Questions tagged [partial-correlation]

Partial correlation is the correlation between two variables when some other variables are controlled for. An example is the partial autocorrelation function in time series.

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Why does inversion of a covariance matrix yield partial correlations between random variables?

I heard that partial correlations between random variables can be found by inverting the covariance matrix and taking appropriate cells from such resulting precision matrix (this fact is mentioned in ...
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Multiple regression or partial correlation coefficient? And relations between the two

I don't even know if this question makes sense, but what is the difference between multiple regression and partial correlation (apart from the obvious differences between correlation and regression, ...
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How to deal with high correlation among predictors in multiple regression?

I found a reference in an article that goes like: According to Tabachnick & Fidell (1996) the independent variables with a bivariate correlation more than .70 should not be included in ...
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ACF and PACF Formula

I want to create a code for plotting ACF and PACF from time-series data. Just like this generated plot from minitab (below). I have tried to search the formula, but I still don't understand it well. ...
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Are standardized betas in multiple linear regression partial correlations? [duplicate]

Since standardized betas are correlation coefficients in bivariate regression, is it the case that standardized betas in multiple regression are partial correlations?
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Difference between autocorrelation and partial autocorrelation

I have read some articles about partial autocorrelation of time series and I have to admit, that I do not really comprehend the difference to a normal autocorrelation. It is often stated that the ...
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Intuition behind the names 'partial' and 'marginal' correlations

Does anybody have an idea about why conditional correlation between 2 variables is called "partial" correlation and the simple correlation between them (so, when not conditioned on any other variable) ...
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Meaning of Square Root of Covariance / Precision Matrices

Say $X \in \mathbb{R}^n$ is a random variable with covariance $\Sigma \in \mathbb{R}^{n\times n}$. By definition, entries of the covariance matrix are covariances: $$ \Sigma_{ij} = Cov( X_i,X_j). $$ ...
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Meaning of partial correlation

From Wikipedia Formally, the partial correlation between $X$ and $Y$ given a set of $n$ controlling variables $Z = \{Z_1, Z_2, …, Z_n\}$, written $ρ_{XY·Z}$, is the correlation between the ...
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Partial Correlation Interpretation

I was calculating a correlation between two variables (A and B) which revealed these variables are highly correlated. I know that one variable is also highly correlated with another one (C), therefore ...
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Why does uncertainty of the autocorrelation coefficient increase as lag increases?

The Python module statsmodels contains functions for ACF and PACF. Below is an example from the docs with a plot that shows the (zero-centered) confidence ...
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Copulas for generating uniform random variables with correlations

I want to generate uniform random variables which have a correlation structure defined by a graph i.e. a variable is only correlated with its neighbors in the graph and is uncorrelated with the rest ...
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Example where a simple correlation coefficient has a sign opposite to that of the corresponding partial correlation coefficient

Give some examples where a simple correlation coefficient has a sign opposite to that of the corresponding partial correlation coefficient and comment on it. It is a question from an examination ...
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What's the intuition behind Velicer's minimum average partial (MAP) test?

In my field both the parallel test and Velicer's minimum average partial (MAP) test are commonly used when researchers are considering how many factors to retain in factor analysis or components to ...
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Geometric intuition for why an outer product of two vectors makes a correlation matrix? [closed]

I understand that the outer product of two vectors, say representing two detrended time series, can represent a cross-correlation (well covariance) matrix. I also know that the inverse of a ...
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In linear regression, what does $\beta_1 = 0$ really mean?

If granted omniscience and we know that $\beta_1$ in a multiple linear regression model is truly 0, what does that mean in words (and math notation)? The model is: $Y = \beta_0 + \beta_1X_1 + \...
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Testing for conditional independence: What's the correct way?

My goal is to check if two variables $X$ and $Y$ are conditionally independent given $Z$. For simplicity, let's assume the joint distribution is multivariate normal. In this case, we can compute ...
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What is the interpretation of "generalized" partial correlations?

