leq x_1,\ldots,x_n\leq 1$: At each step, pick an arbitrary number, say $x_i$. Then randomly (and independently) change its ...
2
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0answers
105 views

Finding the empirical correlation from a covariance matrix

I have this covariance matrix with five variables $X_1$ through $X_5$ in that order. ...
1
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1answer
336 views

Random walk serial correlation

Given a model $$Y_t =b_0 + b_1 \cdot X_t + b_2 \cdot Z_t + e_t,$$ where the error term $e_t$ follows a random walk form of serial correlation $e_t = e_{t-1} + u_t$. Further assume $u_t$ has zero mean ...
2
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1answer
523 views

Inequality concerning the pairwise correlation coefficients of three random variables

I was asked to prove: The correlation coefficients, $\rho_{12}$, $\rho_{23}$, $\rho_{13}$ between three random variables $X_1$, $X_2$, $X_3$ obey ...
0
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1answer
152 views

Covariance and Correlation

Suppose there were m married couples, but d of these 2m people have died. Regard the d deaths as striking the 2m people at random. Let X be the number of surviving couples. Find: a) E(X) b) Var(X) ...
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1answer
321 views

Correlation of Indicator Variables

Show that for indicator random variables $I_A$ and $I_B$ of Events $A$ and $B$: $Corr(I_A, I_B) = Corr(I_A^c, I_B^c) = -Corr(I_A, I_B^c) = -Corr(I_A^c, I_B)$ Deduce that if $A$ and $B$ are ...
2
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1answer
75 views

How can I mathematically show the similarity between these 3 plots?

I have 3 3D plots of field strength measured around an antenna. I want to calculate the mathematical similarity between the points of the field patterns. How can I do this? thanks
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1answer
41 views

What values to choose for correlation?

To work out correlation I'm using the online calculator : http://easycalculation.com/statistics/correlation.php ...
2
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0answers
1k views

What do angle brackets ($\langle\rangle$ ) mean in mathematics/statistics (autocorrelations)?

Okay, so the logarithmic return on a stock is given by: $$r_τ (t) = \ln P(t+τ) - \ln P(t),$$ where τ is the interval of time. I have no problem calculating that. My question comes to the following ...
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1answer
161 views

Find $\operatorname{argmax}_x \operatorname{corr}(Ax, Bx)$ for vector $x$, matrices $A$ and $B$

This is similar to, but not the same as, canonical correlation: For $(n \times m)$ matrices $A$ and $B$, and unit vector $(m \times 1)$ $x$, is there a closed-form solution to maximize the correlation ...
0
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1answer
19 views

Correlation Based Filter

i found this paper. Im interesting in part 2.3 Feature Weighting. The correlation function is known from wikipedia and almoast clear ( i can write a function to calculate the value :) ) But now i ...
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1answer
177 views

Is the relation of having positive covariance well behaved with respect to taking the inverse?

Let $X$ and $Y$ be two random variables, $X$ strictly positive. Assume that Cov$(X,Y)>0$. Does this imply that Cov$(1/X, Y)<0$? I know that being positively correlated is not a transitive ...
0
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1answer
154 views

special matrix in terms of its covariance matrix

How can we find a matrix $S\in \mathcal{M}_{n,n}$ and $Z\in \mathcal{M}_{n,m}$ whose $n$ entries of the $i^{th}$ column $Z_i$ are correlated $Z_i \sim \mathcal{N}(0,S)$ where $S \in \mathcal{M}_{n,n}$ ...
3
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2answers
105 views

Covariance$(X,Y) \geq 0$ if $X,Y \geq 0$?

I was wondering if you can say something about the covariance of two positive variables $X$ and $Y$?
0
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1answer
175 views

How to correlate the timestamps of 2 systems?

Whenever I've done (simple) correlation in the past, I've always had 2 sets of data that had "connected" axes: ...
0
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0answers
105 views

Is the correlation function convex or not?

Suppose the function for statistical correlation is a non linear constraint in a non linear programming model: $$ \frac{\sum_{t=1}^T (p_t - \bar{p})(R_t - \bar{R})}{\sqrt{\sum_{t=1}^T (p_t - ...
0
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1answer
84 views

What is the correlation function in multivariable/vectoral case?

I know that the correlation function between random variables $X$ and $Y$ is defined as $$ \rho_{X,Y}=\mathrm{corr}(X,Y)={\mathrm{cov}(X,Y) \over \sigma_X \sigma_Y} ={E[(X-\mu_X)(Y-\mu_Y)] \over ...
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2answers
2k views

What is a direct correlation?

I have two contrary definitions of for the direct correlation between two variables $X$ and $Y$ Their correlation coefficient is close to $1$. There is a direct causal relationship between the ...
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2answers
127 views

Does $0$ correlation imply independence for marginally normal distributions?

