I am given regression equations, one showing linear regression of x on y, and the other y on x. Both refer to the same set of data-points.
4X - 5Y + 33 = 0 20X - 9Y - 107 = 0
Taking the first to be X (dependent) on Y (independent) => of the form
X = a + bY. I end up with slope value of 1.25
Taking the second to be Y (dependent) on X (independent) => of the form
Y = a + bX. I end up with slope value of 2.22
Now, these values somehow imply that the system of regression lines is invalid? How is that? I am unable to visualize this.
The book states the "rule" being that:
- Both coefficients (slopes) must be less than 1
- Both coefficients (slopes) must be of the same sign
Are these correct? What other constraints exist for a set of regression equations to be valid?