Which of the following statements about correlation coefficient and regression coefficients are correct?

(A) The correlation coefficient is unaffected by change of origin and scale

(B) Regression coefficients are independent of change of origin but not of scale

(C) Correlation coefficient is the geometric mean of two regression coefficients

(D) If one regression coefficient is greater than 1, the other must also be greater than 1

Choose the correct answer from the options given below

Solution

(A) The correlation coefficient is unaffected by change of origin and scale: True, it measures the strength of a linear relationship regardless of the units of measurement. (B) Regression coefficients are independent of change of origin but not of scale: True, changing the scale affects the slope but not the relationship's nature. (C) Correlation coefficient is the geometric mean of two regression coefficients: True, it's a relationship between the regression coefficients in bivariate normal distribution.