Determining to what extent am independent variable drives a dependent variable?


New member
Mar 26, 2020
For dependent variable (d), I have three independent variables (a),(b), and (c) which are good predictors of (d). All dependent and independent variables are time series which correspond to a given quarter of the year. I’ve found that (a) and (d) are related in that quarter over quarter increases in (a) correspond with quarter over quarter decreases in (d), and vice versa, but this isn’t always true. I’ve found that on average a 10,000 unit change (increase or decrease) in (a) results in an average 0.05 unit change (increase or decrease) in (d). While assuming a positive change in (a) will lead to a negative change in (d), and vice versa, I want to explain how much (d) would change given a 560,000 unit decrease in (a), while assuming a 560,000 unit change in (d) corresponds to an average 0.05 unit change in (a). Working that out I get a 560,000 unit decrease in (a) will lead to an increase in (d) of about 2.54.
My question this this: d is driven by more than just a, so I cannot say that if (a) drops by 560,000 we will see (d) increase by 2.54. I’m thinking I could run a multiple regression and get the coefficients of each independent variable (a), (b), and (c). Then somehow use the coefficients or another metric to say that (a) drives x% of the change we observe in (d). Then I could say a 560,000 unit decrease in (a) would correspond with a 1.27 unit increase in (d)? Sorry if I’m not making sense! I’m trying to explain as much as possible so you can see where my thinking is at. Thank you.