Correlation Definition and 370 Threads

Homework Statement Find correlation between random variables x and y in the following: $$P_{x,y}(x,y)=A \ xy \ e^{-(x^2)}e^{-\frac{y^2}{2}}u(x)u(y)$$ Homework Equations The co-variance ##\sigma_{xy}=\overline{(x-\bar{x})(y-\bar{y})}## or ##\sigma_{xy}=\overline{xy}-\bar{x}\bar{y}##...

Is it feasible to calculate a three-point correlation on the lattice? Say, I have two quark fields separated at z_1+z_2 and 0, and a gluon field inserted at z_2. Also I need two gauge links to make this expression gauge invariant: \bar{\psi}(z_1+z_2) \Gamma(z_1+z_2; z_2) F^{\mu\nu}(z_2)...

I want to know how the artificial intelligent become integrated or can improve more automation systems and machine that build in automatic way Display screen, solar cells, lithium ion batteries, printed circuit boards and 3D printers. I know that these automation systems and machine are...

Let 'x' and 'y' be two random variables with zero mean. We find that 'x' is related to 'y' with a correlation coefficient 'c'. Now let us say we are splitting 'x' into correlated term 'xc'and uncorrelated term 'xu' Then we have x= x_c + x_u \\ \overline{x^2}= \overline{(x_c +...

A gravitational field and a magnetic field both decrease in strength at the distance squared. They are two totally different forces so why the correlation?

Hi everyone I'm about to undertake my final year project and i will be researching and writing on THE EFFFCT OF HEAT ON THE MAGNETIC SUSCEPTIBILITY OF TOPSOIL and how it relates to SOIL FERTILITY.. I really need help on how to go about it and i'll also need links on contemporary...

I have simulated a box water molecules (1500 water molecules) using molecular dynamics method in NpT ensemble. I got the time auto-correlation function (C(t) vs t, time) where its function line is parallel to x-axis. Which means the C(t) is zero. I understand the water molecules are...

I need a simple mental physical picture of interface roughness. If the auto-correlation function of surface roughness is Gaussian, does a long correlation length connote a smooth surface or not? I do not seem to be able to find a simple picture that would appeal to me physically. Thanks all for...

As far as I know, friction force is equal to the product of the normal force and coefficient of friction, hence is independent of surface area. So why is it that race cars have wider tyres than conventional vehicles?

Hello! We are trying to verify if an acoustic standing wave has been established in a cavity. In order to do so, we are giving a constant frequency signal to a speaker. We are picking up the signal at two locations, one very close to the speaker(reference signal) and at a particular...

Determinant of "enlarged" Correlation Matrix Hi guys, I am not a physicist but saw that you guys are actively discussing math problems in this forum. I have the following problem that I've been fighting with for some time now: I have a n-dimensional (n >= 3) correlation matrix with the...

Hi all, I think this is probably the only decent question I've come up with about how to handle my future. I really, really want to study cosmology. I am a recent graduate (graduated in May) with a BA in physics. My GPA is mediocre - 3.5 in the major and overall. I'm sort of...

What is the deferences between Exchange and correlation and also what is Exchange-correlation hole?

Hi, Are you aware of any dataset (in R or elsewhere) consisting of a sample from two variables where the correlation coefficient is (approximately) equal to 1, but the variables refer to completely irrelevant things, i.e. one measuring something that happens on Earth and the other something...

Hi all, I'm studying for my Quantum Optics exam and still have problems with the second-order correlation function. The question concerned is question 3b, 3c etc which can be found here: http://www.arago.utwente.nl/comms/sotn/tentamendatabase/optics/qo/351500_Quantum_Optics_2010-11-03.pdf...

I have two variables where the regression line is just the mean as a constant. As such, the correlation is zero. However, when I perform k-fold cross validation (in Weka) this becomes non-zero. I have no idea why this is. The regression line for whatever the test set is will always be a...

Why would a p-value greater than .95 plausibly indicate that the errors/uncertainties were overestimated, i.e. a small chi-square?

