Estimating percentages as the dependent variable in regression I have the rank percentages of students in 38 exams as the dependent variable in my study.  A rank percentage is calculated by (a student's rank / number of students in an exam).  This dependent variable has nearly uniform distribution and I want to estimate the effects of some variables on the dependent variable.
Which regression approach do I use?  
 A: If you are working with Stata have a look at the following example: http://www.ats.ucla.edu/stat/stata/faq/proportion.htm
Here is a quote from this webpage:

"How does one do regression when the dependent variable is a
  proportion?
Proportion data has values that fall between zero and one. Naturally,
  it would be nice to have the predicted values also fall between zero
  and one. One way to accomplish this is to use a generalized linear
  model (glm) with a logit link and the binomial family. We will include
  the robust option in the glm model to obtain robust standard errors
  which will be particularly useful if we have misspecified the
  distribution family."

A: The measure @user13203 proposes may be considered as a continous bounded underperformance score, the lower the better the performance: $y_{ij} $ i-th student underperformance at j-th exam.
Using a logit linearizing transformation where $\mu_{ij}$ may depend on observable student or exams characteristics :
$\ln(y_{ij}/(1-y_{ij})) = \mu_{ij} + e_{ij} + v_i  $
student's unobserved skills are modeled through the random component $v_i$ while $e_{ij}$ models other non systematic unobservables. Correlation between responses (examinations) may be addresed by assming a general covariance structure for $e_{ij}$. Why not a White (or sandwich/robust) variance structure ? Moreover, some of the responses correlation can be accounted within the $\mu_{ij}$ (conditional dependence).
(This is just an idea from my biased experience, comments and critics are more than welcome.)
Unobservable abilities are likely to be correlated with students or exams observables attributes within $\mu_{ij}$. This assumptions makes this model a RE with correlated error components, that can be estimated by ML or a two stage estimator: first stage: a within (or analog) transformation that eliminates $v_i$. Second stage: OLS on the transformed model.
A: You might want to try logistic regression.  The logit transform $\ln(\frac{p}{1-p})$ will spread your response variable out over the real line so you won't get absurd predicted rank percentages like -3% or +110%.
A: A perfect model in this case will map the inputs (whatever covariates you have) to the outputs (the rank of the student in the class).  Another way to think of this is by mapping first to the scores, and then mapping those scores to the rank.  I'm going to ignore error for now.
test score: $y = \sum \beta x$
rank: $ r = R(y)$
In which $R$ is the ranking function.  The problem is that $R$ is a non-linear function that depends entirely on the data itself.  If we assume that we have an infinite amount of data, then we know the complete distribution of $y$, and $R(y)$ is essentially the cumulative density function.  It tells you what percent of people scored worse than you on the test, the area to the left of your score.
This appears to be quite similar to the functional form of the generalized linear model.  I think this is why the logistic regression approach was proposed by @Mike Anderson.  If your exam scores were logistically distributed, then the link function to use would be the logit (its inverse is the cumulative density function we care about).  Similarly, if the scores were normally distributed, the probit function would be the link function.
For your regression, the only way to estimate ranks is to say "given that my data are distributed as X, this point is in the 34th percentile".  Otherwise, how do you know what a two point increase in your test score translates to in terms of rank?  The caveat is that you have to estimate that distribution in order to choose your link function (certain functional forms will make your life a lot easier).  Furthermore, this model isn't going to say "you were the 6th best out of a class of 38", rather "if the test scores were distributed how we think they are, your score would put you in the 15th percentile."
