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Can somebody provide an intuitive difference between correlation and correlation coefficient? During learning of weights of neural network, I want to show how closely the estimated weights are to the known true weights. For this, I was thinking of using the correlation measure. If they are correlated then the value will be close to one. But I am not sure, if it should be the correlation or the correlation coefficient.

Also, what is the difference between the two formula wise and physical meaning wise. Thank you

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  • $\begingroup$ No difference, unless you have some strange textbook that tries to make some sort of distinction. $\endgroup$ – rvl Jul 28 '14 at 0:13
  • $\begingroup$ I'm not sure what distinction you have in mind when you contrast "Correlation" with "Correlation coefficient"... $\endgroup$ – Steve S Jul 28 '14 at 0:14
  • $\begingroup$ Which "two formulas" are you referring to? $\endgroup$ – Glen_b Jul 28 '14 at 0:29
  • $\begingroup$ Correlation in the context of 2 random variables to be independent. Do we say correlation coefficient = 0 or correlation = 0. In other case, in cryptography, when we want to check how good the decryption is, then we measure the correlation. When the decryption is perfect then correlation is high between the original plaintext and the decrypted recovered message. So, what is a correlation coefficient and only correlation? Or are they the same? $\endgroup$ – SKM Jul 28 '14 at 1:45
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Can somebody provide an intuitive difference between correlation and correlation coefficient?

The word 'correlation' has (i) several specific technical senses (most usually the Pearson product-moment correlation, plus many other measures that get labelled as one or another kind of 'correlation' in different contexts), as well as (ii) a more general sense (implying some kind of association, usually monotonic, but without needing any specific 'formulaic' sense of the word).

In the most common usages of the terms, "correlation" and "correlation coefficient" mean the same thing - the Pearson product-moment correlation.

However, it is certainly possible for a single source using both terms to be attempting to draw a distinction, and in that case, for example, it might be that the second form (correlation coefficient) implies one of the mathematically defined technical senses I mentioned in (i), while the first might only refer to the more abstract/general sense of association.

Both senses are discussed here.

If you're referring to a particular use or uses of the terms, you'll need to provide some context, such as a direct quote (with source(s)).

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  • $\begingroup$ What is then the difference between correlation and mutual information if both of them mean how closely 2 random variables are related or how closely 2 signals are related to each other? $\endgroup$ – SKM Jul 28 '14 at 1:50
  • $\begingroup$ @SKM correlation measures the degree of linear association. Mutual information can identify much more general forms of dependence. You can have highly dependent variables for which the correlation is 0. Consider $X$ being symmetric with mean 0, and $Y=X^2$. They're perfectly functionally dependent but uncorrelated. $\endgroup$ – Glen_b Jul 28 '14 at 2:40
  • $\begingroup$ @SKM you might benefit from reading the comments - including links - and Aaron's answer here $\endgroup$ – Glen_b Jul 28 '14 at 2:50
  • $\begingroup$ Thank you for the link. So, correlation and correlation coefficient is the same thing. When we say that weights after training and the actual weights of the system Or when decryption and original message correlation = 1, then it means that the algorithm performed well. We do not say that the correlation coefficient =1. Is my understanding correct? $\endgroup$ – SKM Jul 28 '14 at 5:21
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    $\begingroup$ By context I don't mean "application area" - I mean "within a particular piece of writing" - if a particular author uses a term one way or another, which will generally be clear from the surrounding text. As with "when we say the correlation between 2 variables is 0.8, are referring to the value of the correlation coeff?" -- yes, in that situation, 'correlation' is referring to a correlation coefficient, likely the Pearson one. If, on the other hand, someone said 'there's some correlation between experience and income' they may mean nothing more than some association exists -likely monotonic $\endgroup$ – Glen_b Jul 28 '14 at 14:07

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