Tagged Questions

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

29 views

Transpose is just the way of generalizing a dot product?

It seems like $a^Tb$ is the same as writing $a \cdot b$ in matrix form. 1) Why is $n \times 1$ and $n \times 1$ matrix multiplication undefined? 2) Is this just a generalization of the dot product?...
20 views

How to find covariance matrix from correlation if mean is not given?

I'm given autocorrelation function of gaussian random process: $$R_x(\tau) = 3e^{|-\tau/3|}$$ Now I should find covariance matrix. I know the formula and solutions, where $$C_{xx} = R - E[X]E[Y]$$ ...
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Question about uncorrelatedness of random variables and distributions

I was wondering, if two random variables are dependent, does that mean that they must be correlated? does one imply on the other or vice versa? Also, if I know that a joint distribution of two ...
36 views

Generalizing Pearson's coefficient to determine properties of embedded manifold

I have the following dilemma: We know that for random vectors we have Pearson's coefficient of skewness. I think you all agree that in some sense it measures the shape properties of the ...
33 views

correlation matrix of an AR(1) process

Suppose we have a process whose elements follow an AR(1) pattern with correlation $\rho$. I am confused, concerning the following: The exact form of the $(i,j)$ element of the correlation matrix P is ...
248 views

How can I remove correlated noise spikes from 2 signals?

I have some MRI data collected across time. When the patient moves, this results in a spike in the signal (so I guess it's not really "noise"). I would like to identify and remove these. So far I ...
37 views

Ratio laying within the confidence interval still being depicted as having an influence?

I keep seeing this in research papers. The researchers claim that there is a positive correlation between A and B then subsequently show that they odds ratio/sample mean etc. is IN the confidence ...
1k views

Question on Spearman's Rank Correlation Coefficient

I'm doing some practice questions in my statistics book, and started doing this one: Find Spearman's rank correlation coefficient between X and Y for this set of data: $X$  $13$&...
58 views

Calculate mean and correlation of a stochastic process

I am given the Stochastic process $Y_n$, where $n \in Z$ defined by: $Y_n = X_n - X_{n-1}$ where $X_n$ is a process with independent and identically distributed geometric variables $X_n \sim G(p)$ ...
48 views

Limit of correlation function using transfer-matrix method

This question is about a stochastic process theory. I really very bad in this topic. That's why I have to ask for help. I may mistranslate some terms but I'll do my best to give you right information. ...
147 views

