I have more than 100 variables and the outcome variable is continuous (percentage of remission). I was wondering what kind of model can I use for prediction of these types of response based on the fact that I cannot use classification due to continuous response outcome.
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You may initially think a logistic regression only works on binary outcome variables, but that is not necessarily the case. Outcome variable which are proportions or percentages, such that they are continuous between $0$ and $1$, can also be predicted using the Generalised Linear Model with a Logit link function.
Since you have many variables I would suggest Lassa or Elastic Net regression in oder to avoid oroblems with correlated predictors or overfitting. You can read more here