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A measure of the degree of linear association among a pair of variables.

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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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1answer
25 views

Evaluating the distribution of a continuous variable in a two dimensional space

I have performed a Principal Component Analysis on a set of hydrological indices. Those hydrological indices are derived from the discharge of some rivers (e.g. how long the river needs to get back to ...
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6 views

Which control chart can use for monitoring of covariance matrix of cofficient?

I have a series of panel data, which includes p cross section and t time. I estimated the covariance matrix of coefficients for periods for periods. Now my data includes the individual period and the ...
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8 views

Test the difference between two (genetic) correlations, when only standard errors and z-statistics are available

I have two correlations (genetic correlations actually), their standard errors, and their z-statistics (but I don't know the sample sizes). Is it possible to do a significance test for the difference ...
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21 views

Comparing how similar/different are two paired datasets, and how similar/different are from a third one

First time posting, I hope not to break any rules here. I have 3 datasets, d1, d2, and d3, each with ~5,000 values measured in the same regions (paired data?). I also have additional datasets d1', d1'...
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32 views

how to transform a mixed model estimate into a correlation?

With the following mixed model ...
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0answers
47 views

Confusion in terminologies for simple linear regression model [on hold]

When I try to understand big picture between regression and correlation, the terminologies get in the way, because of different conventions used in statistic books and online materials and also due to ...
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1answer
12 views

How to find false negative rate when there are multiple alternate Hypothesis?

I am testing for zero Pearson correlation and my null hypothesis is $\rho=0$. It is easy to find Type 1 error or rejection of Null hypothesis and hence the false positive rate. However, my ...
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13 views

Graph coloring - what node color represents in a network? [on hold]

I am extracting features from a network, in this case, structural features. In particular, it turns out that the graph coloring is very correlated (Pearson) with the target that I need to classify. ...
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2answers
19 views

Statistical measure for linear regression with two distinct clusters of points

In the following plot, I have a linear regression of 30 points, representing 10 treatments with three replicates each. As you can see, the r-squared value is quite strong (0.83) and the p-value is ...
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1answer
32 views

Variance of $Y|x$ from regression line

Using simple linear regression model, and sample correlation coefficient $r$, for a sample set $X,Y$, the true regression line could be given as below. $$ \hat{Y}|x = \overline{y} + r\dfrac{s_Y}{...
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17 views

Multivariate form of Pearson Correlation?

Suppose I have the following dataset below: With my understanding of Pearson's Correlation Coefficient, I could get a coefficient for Percentage Use vs. Average Age between timepoints. However, is ...
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0answers
11 views

Comparison of two correlations

I want to correlate stock price of one company and stock indice, taking the price at the end of the day for a period of six years. After that, I want to compare the link for two time series, non ...
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1answer
37 views

interpreting correlations from lmer object

I'm having problems understanding how to interpret correlations in mixed models ...
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0answers
12 views

Checking for correlation with different kind of data

I am trying to check if there is a correlation between different variables. I have values for: Nationality ___________________[Nominal] Age ________________________[Continous-Ratio] Height ...
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1answer
24 views

What is the difference between cross correlation and persons r correlation for two different signal?

What is the difference between cross-correlation and pearsons r correlation for two different signals? It will be very grateful if somebody explains with an example
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5 views

Any kind of analysis for multilevel data with correlational hypotheses?

I have collected some complex data and I have some questions on the best way to analyze them in order to answer my research questions. I have a sample of 165 preadolescents. They all come from the ...
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7 views

Cross-sectional correlation snapshot, how?

I have $N$ time series $x_{1t},x_{2t},\dots,x_{Nt}$. I could measure the pair-wise correlations $\rho_{ij}=Corr[x_{it},x_{jt}]$, and get an $N\times N$ correlation matrix. I can also get its largest ...
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15 views

How can I explore how the correlation of two variables vary with another variable?

Say if I have two tests A and B, and I conducted the test for 100 participants, and I suspect that the correlation of test scores of A and B varies with their income, and the relationship may be non-...
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7 views

How to put two correlation matrices into one document [closed]

I have two APA correlation tables which I have exported into separate documents. My question is, how would I make these two correlation tables go into the same document?
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6 views

How to measure correlations in psudo-random datasets?

I have two datasets with millions of y-values. (They are in chronological order so the X values have been omitted as they become merely an index.) ...
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1answer
29 views

Relation between Vector Auto-regressive models and correlation matrix

I am generating a multivariate time series using Vector Autoregressive Models- $$X(t) = AX(t-1) + \epsilon$$ where $X \in R^{n \times 1}$, $A \in R^{n \times n}$ and $\epsilon \in R^{n \times 1}$ is a ...
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8 views

Is this definition of partial covariance correct?

I have been looking for a proper measure-theoretical definition of partial correlation. Let $X_1, X_2, Y_1, ..., Y_n$ be Random Variables. Then the partial covariance between $X_1$ and $X_2$ given $Y$ ...
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1answer
54 views

how to find correlation coefficient when X and Y follows Poisson Distribution?

A bridge is examined for corrosion. It is believed that the corrosion on left side exist is poisson distributed with mean 3 and corrosion on right side is poisson distributed with mean 1.5+0.5X where ...
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1answer
30 views

Correlation of random variables

I am really new to probability and statistics. I have been wondering how common it is for two random vectors to be highly correlated. Correlations of exactly zero and one must have very low ...
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12 views

How to calculate correlation of bit list

I have 5 data streams of seemingly random bits, only 0's and 1's that I need to calculate the correlation between. The datastreams are seemingly random because I should have the same number of 0's ...
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14 views

Pearson's r, Point Biserial Correlation, and Sample Size effects

I am currently trying to test a model for cross-cultural adaption and need to do a simple correlation analysis between the predictor variables (language ability, adaptive motivation, degree of culture ...
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7 views

Which test to assess the degree of concordance between a childs response and their parent response to a questionnaire

I'm looking to assess whether the difference between a child's response, and their parent's response, to a nearly identical questionnaire is significant or not. Some papers have used Pearson’s ...
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21 views

Help in interpreting correlation coefficient and p-value

I have two variables called AC and Final_Coverage which I am trying to find their correlation. The range of ...
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0answers
65 views

Is my Correlation reasoning correct?

