For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].
3
votes
3answers
276 views
Correlation between variables
I asked this question on stats SE but did not find a suitable answer so far. Maybe someone can help.
Given n random variables x1,...,xn (one-dimensional).
The following is known (corr() = Pearson ...
1
vote
2answers
60 views
Relationship between x and y
Studying a financial model from a third party we see:
36month - 1.2 multipler
48month - 1.3333 multipler
60month - 1.5 multipler
I am trying to determine if ...
3
votes
1answer
179 views
Use Pearson's correlation coefficient on a matrix
I have a problem to interpret the following formula which is said to be the Pearson's correlation coefficient:
$$r = \frac{N \left(\sum XY\right) - \left(\sum X\right) \left(\sum ...
1
vote
2answers
924 views
If two Gaussian random variables are uncorrelated, they are statistically independent
I read in a textbook that when two gaussian variables are uncorrelated, then they are statistically independent? How can I prove that?
1
vote
0answers
36 views
Sampling a distribution with restrictions: eliminating the correlation between two variables
I have a collection of 400.000+ word-pairs. Each word-pair has an association strength, which is a measure of how related the two words are to each other (as in cow-milk). Each word-pair also has a ...
4
votes
1answer
89 views
Correlations between neighboring Voronoi cells
For a sequence $X_1,X_2,X_3,\ldots$ of random variables, what it means to say $X_1$ is correlated with $X_2$ is unambiguous. It may be that the bigger $X_1$ is, the bigger $X_2$ is likely to be. If, ...
1
vote
1answer
222 views
Expectation product of pairwise uncorrelated variables
Suppose I have three uncorrelated random variables $X, Y$ and $Z$ (discrete or continuous) such that
$$\newcommand{\Cov}{\mathrm{Cov}}\Cov(X,Y)=0;\quad \Cov(Y,Z)=0;\quad \Cov(X,Z)=0 \tag{$\ast$}$$
I ...
1
vote
3answers
128 views
correlated or independent
Let $(X_1, X_2)$ be a randomly chosen pair out of $\{1,2, \ldots, 20\}$ (draw without repetition).
Are both events $$E_1:=\{X_1 \geq 8\}$$ and $$E_2:=\{X_2 \geq 12\}$$ positive or negative correlated. ...
0
votes
1answer
186 views
indicator variable are uncorrelated, if they are independent?
Is it true that if two indicator variables are independent then they are uncorrelated?
If covariance =0 $\Rightarrow$ uncorrelated
Does the covariance between indicator variables exist?
thx
2
votes
0answers
518 views
Correlation and Regression Question
Two separate tests are designed to measure a students ability to solve problems. Several students are randomly selected to take both tests and the results are:
$$
\begin{matrix}
\text{Test A}(x) ...
1
vote
0answers
91 views
Correlated Random Numbers Between A Range
I am trying to generate random numbers within a range say 57 to 107 which are correlated by a factor of 0.8. The numbers are for illustration simplicity only.
0
votes
1answer
207 views
3D correlation visualization?
Incomer per person (x axis) correlates with life expectancy (y axis).
These two indicators change over time (z axis).
x correlates with y. Moreover, x and y both correlate with z.
The question is: ...
1
vote
1answer
45 views
Long time scale correlation
I have some EXTREMELY noisy data (standard deviation a is greater than the mean), but plotting it with a 15 data point running average does well to get a visual indication of the trending. I want to ...
2
votes
1answer
558 views
Generalized variance
Generalized variance is the determinant of correlation matrix. Does increasing the off-diagonal entries (correlation coefficients) decreases the determinant? Is a proof available?
All elements are ...
1
vote
1answer
77 views
Pearson's Correlation, for comparing a PRNG?
Other than uniformity tests on random numbers of which can be done with other methods, I had wondered if the result of the Pearson Product Moment Correlation function would be an effective means to ...
4
votes
3answers
404 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 ...
