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

learn more… | top users | synonyms

0
votes
1answer
119 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
votes
1answer
290 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
votes
2answers
64 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
votes
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
votes
1answer
196 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 = ...
1
vote
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
votes
0answers
500 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
8k 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
vote
0answers
225 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
votes
1answer
130 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
vote
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
164 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
votes
2answers
648 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
votes
0answers
230 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
306 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
vote
1answer
287 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 ...
1
vote
1answer
195 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
vote
1answer
62 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
votes
2answers
776 views

Step by step correlation calculation

I must understand how I can calculate the correlation for the following probability variables. ...
1
vote
2answers
277 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 ...
2
votes
0answers
133 views

Correlation between an event and a time series

I have a time series, e.g. the daily number of visitors on my blog. I have a set of events of some class, like the days when I made a new posting. I want to measure the effect of a new posting on the ...
1
vote
3answers
1k views

Determinant of a N symmetric square matrix with diagonal 1

What is the determinant of a symmetric $n \times n$ matrix with all diagonals be 1 and all others are $\rho$ (yes correlation matrix)? Anyone can tell me a method to work it out elegantly? Thanks!
5
votes
2answers
826 views

Eigenvalue decomposition of block covariance matrix for Canonical Correlation Analysis (CCA)

Edited: My question is related to a tutorial I was reading. The covariance matrix is a block matrix where $C_{xx}$ and $C_{yy}$ are within-set covariance matrices and $C_{xy} = C_{yx}^T$ are ...
1
vote
1answer
152 views

Independence of quadratic forms

Let us consider the quadratic form $$q_1 = \mathbf{x}_1^\mathrm{H} \mathbf{A}\,\mathbf{x}_1 $$ and the quadratic form $$ q_2= \mathbf{x}_2^\mathrm{H} \mathbf{A}\, \mathbf{x}_2 $$ where ...
0
votes
3answers
245 views

Prove dot product will get maximum

If we have two identical sets $A_1 = A_2 $, and we were asked to get the maximum sum of multiplying one distinct element from $A_1$ by another distinct element of $A_2$, for all elements in $A_1$. ...
2
votes
0answers
237 views

Correlated diffusion processes and covariance matrix

I'm really noob in maths topics so I hope you will excuse me if I use terms which aren't correct. I would like to simulate $n$ dimensional diffusion processes with $n$ noises. Each process has its ...
3
votes
2answers
292 views

Correlation and squared variables

According to my textbooks if two variables are uncorrelated, they are not necessarily independent (unless they are normally distributed). My question is, are 2 variables still not independent if they ...
4
votes
1answer
72 views

PCA vs Correlation

What is the relationship between (first) principal component(s) and the correlation matrix or the average correlation of the data. For example, in an empirical application I observe that the average ...
0
votes
1answer
315 views

Difference between positively correlated graph and a linear relationship?

So I understand the differences between positive and negative correlation and so on. However what I don't understand are the similarities and differences between a positive correlation and a linear ...
2
votes
3answers
140 views

Product of standard deviations

If $u=cx+dy$ and $v=cx-dy$ and $R$ is the co-efficient of correlation between variables $x$ and $y$ and variables $u$ and $v$ have 0 correlation, then how can I prove that ...
2
votes
1answer
727 views

Calculate a whitening matrix without using inverses?

Consider a random column vector $\mathbf{x}$, of dimension $m$. That is, it is a random vector, composed of $m$ random variables. The PDF of the random vector $\mathbf{x}$ is thus the joint-PDF of its ...
2
votes
1answer
100 views

Nonlinear regression with correlated errors

it's my first post here and I'm a newbie in statistics, so please forgive me if I'm doing something wrong or explaining myself badly. Anyway, I have a problem similar to this: How to perform ...
3
votes
0answers
162 views

How to perform nonlinear regression with correlated errors?

I have a nonlinear least squares problem, but the errors are correlated. I could use R's nls function to do the regression if the errors were independent, but I don't know the right way to handle ...
1
vote
0answers
122 views

Windowed Linear Correlation

$\DeclareMathOperator \Cov {Cov}$ $\DeclareMathOperator \Var {Var}$ $\DeclareMathOperator \E {E}$ Consider the following experiment: For $N\geq1$, consider $N$ black balls. Let us paint each black ...
3
votes
1answer
617 views

Necessary and sufficient conditions for a matrix to be a valid correlation matrix.

