# Regressor contribution in OLS regression

Assume I have the following model, estimated using OLS:

$$Y_{it}=β0+β1∗X1_{it}+β2∗X2_{it}+β3∗X3_{it}+ϵ_{it}$$

I know that some methods exist to compute the relative contribution of each variable to the overall goodness of fit (Shapley decomposition for instance). But is there any easy way to measure a time-varying contribution? I.e. the evolution over time of the contribution of each factor?

Probably silly question: what does $$(β1∗X1_{it})/Y_{it}$$ represent? Can this represent some kind of contribution of $$X_1$$ to $$Y$$?

Many thanks