Regression when the response is a proportion that can be 0 or 1 I have two datasets a training and a test dataset. The dependent variable is a proportion and there are 54 predictors which are positive and negative real numbers and another 7 predictors that are text. 
There are three response variables. Total the normalized total number of hits. Treatment the normalized total number during treatment and a percent which is a ratio of the other two responses.
At the moment using lm on the percent prediction data I have a corolation of .4. 85% of the varibles are within 20% of their target. For the treatment response variable using glm in poisson mode i have a correlation of .6 percent but the variables do not match the target data at all.
I have two main issues I need advice on: 
(1) it rejected the text predictors because it said factor has new level(s)
I would like it to ignore the information for those that have new level but not disregard it for those that have the correct information how do i do that? 
(2) To make my dependent variable a real number, rather than a proportion bounded between 0 and 1, I was advised to transform the response using, for example, the logit transform or the Normal quantile function (qnorm in R). The problem is that these transformations (and others like it) will map 0 and 1 to non-finite values. How can I model these data in a regression setting when the response is a proportion that can be 0 or 1? 
Using linear regression with outlier removal I am able to get 2239 of 2583 testing data within 20% of their actual value I would like to have that many within 10%. 
Using the posson distribution glm the amount of treatment correlates with 69%.
Ignoring this second issue for the moment, I transform the y~x1+x2 such that y=log(y/(1-y)) the correlation of my predictions to actual data drops from 6% to 2%
This is what the data looks like after the logit transform

This is what the data looks like before the log distribution

 A: You might want to look at beta regression.  It would be helpful to know what the response variable actually represents, but I would start with logistic regression (O.K. if the proportion represents the average of a large number of Bernoulli trials) and then try beta regression (which is a much more flexible solution, where the residuals are assumed to be from a beta distribution with parameters specified by the regression).
Update: It seems that the data generating process for this problem means that it is not a straightforward regression problem, but instead it has three seperate modes of generating the response, one where it is zero, one where it is one and one where it can be any value in the range (0,1).  The way to approach such problems is by using a compond likelihood.  I have used this kind of approach for modelling rainfall, where there are lots of exact zeros for days where it doesn't rain at all.  The solution is to have a model with three outputs, one which gives the probability that it will rain, and the other two giving the shape and scale parameters of a gamma distribution which represents the amount of rain that you would see if it did rain.  The original paper on this was by Peter Williams, but I can't find it on line, so here is my paper, which should give you the basic idea.
For this problem, you could try having a model with three outputs, one is the probability that the response is an exact zero, one that is the probability that it is an exact one and one that is a prediction of the response if it isn't an exact zero or an exact one.  I doub't you will be able to get some off-the shelf code for this, but it is the approach I would take.
A: if Poisson regression seemed to help it may be because the right thing to do is to treat the outcomes as counts.  But if it is not satisfactory negative binomial regression might be better.  It allows for overdispersion and is a lot more flexible.  The Poisson distribution have the property that the mean equals the variance.  In real examples the variance can be less than the mean (underdispersed) or greater (overdispersed).  Negative binomial regression gets around that problem because the varaince doen't have to equal teh mean.  Joe Hilbe has a nice book dedicated to negative binomial regression for count data models. Maybe you can do that with your software.
A: @Dirkan Beta regression requires logit transformation. The logit transforms of 0 and 1 are -Inf and Inf. This is why beta regression cannot handle 0s and 1s. 
