While logistic regression involves a binomial or multinomial response, it is still reasonable to fit a logistic curve to a continuous response that ranges from 0 to 1. This can be done by fitting a nonlinear model such as p=1/(1+exp(-xbeta)), where xbeta is a linear function of your predictors. Also, Collett (2003, pp 329-330) suggests a quasi-likelihood approach that fortunately is similar to using events/trials syntax in PROC LOGISTIC with the proportions as the events variable, with the trials variable equal to 1, and with the SCALE=DEVIANCE option in the MODEL statement.
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