2
votes
1answer
1k views
What is the standard deviation of multiple correlated random variables subtracted from another random variable?
Wiki states that standard deviation of $X-Y$ is:
$$\sigma_{x-y} = \sqrt { \sigma_x^2 + \sigma_y^2 - 2\rho\sigma_x\sigma_y }$$
I have a number (say 3) correlated random variables to be subtracted ...
2
votes
2answers
136 views
Calculating the correlation between subsequent values in a stream of numbers
I have a stream of integer values being generated $V_1,\cdots, V_n$ and want to calculate how the value of $V_{n+1}$ is correlated to $V_n.$ I would also like to calculate this at run time as ...
3
votes
3answers
165 views
Using Correlation for mouse gesture recognition
I am in need to build a mouse gesture recognition system which will compare given recognition to the the gestures in training data and will say where a given gesture best fits.
I am planning to use ...
1
vote
2answers
3k views
Calculating the variance of the ratio of random variables
I want to calculate $\newcommand{\var}{\mathrm{var}}\var(X/Y)$. I know that the solution is
$$\var(X) + \var(Y) - 2 \var(X) \var(Y) \mathrm{corr}(X,Y) \>,$$
but, how do I derive it from "common" ...
1
vote
2answers
524 views
Intuitive meaning of Pearson Product-moment correlation coefficient Formula
I can't understand the intuition behind Pearson Product-moment correlation coefficient Formula
for bivariate data. The formula is :
$\rho$ = cov(X,Y)/($S_x$ * $S_y$)
where cov is covariance.
$S_x$ and ...
2
votes
2answers
488 views
How to 'minimize' correlation between series
Hi fellow mathemagicians,
let's say that I have 3 series of numerical results (they represent 'drawdowns') :
...
1
vote
1answer
1k views
Proving correlation coefficient = 1 or -1 given X and Y=a + bX
Given $X$ and $Y = a+bX$, I have to prove that:
If $b \lt 0$, then $\rho = -1$. If $b \gt 0$, then $\rho = 1$.
I've gotten to the point where I have:
$$ \rho = \frac{b \cdot \sigma_x }{ ...
-1
votes
1answer
821 views
Cross correlation in MATLAB HELP
I have values from two sensors stored in two vectors A and B. They both represent values of the sensors at times TA and TB which is stored in two other vectors(since it is not uniform sampling) Both A ...
2
votes
1answer
141 views
example on variance of stochastic processes
I saw this expression in a book and I cannot understand how did he get this expression.
Suppose $Z_t$ and $D_t$ are some stochastic processes and we have these expressions,
$Z_{t_k} - Z_{t_{k-1}} = ...
1
vote
1answer
324 views
Correlation between Beta distributions
I have a Computer Science background and not very knowledgeable in Probability and Statistics. So excuse me if my question,notation, or language is flawed. Anyways, the problems is that we have two ...
1
vote
1answer
135 views
What is the characteristic formula for the addition of two lognormal distributions?
If I have two lognormal processes (X and Y) with mean and volatiilty for each and also correlation between the two, what is the characteristic formula of X + Y (i.e. what is the new mean and new ...
0
votes
1answer
231 views
Calculate Correlation between 2 values
I have a random vector $X = ( X_1 , X_2 )$ that has a bidimensional normal repartition with mean $0$ and covariation matrix :
$$
\Sigma = \left(
\begin{array}{ccc}
1 & q \\
q & 1
...
6
votes
4answers
666 views
Going back from a correlation matrix to the original matrix
I have N sensors which are been sampled M times, so I have an N by M readout matrix. If I want to know the relation and dependencies of these sensors simplest thing is to do a Pearson's correlation ...
1
vote
1answer
480 views
Statistics - Correlation between 2 sets of data
If i know the means and standard deviations of 2 sets of data, and i know the slope of the regression line, how can I find the correlation?
edit
Sample 1
SD: 12.37
Sample 2
SD: 7.00
Slope of ...
