My objective is to run a linear regression model with no intercepts, but my data is grouped in the target variable.

My data frame has: id_1, id_2, input_number and target. any combination of id_1 and id_2 is unique and has an associated input number. However, target is the same for every id_1.

I want to find a coefficient for each id_2 such that the sum of coef*input_number over each id_1 ~ target, and I have no real understanding of where to start.