The usual partial correlation between X and Y given the set of variables Z is the Pearson correlation between residuals resulting from the liner regression of X on Z and Y on Z. It can be computed ...
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How could I get a correlation value that accounts for gender?

For instance if I were trying to relate Age and Height, I would do something like this: df <- data.frame(Age, Height) cor(df) How could I get Pearson's r ...
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Partial correlation in panda dataframe python [closed]

I have a data in pandas dataframe like: ...
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SARIMA estimation

I am trying to manually estimate the non-seasonal components of an SARIMA (p,d,q)x(P,D,Q)[s]. I thought the estimation is going the same way like in ARIMA, but the output says somehow something ...
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Derivation of the formula for partial correlation coefficient of second order

I came across this formula in some online resources. $$r_{12.34} = \frac {r_{12.3} - r_{14.3}r_{24.3}}{ \sqrt {(1- r_{14.3}^2 )(1-r_{24.3}^2 )}}$$ I can use this but I wanted a proof of the formula....
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Why is the semi-partial correlation sometimes called the "part correlation"?

I understand the difference between partial correlation and semi-partial and zero-order correlation. This terminology makes sense to me in that the partial correlation of X and Y partials out the ...
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mutual information and maximual infomation coffecient

I am interested in calculating the strength between random variables. I found that the maximal information coefficient is one of the good methods to use and it is robust to the mutual information ...
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Do "splits" in scatterplots indicate anything?

Background I'm exploring how 7 system parameters spanning mechanical, electrical, and physical (size) properties are related. I gathered the 7 specs of 36 different systems, and I plotted every ...
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Interpreting Ljung -Box test results from statsmodels.stats.diagnostic.acorr_ljungbox function (python)

I have a set of daily trading strategy returns and I am trying to prove whether the daily returns are autocorrelated at all. I am hoping to fail to reject the null hypothesis that they are not ...
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Get correlation matrix of 3 variables from any combination of 3 simples/partials

Here is the situation. (This is not a homework problem.) I am writing a program that does Cool And Interesting Things starting with a correlation matrix among 3 variables: call them $X$, $Y$, and $Z$....
Jake Westfall's user avatar
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Partial Cross-correlation in R

I think the title is fairly self-explanatory. I want to compute the cross-correlation between two time series controlled for the values at other lags. I can't find any existing code to do this, either ...
Ben's user avatar
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Interpreting Omitted Variables

I do not fully understand how to interpret the difference between two statistical models where they only differ based on whether a certain variable is included on the right hand side. If the results ...
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Symmetry of Partial correlation

Inspired by the question and the diagram represented in the answer, I am wondering if partial correlation is symmetric? We know that $\rho(X,Y) = \rho(Y,X)$. See here. From , we know that $\...
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What is the relationship between regression and partial correlation

There is a well-answered question here. But unfortunately, I don't even understand how the first equation in the answer is derived. Could someone help explain that? $$\text{Beta:} \quad \beta_{x_1}...
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PACF MA(1) via correlation of prediction errors

It is known (see e.g., Brockwell and Davis, Introduction to Time Series and Forecasting, p. 95) that the $h$th partial autocorrelation $\phi_{hh}$ of a stationary process can be derived by first ...
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Sample ACF and PACF of a random walk

Suppose $X_n$are iid $N(0,1)$ random variables. Define $S_n := \sum_{i=1}^n X_n$. Then $S_n$ is a random walk. Since $Var(S_n) = n$ and $Cov(S_n, S_m) = \min(n,m)$, $S_n$ is not stationary in the ...
Tim's user avatar
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Partial Correlation and Partial (Linear) Regression

Consider the linear regression model $$\boldsymbol y = \alpha + \beta \boldsymbol x + \gamma \boldsymbol z + \boldsymbol u,$$ and denote the OLSE of $\alpha$, $\beta$ and $\gamma$ by $\hat\alpha$, $\...
Syd Amerikaner's user avatar
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How to prove the equivalence of partial correlation and coefficient of partial determination?

