Let two lines of regression be x+y+11=0 and 2x+3y+4=0 for some data. What is the value of correlation coefficient between x and y ?

Step-by-step solution

Let the regression line of y on x be 2x+3y+4=0 . 3y = -2x - 4 y = - 2 3 x - 4 3 The regression coefficient of y on x is b_ yx = - 2 3 . Let the regression line of x on y be x+y+11=0 . x = -y - 11 The regression coefficient of x on y is b_ xy = -1 . The square of the correlation coefficient is given by r^2 = b_ yx b_ xy . r^2 = (- 2 3 ) (-1) = 2 3 Since r^2 1 , our assumption for the regression lines is correct. Furthermore, since both regression coefficients b_ yx and b_ xy are negative, the correlation coefficient