Which of following is not correct about properties of correlation coefficient?

(A) Depends on the origin.

(B) Depends on the scale.

(C) Depends on both origin and scale.

(D) Is independent with respect to origin.

(E) Is independent with respect to unit of scale. 

Choose the correct answer from the options given below :

Pearson’s correlation coefficient is the test statistics that measures the statistical relationship, or association, between two continuous variables.  It is known as the best method of measuring the association between variables of interest because it is based on the method of covariance.  It gives information about the magnitude of the association, or correlation, as well as the direction of the relationship.

PROPERTIES OF CORRELATION COEFFICIENT:

Property 1: Correlation coefficient lies between -1 and +1:  Whenever we calculate the correlation coefficient by any one of the formulae its value always lies between -1 and +1.

Property 2: Correlation coefficient is independent of the change of origin and scale: Correlation coefficient is independent of the change of origin and scale, which means that if a quantity is subtracted and divided by another quantity (greater than zero) from original variables, i.e. U = (X - a)/h and V = (Y - b)/k then correlation coefficient between new variables U and V is same as the correlation coefficient between X and Y, i.e.Corr(x, y) = Corr(u, v). 

Property 3: If X and Y are two independent variables then the correlation coefficient between X and Y is zero, i.e.Corr(x, y) = 0. 

Statements A, B, and C are not true. 

Thus, option 3 is the correct answer.