model for continuous dependent variable bounded between 0 and 1 I'm attempting a multiple regression model where the predicted variable is runoff ratio - the ratio of watershed discharge to the precipitation input. This should generally be bounded [0,1], however, due to measurement error some values > 1 occur.
Originally, I modeled this with the predicted variable un-transformed, but logistic regression has been suggested to me, I also have heard Beta regression suggested. I'm not sure how to proceed, and if these transformations are appropriate to my data:

My questions are:
1) Is a logistic regression appropriate for these data? and 
2) If I were to proceed with logistic regression, would I need to convert the runoff ratios to proportions, or would I apply the logit to the values as they are?
Sorry if these are obtuse questions - I'm new to logit and most of the information I have found is for binary response variables.  
Edited for suggested additions:
As a simple version: I am modeling runoff ratio (rr) as an effect of precipitation (pcp) and antecedent water table position (ant):
rr ~ pcp + ant
rr is a continuous variable. I am not interested in the probability of specific values, rather I'm interested in the values themselves - both to assess the significance of the predictors and as a predictive model. 
Conceptually, I was fine modeling it un-transformed. However, a simple linear regression allows predicted values outside of the physical range of [0,1]. As mentioned above, measurement error does lead to values >1, which I'll eventually have to deal with.
 A: Let "$run$" be the runoff, as measured with error, so that the measured runoff ratio $rr$ is $run/pcp$.  The stated model and its alternatives appear to be in the form
$$rr = \frac{run}{pcp} \sim F(\beta_{pcp} (pcp) + \beta_{ant} (ant) + \beta_0)$$
where $F$ is some family of distributions (such as Beta distributions) and the $\beta_{*}$ are coefficients to be estimated.  The main problem with this is that unless the dispersion of the measurement error in $run$ is directly proportional to $pcp$, the structure of $F$ will be unnecessarily complicated.  Why not algebraically rewrite the relationship as
$$run = \beta_{pcp} (pcp)^2 + \beta_{ant} (ant)(pcp) + \beta_0(pcp) + \varepsilon$$
where $\varepsilon$ represents the measurement error?  The absence of several simple terms in this formula (such as one depending directly on $ant$ as well as a constant term) suggests that the proposed model may be artificially limited.  Thus, ordinary regression (using $run$ or some re-expression thereof, such as a square or cube root, as the dependent variable) to fit a model like
$$run = \alpha_0 + \alpha_{pcp}(pcp) + \alpha_{ant}(ant) + \alpha_{pcp2}(pcp)^2 + \alpha_{ant,pcp}(ant)(pcp) + \varepsilon$$
would be a good way to begin an analysis.  And if indeed the variance of $\varepsilon$ depends on $pcp$, that can be modeled in various straightforward ways.  This approach seems more natural, realistic, and interpretable than hoping the ratio $rr$ would satisfy the more restrictive assumptions of Beta or Logistic regression.
A: Most (if not all) logistic regression routines require the numerator and denominator to be integers, which I do not think is your case.
The beta regression approach seems much more appropriate, though as you mention you will need to deal with the values that are greater than 1 since standard beta regression requires values in [0,1].
Is the precipitation amount used as both a predictor and as the denominator in your response variable (runoff ratio)?  If so you may want to read:

Spurious Correlation and the Fallacy of the Ratio Standard Revisited
  Richard A. Kronmal, 1993, Journal of the Royal Statistical Society.
  Series A.  Vol. 156, No. 3, 379-392.

Which talks about how relationships can be distorted when ratios are used/misused.  You may do better with a model that predicts just the numerator of your ratio.
