# Tag Info

### Analogy of Pearson correlation for 3 variables

It is indeed something. To find out, we need to examine what we know about correlation itself. The correlation matrix of a vector-valued random variable $\mathbf{X}=(X_1,X_2,\ldots,X_p)$ is the ...
Accepted

### Completing a $3 \times 3$ correlation matrix — $2$ coefficients of the $3$ given

We already know $\gamma$ is bounded between $[-1,1]$ The correlation matrix should be positive semidefinite and hence its principal minors should be nonnegative Thus, \begin{align*} 1(1-\gamma^2)-0.6(...

### Is it meaningful to calculate Pearson or Spearman correlation between two Boolean vectors?

I would not advise to use Pearson's correlation coefficient for binary data, see the following counter-example: ...
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### Is it possible to have Pearson correlation coefficient values $< -1$ or values $> 1$?

The formulas you're using have long been known to be numerically unstable. If the squared means are large compared to the variances and/or products-of-means are large compared to the covariances, then ...
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### What is the distribution of sample correlation coefficients between two uncorrelated normal variables?

As a general remark, your questions are usually very clear and well illustrated, but often tend to go too much into explaining your subject matter ("Q methodology" or whatever it is), ...

### Pearson or Spearman?

Neither correlation coefficient presupposes normality. Marginal or bivariate normality is completely irrelevant to the choice between them. They do differ in the questions they ask of the data. ...

### Pearson correlation coefficient is a measure of linear correlation - proof

It is indeed possible to show that the Pearson correlation is essentially the way to measure linearity of association when you elect to use standard deviations to measure the dispersion of random ...
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### Difference between Pearson's r ~= 0 and p > 0.05

The p-values and Pearson's correlation coefficient $r$ measure different things. $r$ measures the strength of the correlation. The p-value, on the other hand, measures how likely you would be to ...

### Is it meaningful to calculate Pearson or Spearman correlation between two Boolean vectors?

Arne's response above isn't quite right. Correlation is a measure of dependence between variables. The samples A and B are both independent draws, although they are from the same distribution, so we ...
Accepted

### Calculate Spearman and Pearson correlation on variables of different units

Pearson correlation, $\rho_{XY}$, divides through by the product of the units and results in a unitless measure. $$\rho_{XY}=\dfrac{ \text{cov}\left(X,Y\right) }{ \sigma_X\sigma_Y }$$ The covariance ...

### What is the difference between linear regression on y with x and x with y?

The insight that since Pearson's correlation is the same whether we do a regression of x against y, or y against x is a good one, we should get the same linear regression is a good one. It is only ...