Question

Which of the following is a property of the correlation​ coefficient?

Select all the correct answers below.

A.

The correlation between x and y is the same as the correlation between y and x.

B.It is always between

minus−1

and 1.

C.

The sign of the correlation tells us the direction of the association.

D.

The correlation is not affected by changes in units or scale.

Answer 1

The formula for correlation coefficient is

So whether we calculate correlation for (x,y) or (y,x ) it will be same .

The rage of correlation coefficient is -1 to 1.

Sign of the correlation tells us the direction of association that means if two variables are positively correlated, then as the values on one variable go up, so do the values on the other variable.

Since the formula for calculating the correlation coefficient standardizes the variables, changes in scale or units of measurement will not affect its value.

So here correct answers are :

• The correlation between x and y is the same as the correlation between y and x.
• It is always between −1 and 1.
• The sign of the correlation tells us the direction of the association.
• The correlation is not affected by changes in units or scale.