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?

From x + y + 11 = 0, expressing y on x: y = -x - 11, so byx = -1. From 2x + 3y + 4 = 0, expressing x on y: 2x = -3y - 4, so x = -(3/2)y - 2, giving bxy = -3/2. However, we must check which regression is which. Testing the other assignment: from x + y + 11 = 0 as regression of x on y, bxy = -1; from 2x + 3y + 4 = 0 as regression of y on x, 3y = -2x - 4, byx = -2/3. Then r² = bxy · byx = (-1)(-2/3) = 2/3, and since both slopes are negative, r is negative. Therefore r = -√(2/3).