Correlation Definition and 338 Threads

I recall reading that, while it is not true for all fields, there is a correlation between standardized test scores and academic performance in math and science. I did a quick search, but couldn't find much information that was specific to math and science. I teach AP Calculus and this subject...

Homework Statement The linear prediction of one random variable based on the outcome of another becomes more difficult if noise is present. We model noise as the addition of an uncorrelated random variable. Specifically, assume that we wish to predict ##X## based on observing ##X + N##, where...

I do not fully understand how non local correlation functions are derived from the differentiation of local ones. Specifically how in the following paper equation 23 is derived from 21 since the paper implies H and dpdq are invariant under time...

Suppose that I have already calculated the two-point correlation function for a Lagrangian with no interations using the path integral formulation. \langle \Omega | T[\phi(x)\phi(y)] | \Omega \rangle = \frac{ \int \mathcal{D}\phi \phi(x)\phi(y) \exp[iS_0] }{ \int \mathcal{D}\phi \exp[iS_0] }...

Homework Statement I'm doing a research project in which there's a survey given to respondents from 3 different groups of education(high school vs university etc) related to STD contraction rates. On the survey there's a question asking how many STD's they have contracted over their lifetime...

The definition I have for a 2-point correlator is $$\langle \phi_1(x_1)\phi_2(x_2)\rangle = \frac{1}{Z} \int \mathcal D \phi \,\,\phi_1(x_1)\phi_2(x_2) \exp-S[\phi],$$ where ##Z = \int \mathcal D \phi \,\,\exp-S[\phi]##. I am trying to understand the overall physical meaning of such a quantity...

Hello, I recently started going through some lecture notes on linear systems and Fourier optics. (By the way, I just started with these, but so far the lecture notes are excellent. If anyone is looking to learn the subject but doesn't want to spend money on a textbook, the lecture notes, and...

Does anyone have a good reference or references that go into detail on rigorous/formal developments of 2-point correlation functions for curvature perturbations (and related perturbations) in the cosmological context? I'm using the TASI lectures in inflation, Mukhanov, and Dodelson but none of...

Hi folks, Been trying to fill some of the more formal gaps in my knowledge by tackling the more technical stuff in P&S Chapter 7. Their derivation of the LSZ formula is quite different to those of books like, say, Srednicki, as they basically Fourier transform the whole argument as I...

I have a byte array of length 16384 bytes obtained from random.org/bytes. There is a random number sequence test program available from http://www.fourmilab.ch/random/ that, when run on my byte array, returns the following: Entropy = 7.989469 bits per byte. Optimum compression would reduce...

Hi! I'm a bit stumped on this computer-science-related statistics (I think that's what it would fall under) problem. It's over here: http://math.stackexchange.com/questions/796517/correlation-between-the-degree-of-two-vertices-in-an-undirected-graph/796526?noredirect=1#796526 It would be...

Homework Statement 1. Assume each birth in a hospital on a given day is independent of one another, and each birth, P(boy)=0.48. What is the probability that the 8th baby born is the 5th girl. 2. Two random variables X and Y have joint distribution given by. What is their correlation. 3. Z...

Using correlation coefficients as x in a regression?? I was reading an article in the Wall street journal and the author was using a rolling correlation coefficient, on a set of variables, as his predictor variable in a linear regression. Basically it was a uni-variate linear regression , y=...

i was given a table for calculating joint and marginal distribution. then i was asked if the variables are positively correlated or not. i know what positive correlation is, but how do i determine that from a table?

Homework Statement Why is the correlation coefficient between -1 and +1? Homework Equations we know correlation coefficient \rho = \frac{E[xy]-E[x]E[y]}{\sqrt{\sigma_{x} \sigma_{y}}} OR r = \frac{\sum ^n _{i=1}(X_i - \bar{X})(Y_i - \bar{Y})}{\sqrt{\sum ^n _{i=1}(X_i -...

Basically, The Ornstein-Uhlenbeck (OU) process (and its time-integral) decribes the velocity of a brownian particle. The OU process is Stationary (in time), Stochastic AND Markovian. Now, I've done an exact, one dimensional, numerical simulation of the OU process similar to D. T. Gillespie in...

x(n)=exp(i(x*n+theta1)) +exp(i(y*n+theta2)) x and y are constants , theta1, theta2 are uniform random on [0,2*pi] R(f) =E[{ exp(i(x*n+theta1)) +exp(i(y*n+theta2)) }exp(-i(x*(n-f)+theta1)) +exp(-i(y*(n-f)+theta2)) }] = 4 products 2 of which will be similar but with the opposite constants...

So I am still studying for CFA level one, and it has been years since I took a statistics course. Anyway, the formula is Correlation=Covariance(x,y)/(standard deviation of x times the standard deviation of y) It is easy enough to calculate...but where did the formula come from? As in...