Hello. I need to find the expectational value of the correlation energy between two electrons which repel each other via the classical Coulomb interaction. This is given by the 6-dimensional integral: \left\langle\frac{1}{|\vec{r}_1 - \vec{r}_2|}\right\rangle...

I've noticed an interesting observation about how the lives of all the people in my elementary AIG (academically intellectually gifted). Out of the 11 of us, the only two not to go to college came from very poor homes. (Even from the beginning, only 4 of us were the kids of a...

How to prove that two poisson processes can never be negatively correlated.

Different correlation coefficient results between Matlab and Excel. Please Help! I have two sets of dat as below. A problem is that MATLAB and excel returns a different value of correlation coefficient (i.e., 0.801 from Excel and 0.786 from Matlab). For Matlab, I used the function...

The quantum physics forum is full of questions about why entanglement can't be used to signal superluminally. My question is this: do these questions usually still make sense if we replace entanglement by classical correlation? For example, I can send Alice and Bob each a random bit but with...

hello, Thank you to understand that this is not a homework! I have to evaluate the uncertainty of a measurement but the baseline is also with uncertainty (correlation). I would like to have some ideas or suggestions on the best way to evaluate the uncertainty. Here is the problem: We...

Hello all. I am not a stats person so I would like some help/confirmation on this one. What I am trying to achieve (if possible) is a metric on how two portfolios (or strategies) are correlated. Imagine there are two portfolios of assets A,B,C,D... with different weights of each asset...

Hi I have stumpled upon the following expression for the correlation function of the photocurrent shot noise for a photodiode <\delta i(t)\delta i(t+\tau)> = \frac{e^2\eta}{h\nu}P\delta(\tau) where η is the quantum efficiency and P the power in the signal. δ(τ) denotes the Dirac delta, which...

We all know that if the covariance is positive then it means that if one increases then the other one also increases. If the covariance is negative it is the other way round. I know to calculate the covariance and deduce the relation between them. But I don't get an intuitive feeling regarding...

Hello everyone, I have a question (perhaps a very noob one as well!) regarding correlation between variables where the number of observations are different between the two sets. So, I have some 32 responses generated from a survey which aim to measure certain variable and I want to...

Hi, Look at \begin{align} & \int d^4 x d^4 x_1 d^4 x_2 d^4 x_3 d^4 x_4 \exp [i(p_1 x_1 + p_2 x_2 -k_1 x_3 -k_2 x_4)] \\ & \times (-i\lambda)D(x_1-x)D(x_2-x)D(x_3-x)D(x_4-x) \end{align} for first order in lambda for 2-2 scattering. In Maggiore I am told to substitute y_i=x_i-x as a...

Hello everyone! I'm coming to notice day by day how our education is purely focused on memorizing and applying formulas rather than understanding the concept. Assume we have the following: $X = aR + N$, and $Y = bG + W$, where $X, Y$ are random vectors, $R, G$ are strongly correlated random...

Hi, Haven't studied math for a while and thought I'd ask you for help. It regards implied correlation based on implied volatility for FX options. (b/c)=(a/c)/(a/b) Var(b/c) = Var(a/c)+Var(a/b) - 2*Sigma(a/c)*Sigma(a/b)*Corr(a/c,a/b) When breaking out the Corr(a/c,a/b) from the...

Is correlation between 2 time-series a useful indicator? In currency pairs for example, sometimes the correlation between 2 pairs (e.g. EUR/USD and GBP/USD) for the past x days is strong, but it can weaken very fast. Should I just take the average over time and go with it, or is there a better...

Hello everyone I'm new here: So I was about to write some SAS or R to do the following, but now I'm getting old enough to realize most things I think of were thought of before (usually by people way smarter than me). I've done some googling, but I haven't found the golden answer yet. I'd...

I've always been told "correlation does not imply causation." However, I've never been told much about whether it can imply a probability of causation. Moreover, there seem to be competing and often misused definitions of "to cause", i.e., use in a syllogistic sense versus use in probabilistic...

I would like to know what is the difference between real-space correlation and redshift-space correlation functions?