Minimize correlation between input and output of a linear system

I am not sure if "minimize correlation" is the right title for this issue but I could not find a better sentence to describe what I would like to achieve. Let's say that I have a black box with ...
If I understand the correlation theorem correctly, it states: $f(x,y) \unicode{x2606} \bar g(x,y) = \mathfrak{F}^{-1} \left\{ F^*(u,v) G(u,v) \right\},$ also called a phase correlation. Above $f(x,... 1answer 70 views Does correlation (PMCC) require variables to be normal When calculating product moment correlation coefficient between two variables, say height and weight, is it necessary that the variables are normally distributed for the PMCC to be valid/relevant. I'... 1answer 26 views Statistics for correlations with many (0,0) values Suppose you have a large but finite collection of tweets. You want to know whether talking about football tends to correlate with talking about basketball. You can generate a table for a few hundred ... 0answers 26 views Question about the relationship between correlations I am trying to figure out the relationship between correlations of variables where one of the variables defined as the difference between two other variables. I have variables x and z, which are ... 1answer 32 views Finding peaks and oscillations in a signal I am working on a problem where I'm analysing a signal and trying to find a measure of whether a roughly Gaussian shape appears or oscillations - though the oscillations may not be periodic. For ... 1answer 44 views Law of large numbers with correlated variables My sample is a series of measurements of the variable$x$. Measurement t,$x_{t}$, is correlated with$x_{t-n}$. However, as n tends to infinite the correlation tends to zero. If the sample grows, ... 2answers 67 views Correlation in scatter plot This may be a very basic matter for statisticians, but I still have no intuition for this sort of thing. Here goes: I have two quantities (the nature of which is irrelevant) which I suspect to be ... 0answers 54 views Calculation the Correlation Matrix of a Random Observation Vector I've googled and looked around on StackExchange but I can't quite find the answer. I'm trying to calculate the correlation matrix R. Below I've included a screenshot of some text that explains how. ... 0answers 37 views The correlation between alpha and beta Consider the following 2-variable linear regression where error$e_i$'s are independently and identically distributed with mean 0 and variance 1; $$y_i=\alpha + \beta (x_i - \bar {x}) + e_i$$ where ... 0answers 43 views How to convert principal components of a$2\times2$covariance matrix into principal components of a correlation matrix All, I am wondering if there is any way to mathematically express the change in direction of the principal components from the$2\times2$covariance matrix to the correlation matrix. In other words, ... 0answers 39 views Data analysis: How did people beat the Great Hall game? This is the game: There is a Great Hall with 102 doors. 100 of these doors lead to one of 100 different side rooms. The 101st door, at the end of the Great Hall leads to the Great Tower, where ... 0answers 27 views Is there any reason that cross correlation would perform well or poorly on sparse binary arrays? I am using matlabs xcorr to correlate simulated photon count data that has some Gaussian random noise set on top of it and it is working fine when the average value in the arrays is greater than one ... 1answer 31 views Which type of correlation should I use? I am beginner in statistics. I have excel table with few columns. I would like to find correlation between the variables. I have to make an essay to my boss and he wants concrete answers. I searchin ... 1answer 281 views How to curve fit an unknown function? I have data which can be described by$y=f(x,z)$where$z$varies from 170 ~ 154. Now values given by$ks$are known sample values that equals value given in the table header,$uks$are unknown ... 1answer 238 views Is it valid to get a correlation between moving averages? I have a 10 day moving average of one set of return data for one stock and a ten day moving ave of another stock. 400 data points and correlating 390. Can I now get a correlation between the two or ... 0answers 36 views Relationship between distributions of correlations$\rho(X^1,Y^1)$and$\rho(X^2,Y^2)$if$X^2=WX^1$,$Y^2=WY^1$and$W$is a known stochastic matrix? I have been stacked for a while with the following problem: Consider two samples of iid observations$X^1=\{X_1^1,\dots,X_n^1\}$and$Y_1=\{Y_1^1,\dots,Y_n^1\}$where$X_i^1 \sim \mathcal{N}(0,1)$and ... 0answers 64 views Let$U=2X$and$V=-3Y$. Find Correlation (U,V) given Correlation$(X,Y)=0.8$. Let$U=2X$and$V=-3Y$. Find Correlation (U,V) given Correlation$(X,Y)=0.8. My Steps: \begin{align} Correlation (U,V) & = \dfrac{Cov(U,V)}{\sqrt{Var(U)\cdot Var(V)}} \\ & = \dfrac{Cov(... 1answer 112 views Wedge Product Formula For Sine. Analogous Formula Generalizing Cosine to Higher Dimensions? So I was day dreaming about linear algebra today (in a class which had nothing to do with linear algebra), when I stumbled across an interesting relationship. I was thinking about how determinants are ... 1answer 43 views Independent variable vs. Uncorrelated variable confusion. How do I interpret this? I'm reading Time Series Analysis and Forecasting by Example by Søren Bisgaard and Murat Kulahci and I'm having trouble conceptualizing a particular passage and it's bugging me enough that I can't move ... 