For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].
0
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2answers
37 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 ...
1
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0answers
20 views
+50
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 ...
1
vote
3answers
126 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 ...
0
votes
0answers
16 views
Calculate the tendency of a set of samples
I develop an application in which I constantly get samples of heart pulse.
I defined an interval of $t$ seconds.
In each $t$ seconds I have $n$ samples.
In every interval, I want to calculate the ...
1
vote
1answer
326 views
Correlation between Beta distributions
I have a Computer Science background and not very knowledgeable in Probability and Statistics. So excuse me if my question,notation, or language is flawed. Anyways, the problems is that we have two ...
2
votes
0answers
16 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.
...
0
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0answers
18 views
Correlation question
I hope someone can help me with this:
Let $c(\rho)=\lim_{n\rightarrow\infty}n^{\alpha-1}\sum_{k=-(n-1)}^{n-1}\left[1-\frac{k}{n}\rho(k)\right]$ where $n=1,2,3,\ldots$, $\alpha\in(0,1)$ and $\rho$ is ...
5
votes
1answer
124 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 ...
1
vote
1answer
27 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 ...
1
vote
1answer
39 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
...
3
votes
2answers
932 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 whole ...
0
votes
1answer
92 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)
...
0
votes
1answer
37 views
Correlation of Indicator Variables
Show that for indicator random variables IA and IB of Events A and B:
Corr(IA, IB) = Corr(IAc, IBc) = -Corr(IA, IBc) = -Corr(IAc, IB)
Deduce that if A and B are positively dependent, then so are Ac ...
0
votes
0answers
39 views
Invariance of the correlation coefficient under linear transformations
Show that for arbitrary random variables X and Y, and constants a ,b ,c ,d with a and c nonzero, Corr(a*X+b, c*Y+d) = Corr(X,Y) if a and c have the same sign
= -Corr(X,Y) if a and c have opposite ...
1
vote
1answer
207 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
1answer
24 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
0
votes
0answers
20 views
Correlation coefficient, ACF,
In my book it says
$\rho_x(h) = \frac{\gamma_x(h)}{\gamma_x(0)}$, which is the definition of ACF, and $\gamma_x(\cdot)$ is the autocovariance.
It then should follow (under conditions of weak ...
0
votes
1answer
43 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
votes
1answer
19 views
What values to choose for correlation?
To work out correlation I'm using the online calculator : http://easycalculation.com/statistics/correlation.php
...
0
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0answers
58 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 ...
0
votes
1answer
139 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 $S \in \mathcal{M}_{n,n}$ ...
0
votes
1answer
15 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 ...
0
votes
0answers
25 views
Probability Density Function and Eigenvalue Spectrum of Correlation Matrix
My question is in the link...
http://www.flickr.com/photos/88684900@N03/8654322505/in/photostream
3
votes
2answers
53 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
votes
0answers
57 views
Sum of correlated conditional variables
I have a normal random variable X with mean $\mu_x$ and variance $\sigma_x^2$. I take readings from only X every day (these observations are independent). I have another normal random variable Y ...
0
votes
1answer
21 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
33 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:
$$
\frac{\sum_{t=1}^T (p_t - \bar{p})(R_t - \bar{R})}{\sqrt{\sum_{t=1}^T (p_t - ...
3
votes
2answers
114 views
Correlation in errors
I'm not good in statistics, so please excuse my noob question.
We want to ask a question from people (say what is $2+2$). They might make mistake. We assume that they give the correct answer with the ...
0
votes
1answer
44 views
What is the correlation function in multivariable/vectoral case?
I know that the correlation function between random variables $X$ and $Y$ is defined as
$$
\rho_{X,Y}=\mathrm{corr}(X,Y)={\mathrm{cov}(X,Y) \over \sigma_X \sigma_Y} ={E[(X-\mu_X)(Y-\mu_Y)] \over ...
0
votes
1answer
38 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
votes
1answer
27 views
Normal distribution $\rho_{X,Y} = 0 \rightarrow X \bot Y$
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 ?
1
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0answers
28 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
votes
1answer
90 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}
...
1
vote
1answer
46 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 ...
3
votes
1answer
78 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 ...
0
votes
1answer
53 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
51 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
0answers
21 views
Iterative Computation of Correlation Coefficient
Given a set of $k$ data points $A$, I have the correlation coefficient between them as $\rho_A$. Now I want to iterate over a new set of data points $B$ (say $j$ of them) and wish to iteratively ...
0
votes
2answers
34 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 ...
4
votes
3answers
407 views
Bounds on off-diagonal entries of a correlation matrix
Assume that all the entries of an $n \times n$ correlation matrix which are not on the main
diagonal are equal to $q$. Find upper and lower bounds on the possible values of $q$.
I know that the ...
0
votes
0answers
29 views
how to compare correlation between random variables?
Suppose I have a random variable, S(k) for starting date of callable bonds, M(k) for the maturity date of the bonds, and C(k) for the called date of the bonds.
$$S(k) < C(k) < M(k)$$
C(k) is ...
2
votes
2answers
6k views
Determining variance from sum of two random correlated variables
I understand that the variance of the sum of two independent normally distributed random variables is the sum of the variances, but how does this change when the two random variables are correlated?
...
2
votes
1answer
114 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
40 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
18 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 ...
1
vote
0answers
44 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) := ...
1
vote
0answers
76 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 :
...
0
votes
0answers
33 views
Correlation Coefficient dealing with discretely distributed variables
I'm a bit stuck on this practice problem I have for my HS business stats class. I'd appreciate any help to get the solutions. Thank you.
Exercise #22: Let X and Y be discretely distributed random ...
1
vote
3answers
497 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 ...
2
votes
1answer
30 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 ...
