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

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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 ...
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1answer
321 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 ...
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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 ...
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1answer
89 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 ...
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2answers
103 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 ...
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884 views

Pseudo-random binary sequence generated by shift register

Binary sequence generated by shift register with feedback have periodic properties. A simple 4-bit shift register shown in Fig (a). For the initial condition shown, it can be verified that the ...
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3answers
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Correlation between two linear sums of random variables

I understand how to create random variables with a prespecified correlational structure using a Cholsesky decomposition. But I would like to be able to solve the inverse problem: Given random ...
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52 views

Finding out whether or not two graphs are “close”, given 20 points on each graph whose Xs do not match

Let's assume we have two graphs where: Each graph has 600 points per minute. We're allowed to get only one point per minute. We do not get the same point per minute in both graphs. So for example, ...
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2answers
431 views

Error of Pearson Correlation Coefficient

I have a data set expressed as in the figure here. 'y' is some measured quantity with known error and 'fit' is some attempt to fit a function with zero error. In order to evaluate the quality of the ...
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205 views

Cross Correlation

The cross-correlation function is defined as follows if $\bar{f}$ is the complex conjugate of $f$ and we assume that $f$ is real, such that $\bar{f} = f$. $$ \begin{align} f \star g &= ...
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1answer
130 views

In search of memorable example of “(Pearson-)uncorrelated $\not\Rightarrow$ independent”

I am looking for an easy-to-remember (and non-trivial) example that vividly illustrates that the "uncorrelatedness" (in the sense of Pearson) of two random variables $X, Y$ does not imply that $X$ and ...
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1answer
108 views

Find 3 normal variables which are linear combinations based on 3 ind std normal variable given a correlation matrix

I am given $3$ normal random variables $X_1$,$X_2$,$X_3$ which are linear combinations of $Z_1$,$Z_2$,$Z_3$. $Z_1$,$Z_2$,$Z_3$ are mutually independent standard normal variables. I am given a ...
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1answer
141 views

Given $Z_1$ and $Z_2$ independent normal variables, find a pair $X_1,X_2$ with correlation $p$

I am given $Z_1$ and $Z_2$ independent standard normal variables, I have to find two random variables $X_1$ and $X_2$ with correlation $\operatorname{corr}(X_1,X_2) = p$, where $p\in (−1, 1)$. Any ...
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1answer
293 views

Calculate Upper Lower bound in $4\times 4$ correlation matrix

Let $X_i$, $i = 1,2,3 4$, be random variables on the same probability space such that $$\begin{align*} \mathrm{corr}(X_1,X_3) &= 0.3;\\ \mathrm{corr}(X_2,X_3) &= 0.1;\\ ...
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2answers
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Autocovariances and Autocorrelations of Processes

I have two questions that are related to calculating autocovariances and autocorrelations of processes. Let's say we have a simple process: $y_t = ε_t + ε_{t-1}$ $ε_{t} =$ standard normal random ...
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233 views

Geometric interpretation of element by element division of one vector by another

This is my first post here, and I'm not a mathematician, so please go easy on me :) In statistics there is a geometric interpretation of correlation that uses basic vector geometry. This is fairly ...
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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? ...
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578 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 ...
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2answers
65 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 ...
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1answer
370 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 ...
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2answers
3k 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?
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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 ...
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1answer
183 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, ...
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1answer
561 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 ...
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3answers
136 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. ...
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478 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
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915 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) ...
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128 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.
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1answer
462 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: ...
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1answer
54 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 ...
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1answer
2k 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 ...
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1answer
108 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 ...
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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 ...
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1answer
4k 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 ...
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2answers
179 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 ...
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3answers
209 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 ...
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2answers
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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" ...
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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 ...
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2answers
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How to 'minimize' correlation between series

Hi fellow mathemagicians, let's say that I have 3 series of numerical results (they represent 'drawdowns') : ...
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1answer
3k 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 }{ ...
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1answer
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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 ...
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1answer
189 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}} = ...
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1answer
613 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 ...
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1answer
242 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 ...
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1answer
312 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 ...
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4answers
895 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 ...
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759 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 ...