I have tabular data that records, on each row, a number of parameters to do with a patient's life-style, medication intake etc; plus the DV, that represents the severity of the symptom experienced in each day. Thus, one row represents one day, and the dataset is repeated-measures, as all observations come from a single subject.
I am trying to identify which of these factors (if any) has the most predictive power in determining the DV. Only vague hypotheses exist: any of these predictors (or interactions thereof) can be suspected to cause the symptom; it's also difficult to estimate whether to expect a small or large effect size.
I guess multiple regression is the go-to tool here, but the following features of this dataset give me doubt:
1) the DV values in each row are of a very limited range (most around 3 to 5, scale is 0-10)
2) there are many regressors defined (around 20), due to the vague hypotheses. Related to that, I know that roughly 10-20 observations are needed per predictor. I currently have N=40 rows, so the question is how to balance the many predictors with the few observations, in order to obtain a meaningful result. Namely, should I collect more observations, or try to restrict the predictor space, e.g. try to identify and keep the more likely predictors, or group them into categories?
LATER EDIT: Assuming I do the multiple regression, I get the betas for each regressor, and I sort them to find the best predictor, would it be correct to then report the correlation between the DV and that one predictor, given that, regardless of how much variance in the DV it explains, there is still (likely) an interaction between that and other predictors?