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

Regression of y on x: from x + y + 11 = 0, y = -x - 11, so b_yx = -1. Regression of x on y: from 2x + 3y + 4 = 0, x = (-3y-4)/2, so b_xy = -3/2. Check: |b_yx · b_xy| = 1·3/2 = 3/2 > 1, so we swap. Take y on x from 2x+3y+4=0: y = -(2/3)x - 4/3, b_yx = -2/3. Take x on y from x+y+11=0: x = -y-11, b_xy = -1. Then r² = b_yx · b_xy = 2/3. Since both slopes negative, r = -√(2/3).