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Thread: Mutliple Regression with a known coefficient

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    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?

    Thanks in advance,
    Lee

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    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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