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  • Compute sample analog of law of total variance [ V(Y) = E(V(Y|X)) + V(E(Y|X)]

    I am trying to see how much of the variance of a variable Y occurs between groups of a categorical variable X, and how much is within groups of X. For that, I thought of computing the sample analog to the law of total variance [ V(Y) = E(V(Y|X)) + V(E(Y|X)]. Is there a simple way to compute this in Stata?

    This is how fas as I got, in a reproducible example:


    Code:
    sysuse auto, clear
    *V(Y) 
    sum price
    
    *V(E(Y|X) : un reg on FEs and calculte their average
    egen make2=group(make)
    reg price i.make2, nocons
    matrix FEs = e(b)
    scalar V_FEs= mean(FEs) // this is giving an the erro message
    unknown function mean()
    
    *E(V(Y|X))
    predict y_resid, resid
    *somehow compute the by group variance and average them
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