Difference between two regression coefficients

#1
Hi All:

This is the context. I have three x variables with following relationship: x1 + x2 = x3. Now, I run these two equations:

y = a1 + b1x1 + b2x2 + e1
y = a2 + b3x1 + b4x3 + e2

My question is, what is the difference between b2 and b4? I can understand b2 - it's the effect of x2, which is independent of the effect of x1 (b1). But since x3 contains x1, how do I interpret b4?

Thanks in advance for all your help. HS
 

hlsmith

Omega Contributor
#2
What is the purpose of this exercise?

I believe if you think about this as non-euclidian geometry. You could plot the relationship between y,x1; y,x2, y,x3. You will have three lines and x3 will be a vector blend between the two other lines. The model may run, however, I believe the standard error will be very big.