The regression line of y on x is 3x+4y+8=0, and the regression line of x on y is 4x+3y+7=0. What is the value of the Pearson correlation coefficient?
Note: If you haven't seen it already, you may find our Pearson Correlation Coefficient Tutorial helpful in answering this question.
y = (-3/4) * x - 2
x = (-3/4) * y - 7/4
b1 = -3/4
b2 = -3/4
p = b1 (x_std / y_std)
p = b2 (y_std / x_std)
p * p = b1 * b2
so, p = sqrt(9/16)
=> p = +/- 3/4
here, both slope are negative so that, p = -3/4