Tagged Questions
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
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
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
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
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 ...
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
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
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}
...
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
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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
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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
496 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
59 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 ...
2
votes
2answers
86 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
100 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 ...
0
votes
2answers
85 views
Step by step correlation calculation
I must understand how I can calculate the correlation for the following probability variables.
...
5
votes
2answers
209 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
61 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 $$
where ...
1
vote
0answers
89 views
Windowed Linear Correlation
$\DeclareMathOperator \Cov {Cov}$
$\DeclareMathOperator \Var {Var}$
$\DeclareMathOperator \E {E}$
Consider the following experiment:
For $N\geq1$, consider $N$ black balls. Let us paint each black ...
3
votes
2answers
114 views
Correlation in errors
I'm not good in statistics, so please excuse my noob question.
We want to ask a question from people (say what is $2+2$). They might make mistake. We assume that they give the correct answer with the ...
0
votes
0answers
48 views
Determining how much closer a sequence is to another series?
I am supposed to make a game in which a range of numbers starting from 1 are scattered across the screen and the player has to click them in series. Somewhat like this but much less range,
You have ...
0
votes
0answers
147 views
Combine dependent variables into index that best matches independent variable?
I'm an undergrad working in a geochemistry lab for the summer. My job requires a good amount of statistical analysis, something that I'm not very familiar with.
I'm looking for an way to blindly ...
1
vote
1answer
137 views
Pearson Product Moment Correlation Coefficient for linear relationship only?
Pearson Product Moment Correlation Coefficient method is used only if variables are linearly correlated.
But if they are linearly correlated, then correlation coefficient $$r=\pm 1$$ only.
Then why we ...
3
votes
2answers
55 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
21 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 ?
0
votes
1answer
42 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
177 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 ...
1
vote
1answer
59 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
172 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 ...
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 ...
2
votes
2answers
65 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 ...
2
votes
2answers
770 views
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 ...
1
vote
2answers
234 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 ...
1
vote
1answer
85 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 ...
2
votes
0answers
168 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 ...
3
votes
3answers
279 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 ...
3
votes
1answer
183 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
932 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 ...
2
votes
0answers
528 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:
$$
\begin{matrix}
\text{Test A}(x) ...
1
vote
1answer
45 views
Long time scale correlation
I have some EXTREMELY noisy data (standard deviation a is greater than the mean), but plotting it with a 15 data point running average does well to get a visual indication of the trending. I want to ...
1
vote
1answer
77 views
Pearson's Correlation, for comparing a PRNG?
Other than uniformity tests on random numbers of which can be done with other methods, I had wondered if the result of the Pearson Product Moment Correlation function would be an effective means to ...
2
votes
1answer
1k views
What is the standard deviation of multiple correlated random variables subtracted from another random variable?
Wiki states that standard deviation of $X-Y$ is:
$$\sigma_{x-y} = \sqrt { \sigma_x^2 + \sigma_y^2 - 2\rho\sigma_x\sigma_y }$$
I have a number (say 3) correlated random variables to be subtracted ...
3
votes
3answers
166 views
Using Correlation for mouse gesture recognition
I am in need to build a mouse gesture recognition system which will compare given recognition to the the gestures in training data and will say where a given gesture best fits.
I am planning to use ...
1
vote
2answers
3k views
Calculating the variance of the ratio of random variables
I want to calculate $\newcommand{\var}{\mathrm{var}}\var(X/Y)$. I know that the solution is
$$\var(X) + \var(Y) - 2 \var(X) \var(Y) \mathrm{corr}(X,Y) \>,$$
but, how do I derive it from "common" ...
1
vote
2answers
532 views
Intuitive meaning of Pearson Product-moment correlation coefficient Formula
I can't understand the intuition behind Pearson Product-moment correlation coefficient Formula
for bivariate data. The formula is :
$\rho$ = cov(X,Y)/($S_x$ * $S_y$)
where cov is covariance.
$S_x$ and ...
1
vote
1answer
1k views
Proving correlation coefficient = 1 or -1 given X and Y=a + bX
Given $X$ and $Y = a+bX$, I have to prove that:
If $b \lt 0$, then $\rho = -1$. If $b \gt 0$, then $\rho = 1$.
I've gotten to the point where I have:
$$ \rho = \frac{b \cdot \sigma_x }{ ...
1
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 ...
1
vote
1answer
137 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 ...
