Deriving monthly study schedule best correlated with exam outcomes I've recently conducted a survey of students in a class who had recently taken a difficult examination. Part of the output data is like so:


*

*x_Jan=Hours spent studying weekly in Jan [0 ... n hrs/wk]

*x_Feb=Hours spent studying weekly in Feb [0 ... n hrs/wk]

*(and so on to x_Dec)

*y=Exam score


Here's an example month:

How can I analyze this data to know what amount of time spent studying weekly per month is best correlated with examination outcomes? For the sake of simplicity, I think the question & answer can be simplified to a single month (x), and the solution to multiple months can be easily extrapolated.
On the surface, one might guess those who spend the most time studying perform the best, but, looking at the data qualitatively, it is evident that it isn't quite the case--for example, perhaps some students spend too much time studying too early, or too much time studying too late. I hope to use the data to help students prepare an effective study plan and schedule. 
I considered doing linear regression comparing 0 hours to each of X hours vs test score, but sample size quickly becomes a limiting factor. I'd have to bin the data fairly wide to get any significance. (i.e. 0 to 20, 21 to 40, etc.).
Any suggestions? I appreciate your insight!
 A: You are right that the data are best combined into a single covariate, namely hours.  There is no reason to believe that studying for 2 hours in January is any different than studying for 2 hours in February, provided the hours studied are for the same test.  I'm assuming here that this is the only test the students are taking (e.g. no tests in other courses) which is obviously false, but without that data it is something we have to live with.
Linear regression is not a good idea. Your model will tell you that studying sufficiently long will guarantee you a perfect score or higher, which is ridiculous.
One method may be to transform the scores to be between 0 and 1 and then do a logistic or beta regression.  That way, your predicted mean would be constrained to be within the unit interval and you will avoid problems like the one I have mentioned earlier.
I would caution you from relying too heavily on the inferences made from whatever model you construct.  There is a great deal of between subject variability in this data, so just because your model predicts that studying 4 hours will result in an A on average does not mean that you, or anyone else, are guaranteed an A because you sit starting at your books mindlessly for 4 hours.
