# Thread: Mutliple Regression with a known coefficient

1. ## Mutliple Regression with a known coefficient

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?

Lee

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

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