Correlation of a 2D array and its transpose

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I was working on a tabular data and was thinking about the correlation meaning in here: We are taking a sample of several Whisky drinks and their corresponding rating on various taste criteria.

Consider this table:

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The table shows the taste criteria of several samples of Whisky drinks.

So getting the Pearson Correlation of the table :

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Question 1
Is my understanding of correlation on this example correct: It shows if any linear relationship between different tastes exists for example if taste criterion 1 is positively correlated to criterion 2 then they increase together and decrease together in the various drinks.

Next Table : Now consider taking the transpose of the table we obtain the following table

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Applying Pearson correlation function leads to the following table

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Question 2 what does this correlation table mean ?

Best Answer

Question 1

So, in question 1, your understanding is correct. Since the Pearson Correlation is defined as $$\rho_{X,Y} = \frac{cov(X,Y)}{\sigma_X \sigma_Y}$$

The more $\rho_{X,Y}$ is close to $\pm 1$, the more a linear relation between $X,Y$ exists (i.e. you could write $X = aY + b$ or $Y = aX + b$). The other case is that when $\rho_{X,Y} = 0$, i.e. no correlation exists.

Question 2

The second table is calculating the correlations of different drinks (observe that the table is indexed by drink indicies), whereas the first table is calculating the correlations between the different characteristics of drinks (i.e. Body, Sweetness, ...) (observe that the table is indexed by drink characteristics).

Btw, are those tables generated on R or Stata?

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