I have a dataset with 15 binary covariates and a continuous response variable bounded between 0 and 1. The binary variables represent correct or incorrect answers on a short test and the response variable is a measure of the same test takers performance on a related but more advanced and reliable test. I would like to select the best variables and weights to predict the score on the more advanced test. What would be the best way of doing this?
PS. I'm not a statistician but a computer scientist with only basic statistics and machine learning in my portfolio.
(Side note: One idea I had was to use some kind of logistic L1 or L2 regularized regression, however, glmnet does not seem to accept non-binary response variables when fitting a logistic model, which I guess is reasonable for normal use. The built-in glm function does accept a (0,1)-bounded response but does not perform regularization. If this approach seems reasonable, any tips on suitable packages or would I have to implement it myself? Other ideas I had was using "normal" regularized regression, or perhaps Principal Component Regression, however, I have tried both these and they give very different results and neither perform very well.)