# Questions tagged [correlation-matrix]

A $k\times k$ matrix of correlations between all pairs of $k$ random variables. All its diagonal elements are equal to one.

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### Test for multicollinearity with binary and continuous independent variables

I have a question concerning multicollinearity: I have several independent variables. Some are binary and some continuous. The dependent variable is binary. Can I use the Pearson correlations to test ...
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### Sample covariance of t distribution and degree of freedom

If $X$ is a P by N size matrix, $X_{ij} \sim N(0,\sigma_i^2)$ if I standardize this X matrix with sample mean and sample variance (assuming I don't have access to the population mean and variance) I ...
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### Sample correlation matrix: $\hat{\mathbf{R}} = - \sum_{i=1}^{N}\sum_{j=1}^{N} \mathbf{x}_i \mathbf{x}_j^\top$?

Suppose we have the set $\{\mathbf{x}_i\}_{i=1}^{N}$, where $N$ is the size of the data set and $\mathbf{x}_i \in \mathbb{R}^m$ is the $i$th $m$-sized regressor. The question is simple: how to compute ...
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### Looking at how covariance/correlation between variables differs in two groups?

I have a few hundred variables representing different biomarkers. These variables have been measured in both cases and controls. The underlying units of measurement are not important, so I have ...
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### How can I compare one full PCA model to two smaller ones?

I have nearly 30 variables going in to a large PCA, but the variables really fall into two conceptual categories. I want to test whether leaving all the variables to correlate freely with one another ...
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### Generate two random correlation matrices which share equal correlations

My setting is, I want to simulate a data set in two conditions, e.g. control and disease. I want them to share mostly the same correlations except some should be different to simulate a "signal&...
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### How to pick a subset of the rows of a matrix data sample so that the resulting correlation matrix of the curated data approaches the identity matrix?

If I have a data sample in the form of a matrix $X$ of dimensions $n \times m$, is there a standard procedure to optimally pick $n'$ rows ($n'$ fixed) of the matrix $X$ so that $C_{X'}$, the ...
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### What is the null and alternative hypothesis of a chi square test whether a single matrix is an identity matrix?

Say I had a correlation matrix: $$M = \begin{bmatrix} 0.8 & 0.1 & 0.1\\ 0.3 & 0.7 & 0.1 \\ -0.1 & -0.2 & 0.9 \end{bmatrix}$$ I want to show that it is approximately an ...
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### Correlation bounds in terms of spectral radius

My application requires that the following is true for random variables $X$, $Y$ in $\mathbb{R}^d$ with $E[X]=0, E[Y]=0$ and spectral radius $\rho$ $$\rho(E[XX]^{-1}E[XY]E[YY]^{-1}E[YX])<0.5$$ Can ...
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### What came first, the covariance or the correlation matrix?

Covariance can be calculated from correlation and correlation can be calculated from covariance. Is it sufficient to refer to them as only transformations of one another? Is one considered more of a ...
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### How can one derive the original data from the correlation- or covariance matrix of that data?

How can one derive the original data from the correlation- or covariance matrix of that data? I know the way a new, reduced dataset can be calculated from the correlationmatrix and it’s eigenvectors ...
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### Clustering data based on correlation

I have a dataset where each row represents a sample and each sample is described by its chemical composition. You can see the 10 first rows of the dataset in figure 1. Figure 1 - Each row represent a ...
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### Bounds for common correlation of uncorrelated random variables with another random variable

Suppose we have a random variable $y$ and a collection $(x_1,\dots,x_n)$ of $n$ random variables that are all uncorrelated: $\operatorname{corr}(x_i,x_j) = 0$ $\forall i \ne j$ and that all have the ...
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### Correlation matrix: decline in correlation

I performed a correlation matrix with Python. The following variables were included total_equity,net_income,...
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### Calculate unbiased standard errors for a regression from latent factor correlations

I have a SEM where various latent variables are correlated with each other. I want to use a subset of these correlations to run a regression. This can be done easily enough to find point estimates, ...
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### How to determine mse of estimate from correlation matrix of estimate error?

I have a model of an information transmission system Y = XH + N, where X is a diagonal matrix with the transmitted "symbols" (known), H is a column vector which distorts the transmitted symbols and N ...
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### Eigenvectors for correlation and covariance matrix PCA

I know the generally reasons of using correlation matrix vs a covariance matrix when doing PCA (and visa versa) however when thinking about the eigenvectors (principal components of the data) of each ...
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### Change in eigenvalues due to perturbation to a correlation matrix

Let $A$ be a $m \times n$ matrix defined as $A = \Big[\frac{a_1}{\|a_1\|} \cdots \frac{a_n}{\|a_n\|}\Big]$ and $a_k \in \mathbb{R}^{m\times 1}$ where $k \in [1,\dots,n]$. Now, we define a ...
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### How to simulate random correlation matrix containing off diagonal structures

I want to simulate a correlation matrix which has some off-diagonal structures and also should have some hierarchical structures. For simulating correlation matrices which contain hierarchical ...
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### Do the Determinants of Covariance and Correlation Matrices and/or Their Inverses Have Useful Interpretations?

While learning to calculate covariance and correlation matrices and their inverses in VB and T-SQL a few years ago, I learned that the various entries have interesting properties that can make them ...
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### Cluster analysis using the posterior distribution of a Bayesian correlation matrix

Background and Problem I recently ran a Bayesian multivariate epidemiological meta-analysis on prevalence estimates for several disorders. This analysis included a probit-based model to deal with the ...
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### Does using a covariance matrix of scaled and centered variables compare with using a correlation matrix?

I have some data with features which have different units of measurements. Here, by data, I'm trying to say that the row represents the observations and column the features. There are correlations ...
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### Correlation matrix for biostatistics [closed]

I want to convert the expression of the genes from an array to a gene correlation matrix, to know the correlation of each gene with the other genes. I have 6 samples, 3 controls and 3 test, is it ...
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### correlation matrix test: is this code correct or is it missing a multiple comparisons correction?

I have $m$ variables $x_1,\dots,x_m$, measured in $N$ independent tests $\{x_{i1},\dots,x_{im}\}_{i=1}^N$, leading to the design matrix $X$. I noted that the demo function ...
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### Check whether a sample correlation matrix is valid [duplicate]

Is it possible to have the following sample correlation matrix for $x$, $y$, $z$? $\begin{pmatrix} 1 & 0.8 & 0.2 \\ 0.8 & 1 & 0.7\\ 0.2 & 0.7 & 1\end{pmatrix}$ Where a 3 by 3 ...
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### Reporting Fisher-transformed Pearson's correlations when the magnitude of difference is relevant

My field regularly demonstrates a certain type of result with pairwise Pearson's correlation matrices between predicted and measured data. As soon as such correlations become high, Fisher-transforming ...
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### Is there a serious problem with dropping observations with missing values when computing correlation matrix?

I have this huge data set with like 2500 variables and like 142 observations. I want to run a correlation between Variable X and the rest of the variables. But for many columns, there are entries ...
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