Hi, I have been trying to write a code to calculate velocity correlation function so that I can obtain a frequency spectrum for my system on taking a Fourier transform. For testing my code I generated a sine wave data and calculated vcf and took dft. I got correct frequency value but the peak...

I'm currently trying to make some intuitive sense out of Quantum field theory, but I'm not really understanding the vacuum. Consider a real (or complex, with + in the right places) scalar particle (a Klein-Gordon field). Now consider the propagator (or correlation function) G(x-y)=...

We have 18 subjects chosen at random, and they are rated by 6 randomly selected raters, and there is no requirement that the same rater rate all the subjects, we have a completely random one way design. Reliability is assessed with a ICC(1,1) or ICC(1) model depending on convention. The table...

I have a bunch of data for volleyball and I am trying to figure out how correlated certain stats are to winning a game. Here is a small example of the data set. Pts Err Diff EFF% Win 21 10 11 .360 1 21 10 11 .350 1 18 11 7 .250 1 14 6 8 .280 1 19 10 9...

Homework Statement I uploaded a picture to describe the problem. Oh yes, if anyone is wondering, the constant "c" = Var(R2) = 0.0046 . Homework EquationsThe Attempt at a Solution I uploaded my attempt at the solution. However, my method took me forever to get the answer, if I tried to do...

Homework Statement Prove the following: Let \rho be the correlation coefficient. Prove: \rho(X, Y) = 1 \iff P(Y=aX+b) = 1Homework Equations \rho(X, Y) = cov(X,Y)/\sigma_x\sigma_y The Attempt at a Solution I have no idea how to prove this, I know that rho must lie between 1 and -1 (inclusive)...

Hello all, Imagine two spin 1/2 particles that are entangled, going towards two stern-gerlach apparatuses, with some relative angle. Now imagine one stern-gerlach device measures the spin of one of the particles as up. What is the chance that the other stern-gerlach device measures the spin...

hi i want to know that what is quantum and classical correlation. is there any book or paper? thanks

I wanted to compute the conditional pearson correlation (CPC). First, I wanted to make sure if it is OK to use the absolute pearson correlations in the computation of CPC. Becuase I think only the strength of pairwise correlations should be considered in computing CPC, and not the sign. Second...

Homework Statement Homework Equations SS(x-(mean x))(y- (mean y) f(x,y) dxdy (note: SS=integers for x and y) The Attempt at a Solution

I am confused how to interpret the result of preforming a normalized correlation with a constant vector. Since you have to divide by the standard devation of both vectors (reference: http://en.wikipedia.org/wiki/Cross-correlation#Normalized_cross-correlation ) , if one of them is constant (say a...

Hi I have a stationary gaussian process { X_t } and I have the correlation function p(t) = Corr(X_s, X_(s+t)) = 1 - t/m, where X_t is in {1,2,..,m}, and I want to simulate this process. The main idea is to write X_t as sum from 1 to N of V_i, X_t+1 as sum from p+1 to N+p V_i and so on, where...

Homework Statement Let x(t) be a transmitted radar pulse. The received radar pulse is y(t). y(t)=ax(t-t_{d})+v(t) Where v(t) is the additive noise and td is the time delay. The signals x(t) and y(t) are sampled and processed digitally to determine the delay The discrete time signals...

I'm new to the field of signal processing and currently reading a paper which it uses cross-correlation of two signals for detecting some machine failures. But I'm confused with the complex conjugate in the equations. Take equation from wikipedia as example: (f\star g)(t)\equiv \int_{-\infty...

Hello everyone, I've got a quick question... Given two entangled photons, going through a polarization filter with relative angle a, what is the correlation between the two "answers" (whether the photon is blocked or let through)? I believe it's either cos(a) or cos^2(a), but I'm not sure...

I've searched the forums but am unable to find an answer to this: Given two variables with a correlation, you can predict one from the other using the familiar E(Y|X) = EY + r * s_y * (X - EX) / s_x What I want to know is how to predict values from multiple variables, especially when these...