I am taking a regression course. Suppose there are two linear regression models \begin{aligned} M_1: & y = \beta_0 + x_2\beta_2 + \epsilon \\ M_2: & y = \beta_0 + x_1\beta_1 + x_2\beta_2 + \...
ForStudy's user avatar
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Recurrent PACF expression on ACF and PACF of lower order

Let $\rho_{partial}(n) = Cor(Y_t, Y_{t-n}|Y_{t-1}=\mu,\cdots Y_{t-2}=\mu, Y_{t-n+1}=\mu)$ where $\mu$ is the mean of stationary process. I know that $\rho_{partial}(1)= \rho(1)$ and that $\rho_{...
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what does it mean if the partial auto correlation function of a time series have a value >+1 or <- 1?

I have a time series data and I applied the first difference operator to make it stationary. When I plot the partial autocorrelation function of this differenced time series, I find peaks with value >...
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Interpretation of Mantel r correlations

I am using mantel() in R package ecodist to perform a series of partial Mantel tests. I am examining the correlation between a species composition (Bray-Curtis ...
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When is regressing out factors serially, equivalent to a simultaneous model?

I have two factors $a,b \in R^M$ which I wish to regress out of my variables $Y \in R^{M \times N}$. $b$ is a function of the variables $Y$ and is defined as: $b = \frac{1}{N}Y1$ Regressing out the ...
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Term for two variables that are "too close for control"

Sometimes we are tempted to assess a relationship of X1 with Y while controlling for X2, but it would be a mistake, because X2 is not merely correlated with Y -- it is more closely associated than ...
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How to check if two variables are dependent given a third variable? [closed]

In R, I have a dataset of many variables and based on correlation matrix I see that some of the variable are correlate with the others. For simplicity, let's assume ...
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Why are the diagonal entries of the inverse of the correlation matrix related to correlation with all other variables?

For an inverted correlation matrix $C^{-1}$, I read that its diagonal elements are related to the multiple correlation between measure i as a criterion predicted from all other measures in the set, ...
ahala's user avatar
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What is the difference between the anti-image covariance and the anti-image correlation?

What is the difference between the anti-image covariance and the anti-image correlation? How are the matrices of these coefficients computed, and what is the meaning of their elements?
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Can we identify ARIMA model without looking at ACF and PACF plot?

Can we identify ARIMA($p,d,q$) model without looking at the ACF and PACF plots? I am trying to write a generalized R programme for fitting time series models. We may find out the orders $p$, $d$ and $...
Shahnawaz's user avatar
3 votes
1 answer
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Relationship between beta and t-value in Shen (2018)

As far as I know [source], $$t_{\widehat{\beta}} = \frac{\widehat{\beta}}{\widehat{SE_{\beta}}}.$$ It means the sign of the t-value should be the same as the sign of beta. In Table S1 of Shen (2018), ...
John Smith's user avatar
3 votes
1 answer
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estimate precision matrix with given spatial sparsity pattern

I have a set of $n$ measurements of $p$ variables $\xi_i$. I am interested in the inverse covariance or precision matrix $P$ of the variables, but because $p \gg n$ and because of limited storage ($p$ ...
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Partial correlations among three distance matrices

I am trying to test the hypothesis that related species should deviate more in niche space the more they overlap in geographic space. In other words, related species either forage similarly and don't ...
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partial correlation for logistic regression

I am looking for an equivalent of partial correlation but for logistic regression. I.e., I want to have a measure of an effect a variable have on the outcome, independent of other variables in the ...
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What is the relationship between the standardized multiple regression coefficient & the semi partial correlation for models with k>2 predictors?

I have found myself Googling this question more than once: ¿What is the relationship between the standardized multiple regression coefficient (the standardized partial slope) and the corresponding ...
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Deriving Pearson correlation from regression results

If the common regression results as typically reported in an empirical primary study (sample size n, regression coefficients (Betas), t-statistic, p-value, R^2, adj. R^2) are given in the case of more ...
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