Homework Statement I wish to determine whether a SINGLE instrument provides reliable measures (test-retest reliability). This single instrument is not random (it's the only one available), and I will take 10 measurements for each individual that is part of a control group (and then again for...

Hi. I have a doubt on the derivation of the correlation function for the velocity and position in Brownian motion from the Langevin equation. I have that for a brownian particle: ##\displaystyle v(t)=v_0e^{-\frac{\gamma}{m}t}+\frac{1}{m}\int_0^{t}dse^{-\frac{\gamma}{m}(t-s)}\xi(s)## (1)...

What is "Correlation length"? Hi everyone, I want to know meaning of "correlation length". Correlation function is usually used in statistics, so I think correlation length also similar meaning. But some paper used correlation length to explain roughness factor. Plz, anyone reply...

Hi, I'm trying to figure out something I'm pretty sure is true, but don't know how to prove it. I couldn't find the answer with a google search, but hopefully someone here knows the answer! So I have a linear least squares multiple regression model: Y=a+bX1+cX2+e where a is the intercept, X1...

Hi all, Do anyone know what is the spin correlation and what its relation to theNarrow Width Approximation. Regards, Safinaz

Background: My lab group has taken a number of measurements of gas levels over 15 minute period every 15 seconds. We actually used a gas sensor and computer interface to do it so it pretty much did all the work. In calculating the errors for the data, using the uncertainties given in the user...

For a two-point correlation function, it's my understanding we can interpret this as the amplitude for a particle to propagate from one point to another. Is there a similar interpretation for 3- or higher-point correlation functions? When are these used? Thanks!

While reading Zurek paper Decoherence and the transition from quantum to classical -- REVISITED, he makes the statement: What exactly is a "robust enough" correlation (from a interaction with the environment)?

Hi, I would like to know, how do I evaluate the quality of correlation? Specifically, I have a set of N datapoints, each represented by k features. I want to know how the k features correlate with each other, and therefore, I created a k by k correlation matrix. I am using R-value, so the...

Homework Statement ##X##, ##Y## and ##Z## are uncorrelated random variables with variances \sigma^{2}_{X}, \sigma^{2}_{Y} and \sigma^{2}_{Z}, respectively. ##U=Z+X## and ##V=Z+Y##. Find \rho_{UV}. Homework Equations \rho_{UV}=\frac{Cov(U,V)}{\sqrt{Var(U)Var(V)}} The Attempt at a Solution...

I've been reading Coleman's notes and the book on QFT by Ticciati. There they both place a lot of emphasis on computing the scattering matrix S. I can follow their computations (using Wick's theorem etc.) but I don't really have a good understanding of what S actually tells you. Ticciati even...

Hello, I have just started learning these things, would really appreciate any help on this. There are 4 nodes in a network (say A,B,C,D)and each node has certain failure probabilities( P(af),P(bf),P(cf),P(df) ). Then,I have this 4x4 correlation Matrix which contains the correlation...

The model of damped harmonic oscillator is given by the composite system with the hamiltonians ##H_S\equiv\hbar \omega_0 a^\dagger a##, ##H_R\equiv\sum_j\hbar\omega_jr_j^\dagger r_j##, and ##H_{SR}\equiv\sum_j\hbar(\kappa_j^*ar_j^\dagger+\kappa_ja^\dagger...

Entanglement swapping - any correlation between previous partners? Is there any correlation between previous partners/group in entanglement swapping? The question is illustrated with an example below: Alice has A & B entangled Bob has C & D entangled Charlie entangles B & C, which...

Homework Statement Consider a physical system made of 2 particles , particle (1) and particle (2)of the same mass m, which don’t interact with each other and which are both placed in an infinite potential well of width a. Denote H(1) and H(2) the Hamiltonians of each particles by |ψ1> and...

Homework Statement Homework Equations r=\frac{S_{xy}}{S_{x} S_{y}} S_{x}=\sqrt{\Sigma(x-\bar{x})^2} The Attempt at a Solution I have calculated the value of Sx several times and I got 43.3 but the answer key said that Sx = 11.2 1. Is my formula correct? 2. If yes, is my...

Homework Statement calculate the rank order correlation between the following data: 6, 5, 4, 2, 3, 3, 8, 3, 7, 6, 7, 5, 5, 4, 2, 7, 6, 2, 4, 6 4, 3, 6, 7, 6, 7, 1, 9, 1, 2, 3, 4, 5, 5, 7, 1, 2, 9, 5, 4 Homework Equations Following the output from...

Hi, I have these 2 problem, that I'm not so sure how to handle. 1-Let $$X_1,X_2,...,X_n$$ independant Random variable that all follow a continuous uniform distribution in (0,1) a) Find $$E[Max(X_1,X_2,...,X_n)]$$ b) Find $$E[Min(X_1,X_2,...,X_n)]$$ where E is for the...

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 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...