Yes, it's called multivariate regression. But only do it if it makes sense to combine the dependent variables in some sort of linear combination - otherwise just do separate regressions for each dependent variable.
Ok so you have-
Income Household size and Amount charged
you have to estimate regression equations first for annual income as indepent and then household size as independent. If you want to use this data to figure out which variable is the better predictor, does that mean you do each seperatly:
First using annual income as independent (househld size and amount as dependent) then household size as independent (income and amount as dependent) or do you leave out "amount charged" totally and just do size as independent and income as dependent and visa versa?