It's not too hard to see that any correlation matrix must have certain properties, such as all entries in the range -1 to 1, symmetric, positive semi-definite (excluding pathological cases like ...
4
votes
2answers
148 views

Correlation in errors

I'm not good in statistics, so please excuse my noob question. We want to ask a question from people (say what is $2+2$). They might make mistake. We assume that they give the correct answer with the ...
1
vote
1answer
329 views

Pearson Product Moment Correlation Coefficient for linear relationship only?

Pearson Product Moment Correlation Coefficient method is used only if variables are linearly correlated. But if they are linearly correlated, then correlation coefficient $$r=\pm 1$$ only. Then why we ...
11
votes
2answers
13k views

Generating correlated random numbers: Why does Cholesky decomposition work?

Let's say I want to generate correlated random variables. I understand that I can use Cholesky decomposition of the correlation matrix to obtain the correlated values. If $C$ is the correlation ...
3
votes
2answers
160 views

Proving that the magnitude of the sample correlation coefficient is at most $1$

How can you show that the magnitude of the sample correlation coefficient is at most $1$? The formula is huge, I'm not even sure how to approach this. Can anyone point me in the right direction? ...
1
vote
0answers
37 views

Dynamic Light Scattering

In DLS does the combination of the Time Average and Ensemble Average give a better statistical average than the results shown by each case considered separately ?
1
vote
1answer
772 views

Probability that one normal distribution is greater than the other when they are correlated i.e (Not Independent)

Would like to know how to approach this question: Probability that one normal distribution is greater than the other when they are correlated i.e (Not Independent). Seen the solution for the ...
0
votes
1answer
58 views

What is a common way to measure the “goodness of fit” of an individual data point to a correlation?

Let's say I have a collection of data points (X & Y values) that show some correlation when, eg, Pearson's correlation formula is applied. What is a good measure for determining which data points ...
1
vote
1answer
441 views

Correlation Coefficients with Unequal Data Sets

I would like to determine the correlation coefficients of two timesets of data with unequal entries to detemine how often they move together. I am performing the following computation but would like ...
2
votes
2answers
2k views

Correlations between 3 random variables

I have a question as follows: The correlation coefficients between three random variables are x, y, and z respectively. What relation do x, y, and z have to satisfy? Can someone help me? Thanks very ...
2
votes
1answer
70 views

Given series $A$ and a correlation, is it possible to randomly calculate a fitting series $B$?

With reference to the original thread on Stackexchange, my question is as follows. Usually, one would enter two value-series and a script or program calculates the correlation. For instance, with $x ...
0
votes
0answers
294 views

How to find a correlation and whether it is statistically significant

I have 2 columns with numers in them, x and y. I'd like to find out what y could be if x = n and how strong the correlation is, if it's statistically significant or not. How do I do that? Pretty ...
0
votes
1answer
328 views

MATLAB's implementation of cross correlation

Wikipedia gives the cross-correlation as $$ \begin{align*} (f \star g)[n] = \sum^{\infty}_{m = -\infty} f^{*}[m] g[n+m] \end{align*} $$ MATLAB's documentation gives ...
6
votes
3answers
3k views

Correlation Coefficient and Determination Coefficient

I'm really new to linear regression and am trying to teach myself. In my textbook there's a problem that asks why $R^{2}$ in the regression of $Y$ on $X =$ the sample correlation between X and Y the ...
2
votes
1answer
93 views

constructing “pseudonoise” sequences other than (2^n)-1? (low cyclical autocorrelation)

Pseudonoise LFSR sequences of length $N = 2^k-1$ have the nice property that their cyclical autocorrelation is $N$ when the sequence is lined up with itself, and $-1$ elsewhere. Is there a way to ...
3
votes
2answers
107 views

Independence of Random Variables (kernel ICA)

In the paper Bach, F. R., & Jordan, M. I. (2002). Kernel Independent Component Analysis. Journal of Machine Learning Research, 3(1), 1-48. doi:10.1162/153244303768966085 I stumpled upon ...