I am trying to model percentages which are in the closed interval [0,1] .

Specifically, I am not modelling the probability of a yes/no outcome (for which logistic regression is often used), but I am modelling a continuous numeric variable which can take all the values in the [0,1] range, including 0 and 1.

I thought of running a linear regression on the logit transformation, ln[y/(1-y)], but it's not defined at the extremes 0 and 1, which is a huge problem because my data is concentrated exactly at the extremes.

I know I could use decision trees or neural networks, but I was wondering if there is any way to apply a regression model to this problem.

Examples of this kind of modelling are the % of time available spent on a certain task, the % of money available dedicated to a given activity, etc.

Thanks a lot for any insight!