# How do I use a distribution as an independent variable in a regression?

I'm trying to build a regression model that predicts Trump's vote share in a county in the 2016 election, given demographic data about that county. One of the demographic variables I would like to use is the distribution of income in that county; i.e. the % of people in the county earning <$$10k,$$10k-20k,etc. If I use the % of people in each bin as an independent variable, then intuitively the coefficient estimates for "nearby" bins would have high collinearity and be prone to overfitting. How do I use the prior knowledge that "%<10k" and "%10k-20k" variables should have a similar (but unknown) effect on Trump vote share in my regression?

Edit: To be clear, I would use n-1 variables to represent n income bins.

• Actually, the collinearity would be perfect since all bins in each county should sum to 100%. Also, welcome to CV! – JTH Aug 2 '20 at 23:08
• Oh I was planning to use n-1 variables for n bins. Should I edit the question to make that clearer? – KD89042 Aug 2 '20 at 23:21