# When the response variable is a proportion (r/n) in proc logistic, how to express the model in terms of $\pi, \alpha, \beta$?

A (SAS documentation file) (page 1906) on "The LOGISTIC Procedure" gives the following procedure-

proc logistic;
model r/n=x1 x2;
run;


Here, n represents the number of trials and r represents the number of events.

Question 1: The response variable - r/n will produce proportions, therefore, it's not either 0 or 1. In that case, what kind of logistics model it is? Ordinal?

Question 2: If there are 4 groups formed according to very high, high, medium and low levels of exposure in predicting a disease outcome, and if I want to use r/n as response variable using the proc logistic (as mentioned above) with a single exposure variable, what will be the model expression in terms of pie, alpha and beta? In other words, I have a 4x2 table with 4 levels of exposure, and 2 outcomes- disease and non-disease.

Hope at least one expert will come forward to answer this simple question. Many thanks in advance!

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The response is not a proportion. The SAS notation "r/n" juste means "r among n". –  Stéphane Laurent Oct 28 '12 at 6:39
Expanding on @StéphaneLaurent 's answer, this is just a different way of writing the same thing. The two notations are convenient with data in different formats. –  Peter Flom Oct 28 '12 at 12:31