I am trying to understand how to arrive at $r = \dfrac{Cov(X,Y)}{\sigma_X\sigma_Y}$ with a logical narrative. This in fact is kind of continuation from my this unanswered question. I see that by ...
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47 views

How to derive correlation using regression without empirical proof?

I just finished learning MLE, Regression, Covariance and now in to Correlation.I want to transform logically from Regression to Correlation using Covariance. Regression: A simple regression model ...
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10 views

Not normally distributed data and point-biserial correlation

If the data for the continuous variable is not normally distributed (shapro-wilk sig = .000) can you still use a point-biserial correlation?? I have run the point biserial correlation to see and it ...
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2answers
222 views

Uncorrelatedness + Joint Normality = Independence. Why? Intuition and mechanics

Two variables that are uncorrelated are not necessarily independent, as is simply exemplified by the fact that $X$ and $X^2$ are uncorrelated but not independent. However, two variables that are ...
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1answer
47 views

Correlation with $\theta$ and with $e^{i\theta}$

I have a procedure for generating a random complex number $z=|z|e^{i\theta}$ (the procedure is quite complicated, but irrelevant for the question). I want to check whether the modulus and the argument ...
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8 views

Correlation 2D vector fields

Having multiple (hundreds) of 2D flow maps, ie vector fields how would one find statistical correlation between these? Plotting yields, for visualization purposes only: I am thinking about comparing ...
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1answer
19 views

Correlation coefficient with noisy data

I am trying to analyse the dependencies between some variables, looking at the Pearson and Spearman correlation coefficients (for now, at least). The problem is that one variable has known errors (for ...
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0answers
35 views

Simulate correlation matrix using a given structure

I want to generate correlation matrix such that it follows the below structure $$\Sigma = B \Lambda B^T $$ where $\Lambda$ is a diagonal matrix containing positive elements, $\Sigma \in R^{n \times n}...
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1answer
45 views

Test statistic for lopsidedness of transition matrix

I'm trying to figure out how to estimate, given a transition matrix for a stream of distinct things, what the p-value is that the underlying stream is memoryless. In order to simplify the problem, I'm ...
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1answer
82 views

Correlation between an observation and its rank in a random sample

Suppose $X_1,X_2,\ldots,X_n$ are i.i.d random variables with an absolutely continuous distribution. We say the observation $X_i$ has rank $R_i$ if $$X_i=X_{(R_i)}\quad,\,i=1,2,\ldots,n,$$ where $X_{(...
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1answer
13 views

How do I find out if there is a relationship between confidence (continuous variable) and accuracy(categorical)

I am looking finding out if confidence (rated between 0 and 10) has an effect on accuracy (correct or incorrect) and am unsure what test to run. My study is looking at how line up condition (PACE ...
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0answers
21 views

Pearson and R^2 Correlation between three variables

Get it from someone else but don't quite know how to answer. If $\rho_{X,Z}=0.4$, $\rho_{Y,Z}=0.3$, what is the range of $\rho_{X,Y}$? Here $\rho$ is the Pearson correlation coefficient. We run a ...
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1answer
37 views

Confusion with covariance

For distributions of random variables X and Y, their covariance can be defined as the difference between the multiplication of X and Y, normalized by their joint probability and the multiplication of ...
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1answer
54 views

P-value from sum of bootstrap vs ttest are different [closed]

I am learning about bootstrapping and I am calculating the correlation between x and y, between two independent groups with each size n=8 and n=24, respectively. Their distributions are non-Gaussian ...
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45 views

How to detect relationship between two variables over time?

Considering there are two series Sa, Sb over time T.Series Sa doesn't have a defined range and can range within any values , Sb ranges within 0-1. There are already pattern in the data such as when Sa ...
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27 views

Python generating correlated discrete numbers

firstly if you need some extra context, here is my question on the original post: https://stackoverflow.com/questions/53123638/python-generating-numbers-according-to-a-corellation-matrix?noredirect=1#...
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6 views

Finding patterns of co-occurrence in survey responses

I have responses from 3000 respondents to a number of survey questions and their options. Treating them as binary variables, I get a matrix of respondents vs 1/0 responses (like eg Surveymonkey ...
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1answer
22 views

Interpreting correlation coefficient after log transform

I have a pair of variables X and Y that exhibit non-linear relationship. The relationship is linearised by applying log10 transform to both (checked using scatter plots). Untransformed variables have ...
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1answer
30 views

How we can avoid making L2 regularization causing the model to learn a moderate weight for some non-informative features.?

Referencing to an example explained in free google machine learning course Imagine a linear model with 100 input features: 10 are highly informative. 90 are non-informative. Assume that all ...
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27 views

Does it make sense to maximize Person's correlation instead of minimizing MSE?

I can understand why it makes sense to maximize $R^2$, but I'm not so convinced that it makes sense to maximize Pearson's $R$. Partially because I don't understand how the "degree of linear ...
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1answer
26 views

Visualize Covariance when only probability mass and marginal functions are given

I am trying to intuitively understand Covariance like here. So if a random sample set given, I could draw rectangles with them, one of the cornes being fixated on mean $(\overline{x},\overline{y})$. ...