Here, this will make everything clear for my friend Joshua Holland:

The regression model uses dummy variables to allow the estimated base level of turnout and the estimated effects of the machine 3 allocations and the polls open elapsed times to vary across the three subsets of precincts.

Specically, using Ai to denote the proportion African American in precinct i, I dene two dummy variables using the following rules:

LOWi = (1; if Ai < 0:0170; otherwise MEDi = ( 1; if 0:017 Ai :15650; otherwise LOWi = 1 only if precinct i is in the set of precincts that have the lowest proportion African American, and MEDi = 1 only if precinct i is in the set of precincts that have an intermediate

proportion African American. Using MRi to denote the natural logarithm of the voting machines per registered voter ratio and Pi to denote the polls open elapsed time, the linear predictor in the

model may be written as follows. Zi = b0 + b1Pi + b2MRi + LOWi(b3 + b4Pi + b5MRi) + MEDi(b6 + b7Pi + b8MRi) + b9Ai :

With this formulation, the estimated effects for each set of precincts may be recovered as follows: Zi = 8>< >:

b0 + b3 + (b1 + b4)Pi + (b2 + b5)MRi + b9Ai; low proportion African American b0 + b6 + (b1 + b7)Pi + (b2 + b8)MRi + b9Ai; medium proportion African American b0 + b1Pi + b2MRi + b9Ai;...

from http://www-personal.umich.edu/~wmebane/franklin2.pdf

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