Thanks everyone for the help, I found the solution to was I was looking. As you guys suggested, the regression was the “wrong” approach. I mean it was just a way of describing the data, but the end goal wasn’t to have a perfect fitting with the process generating the data.
I was trying to describe how coherent or not were responders of a particular survey and cluster them. the scope so is not to interpolate the results perfectly, because the results are inherently non-coherent as coming from people with different opinions. But rather find few parameters that can describe the groups.
I was in a way looking at the problem from the wrong perspective. Thanks all for the feedback and the suggestion of rethinking at the entire process!