Assume $X \sim \mathcal N(\mu_1, \sigma_1^2)$ and $Y \sim \mathcal N(\mu_2, \sigma_2^2)$. If $\rho_{X,Y} = 0$ then $X \bot Y$. Can someone give a hint why this is true ?
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0answers
48 views

Sorting Vectors based on their correlation

This problem [question]: Sort vectors according to their distance between them is about sorting vectors based on the distance between them. What about sorting vectors based on the correlation ...
0
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1answer
126 views

The science of pearson product moment correlation coefficient

I need to compare two sound signals for similarity, I took cross-correlation of both the signals and I got a cross-correlation signal, now I intend to use pearson correlation coeff formula to get the ...
0
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1answer
211 views

Pearson Correlation Coefficient Interpretation

Let $X=(1,2,3,...,20)$. Suppose that $Y=(y_1,y_2,...,y_{20})$ with $y_i=x_i^2$ and $Z=(z_1,z_2,...,z_{20})$ with $z_i=e^{x_i}$. Pearson correlation coefficient is defined by formula \begin{equation} ...
0
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1answer
117 views

correlation between two different variables

I am studying stochastic processes and found the next problem: Let $A$ and $\Phi $ be two independent random variables such that $E(A) = 0$, $E(A^2) < \infty$, and $\Phi$ is uniformly distributed ...
0
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1answer
276 views

Intraclass correlations can be negative, yet they are a ratio of two variances (which are positive)

Estimates of intraclass correlations can be negative, yet they are a ratio of two variances -- the variance of the means of the classes to the variance of the entire set of values. What is a neat ...
0
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2answers
62 views

Correlation bound

Let x and y be two random variables such that: Corr(x,y) = b, where Corr(x,y) represents correlation between x and y, b is a scalar number in range of [-1, 1]. Let y' be an estimation of y. An ...
3
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1answer
1k views

quadratic relationship

Detection of linear relationship is possible with correlation coefficient. If absolute value of correlation coefficient is 1, then the relationship is linear. Is there any way for detecting quadratic ...
0
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1answer
176 views

Relationship between Correlation and Bayes Theorem

Is there some relationship between the correlation of two random variables, and Bayes Theorem? A bit of background intuition, if W = random variable denoting number of women in a room, and L = ...
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0answers
23 views

Estimating the likelihood of independence of two discrete variables using the co-occurrence count matrix.

I have some data about users from different regions visiting different directories of some website. Aggregating that data I get the co-occurrence frequency matrix (for regions and directories). Now I ...
2
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0answers
461 views

Pearson correlation and metric properties

Assuming that the data set was $z$-standardized to zero mean and unit variance (also assuming that it does not contain constant vectors). Then Pearson's r reduces to Covariance: $$\rho(X,Y) := ...
3
votes
4answers
7k views

Correlation between three variables question

I was asked this question regarding correlation recently, and although it seems intuitive, I still haven't worked out the answer satisfactorily. I hope you can help me out with this seemingly simple ...
1
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0answers
207 views

Cross-Correlation (and finding Correlation error ) of two digital sequences.

In a IEEE paper, I saw a formula for WUInt(ti+1) as , Reference : ...
2
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1answer
124 views

Find data to perform regression analysis

I'm trying to find some data (two continuous variables that I believe are correlated) online for which I can perform a regression anaylsis, my assignment sheet says: The data may be found anywhere ...
1
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0answers
95 views

Compute significance of Kendall tau-b?

I have so-far tried all ways of computing kendall tau significance (where there are ties) described here. However, none of them works good, even for relatively large vectors. I think the problem is ...
3
votes
1answer
154 views

Autocorrelation of wrapped Wiener process

Let $\phi(t)$ be a Brownian Walk (Wiener Process), where $\phi\in[0,2\pi)$. As such we work with the variable $z(t)=e^{i\phi(t)}$. I would like to calculate $$E(z(t)z(t+\tau)).$$ This is equal to ...
2
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2answers
607 views

Time series and social network analysis

I am interested about plotting graphs of a phenomenon and study it using tools from social network analysis. Suppose the nodes are time series, and that the links between the nodes are the correlation ...
0
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0answers
223 views

Autocorrelation derivation using fourier transform

I am stuck with basic understanding of the Auto-correlation derivation of a simple signal and I would be pleased if you could help me out with that. Lets have a signal $x(t)=\cos(2\pi{f_{0}}{t})$. ...
2
votes
2answers
288 views

Relationship between variances in perfect correlation

I have two random variables $X$ and $Y$ with mean and standard deviation $(\mu_1,\sigma_1)$ and $(\mu_2,\sigma_2)$ respectively. I know that for perfect correlation the relationship is given by a ...
1
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1answer
276 views

Find correlation of x and y, given E(Y|X) and E(X|Y)

Suppose that X and Y are random variables such that E(Y | X) = 7 - (1/4)x and E(X | Y) = 10 - Y . Determine the correlation of X and Y . Edit: So far I've got E(x)=4 E(y)=6 Now I'm trying to ...
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1answer
177 views

How to increase the correlation?

I have three vectors of numbers with the same dimensionality, $A$,$B$ and $C$. What is the most suitable number $x$, which maximizes the correlation of $A$ and $B+xC$ . To what extend can I increase ...
1
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1answer
61 views

How can I show that $z_i =\cos(iw)$ where $w$ is uniform on $[0,2\pi]$ is a white noise process?

How can I show that $z_i =\cos(iw)$, where $w$ is uniform on $[0,2\pi]$ is a white noise process? So far, I have shown $E(z_i)=0$ by integrating. However, I need to show ...
0
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2answers
709 views

Step by step correlation calculation

I must understand how I can calculate the correlation for the following probability variables. ...
1
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2answers
274 views

Linear vs non-linear Correlation

How do i check that two random variables satisfy the requirements for computing correlation via Pearson or Spearman? If the data is non-linear/ non-Monotonic, are there other tests i could use to ...