one single value target variable
Welcome to the site! As Media has mentioned it is a classification problem not prediction problem. If you meant Logistic Regression then it makes sense. 

You need to remember one thing if the outcome is only one value then algorithm would also return the same value irrespective of anything. if you don't have negative cases then you cannot use Logistic regression and it doesn't know when to say 0 as the model wasn't trained on it. 

If possible using Business Matter Experts advice populate some dummy data for 0's and balance the data. Train your model and see what the model is going to say.

Else you cannot use any kind of classification algorithm.