Mutliple Regression with a known coefficient

#1
I'm performing multiple regression on a linear model with several independent variables to generate equations such as:

W = aX + bY + cZ
X = dW + eY + fZ
Y = gW + hX + iZ
Z = jW + kX + lY

etc...where (a,b,c...) are coefficients of the independent variables.

However, in some cases I want to specifiy a particular value for one or more of the coeffifients:

W = aX + (0)Y + cZ
X = dW + eY + fZ
Y = gW + hX + (1)Z
Z = jW + kX + lY

Does anyone know of a method that I can use to do this? I'm not looking for software specific things, I'm just wondering if this is possible with basic multiple regression?

Thanks in advance,
Lee
 

BioStatMatt

TS Contributor
#2
This is possible. Say you have Y = aX1 + bX2 + cX3, and would like to specify b. In this case, all the values of the form bX2 are known. You can then restate the model as:

Y - bX2 = aX1 + cX3

So, let Z = Y - bX2. Calculate all the Z values, and regress

Z = aX1 + cX3

This will give you the coefficients a and c that you are interested in.

~Matt