How to include limited independent variables in linear regression models? I want to determine the impact of competition on quality using linear regression. Competition is represented by the Hirschmann-Index (HHI), which is an indicator for market concentration. It can take values in a range from 0 up to 1, where 1 represents a monopoly. The indicator that should represent the quality is a percentage value.
Now, my question is how do I have to take in account that the HHI is a limited value (0-1)? Are there any restrictions or modifications that have to be made?

A common misconception about regression is that there are (normal) distribution assumptions about the features, which there are not.
I might be concerned about a nonlinear relationship with the outcome or interactions with other features, but these are always possibilities. Methods to remedy these issues range from domain knowledge to flexible models with splines to neural networks that figure out the nonlinear relationships and interactions.