0answers 23 views FFT of k*k matrix from FFT of a j*j matrix FFT of matrix a j by j matrix, A \begin{bmatrix}1 & 2\\3 & 4\end{bmatrix} = \begin{bmatrix}10 & -2\\-4 & 0\... 2answers 77 views What is the rigorous justification for using inner products as a function of similarity between two vectors? In machine learning, it is a common thing to define similarity measures, specially using the so call Kernel function. Kernel functions are defined though through inner products of feature vectors:... 2answers 136 views Correlation of Proportions To introduce my question, here is a small simplification for consideration: LetX,Y$be independent random variates, each with finite mean and variance. Interestingly, $$\text{Corr}\big(\frac{X}{X+Y},... 0answers 59 views Increase the probability of correct prediction using multiple regression First off let me begin by saying that I'm brand new to statistics and I would appreciate it if you could dumb down any answers for my problem. I am trying to create a general prediction of how much a ... 1answer 925 views Uncorrelated but not independent random variables Is it possible to construct two random variables X, Y both of them assuming exactly two non-zero values which are uncorrelated, i. e. \mathbf{E}[X \, Y] = \mathbf{E}[X]\,\mathbf{E}[Y], but not ... 1answer 99 views Conditional Probability Distribution for two Discrete Uniform Random Variables with given Correlation Coefficient I consider a problem with two random variables X, Y \sim Unif\{a,b\}, for which I want to set a correlation coefficient Corr(X,Y)=\rho. Now, I am interested in the conditional probability mass ... 1answer 191 views Cross Power Spectral Density from Individual Power Spectral Densities Let X and Y be two zero-mean, wide-sense stationary random processes. The power spectral density of a process is the Fourier transform of the process's auto-correlation function. The cross power ... 1answer 946 views Probability of three events occurring given correlation? I am facing a problem that I cannot find the answer to. I have three variables, A, B and C. There are only two possibilities for each of these, A either happens or it does not, B happens or it does ... 0answers 116 views Correlation Matrix using Matrix Algebra, not the Same as Result from Excel I am attempting to verify a calculation found at another question on this site. The formula is said to provide a correlation matrix using q = D-1ED-1 where q is the correlation matrix; E is the ... 2answers 37 views correlation between \sum_{i=1}^{98}X_i and \sum_{i=3}^{100}X_i Let X_1,...,X_{100} be iid N(0,1) random variables. The correlation between \sum\limits_{i=1}^{98}X_i and \sum\limits_{i=3}^{100}X_i is equal to (A) 0 (B) \dfrac{96}{98} (C) \dfrac{98}{... 0answers 45 views How to find covariance of sample mean and sample standard deviation I have a question to find the covariance of sample mean and sample standard deviation based on the following: I have tried something on my scratch paper, but for some reason, I cannot upload on here.... 1answer 64 views Linear Regression and finding Correlation Coefficient In a Simple Linear Regression y= \alpha + \beta x + \epsilon , we gather this information: S_y=20, S_x=5, \widehat{\beta} = 0.2 how I could find Instance Correlation Coefficient between x and ... 0answers 113 views Covariance matrix using squared exponential function I'm writing down the covariance matrix K of a vector X using squared exponential covariance function, and then evaluating the determinant of the matrix K. Let's say i add a new point to X , and ... 0answers 16 views Augmenting a matrix with a highly-incorrelated column Consider a binary matrix:$$\begin{pmatrix} 1 & -1 & 1 \\ -1 & 1 &1 \\ \vdots & \vdots &\vdots \\ 1 & 1 & -1\end{pmatrix}$$with a random distribution of 1 and -1 ... 1answer 42 views Given f(x) and two correlated random variables x & y, how do I estimate the correlation of f(x) & f(y) I have a smooth continuous well-behaved function f(x), where f(x) is positive and mononically increasing with x, and x is positive real continuous variable. Given the mean, variance, and correlation ... 0answers 20 views Convergence under rank correlation I have a following setup: Let$c\in{\Bbb R}$,$R^2\in [0,1]$and$\Psi,\varepsilon_1,\varepsilon_2,\ldots$independent random variables on a probability space$(\Omega,{\cal A},{\Bbb P})$. Define the ... 1answer 66 views increment of Brownian motion squared [closed]$(W_t)_{t \geq 0}$is Brownian motion, assume t>s, does$E[(W_t-W_s)^2W_s^2]=(t-s)s$? In other words, are$(W_t-W_s)^2$and$W_s^2$independent? 0answers 21 views Why is pure sample covariance a bad metric to understand the degree of correlation between two variables? Covariance helps you understand how variables are linearly related. Would it be possible to have two pairs of variables in a deterministic relationship (i.e. linearly correlated variables) that have ... 0answers 50 views Two forms of cross-correlation Wikipedia and MATLAB defines cross-correlation in this way. In time series analysis (P21), it defines cross-correlation upon cross-covariance: Let$\{X_t\}$and$\{Y_t\}$be two time series,$\mu_{xs}...
Say we have stochastic differential equation $\frac{dx}{dt} = n(t)$ where $n(t)$ is a noise process. $n(t)$ has a correlation function $R(t - t') = <n(t)n(t')>$ If the noise process is white ...