How to do regression when dependent variable is a proportion or bounded (ranging from 0 to 1)?

If dependent variable is a proportion (ranging from 0 to 1), then your predicted values must be a proportion, logically. Therefore we use logit transformation of dependent. Before we proceed further we need to know some terms:

1. Ogive/ sigmoidal/ flattened S-curve: It is linear in middle part, but categorical on extremes
    
2. Logit transformation: If your dependent variable is ranging from 0 to 1, e.g. any proportion, then use logit transformation. For Example: If x is dependent then logit transformation is ln(x/(1-x)).

If most of the dependent values are ranging in middle linear part of the curve (from 0.3 to 0.7), we can use simple OLS instead of logistic regression. (http://www.theanalysisfactor.com/proportions-as-dependent-variable-in-regression-which-type-of-model/)