Unable to calculate correlation value

Question

I am trying to find the correlation between the two columns of numbers below:

 2.000000000 2.333333333
 2.333333333 2.000000000
 2.666666667 2.000000000
 1.333333333 2.000000000
 2.333333333 2.333333333

The correlation value given is 0.00362318840579711.

I am not really sure which correlation is used in order to get the above value.

Can anyone tell me which correlation is used?

Answer 1

What you have there is the squared Pearson correlation.

It's not possible to say which of several equivalent forms might have been used to calculate it, but if the first column are x's and the second column are y's you can get it using:

$r = \frac{\sum_i (x_i-\bar{x})(y_i-\bar{y})}{\sqrt{[\sum_i (x_i-\bar{x})^2]\,\cdot\,[\sum_i (y_i-\bar{y})^2]}}$

and then squaring it.