Often variables correlation is inspected to check the dependency between the two variables. However, consider the following dependency between ‘y’ and ‘x’:

y = sin(x)

This is often possible in case of signal data. In reality, a data scientist will not know that there exists any relation between the two. There will be just some data points of various ‘y’ corresponding to ‘x’. A correlation coefficient of such a pair of data will be close to 0 (if the range of x is all real numbers).

However, if the range of ‘x’ (domain of ‘y’) is restricted to only 0 to pi/2 then the correlation coefficient will be very high.

Note that only when ‘y’ increases as the ‘x’ increases or the vice versa, is when the correlation coefficient.