 # How can I determine the relative contribution of predictors in multiple regression model?

I ran the model with pyMC3 and got intercept with relative coefficients for each predictor:

y = b0 + b1x1 + b2x2 + … + bnxn

I can’t find anywhere how to evaluate independent contribution (e.g., in percentage) of each predictor.
I’m looking for how many % each independent variable contribute/

Should I calculate az.r2_score for model with all variables and then take each variable out and monitor changes in az.r2_score ? Not sure if it relevant to my question.
Thank You.

Can you say more about what you mean by “contribution”?

Sure. Thanks for getting back to me.

So lets say ‘y’ - made profit.
x1 - number of times comercial was shown on channel 1
x2 - number of times comercial was shown on channel 2

xn - number of times comercial was shown on channel n

I want to know how much each channel contribute to the a profit.

Example:
My profit is \$3000 and 20% comes from channel x1, 30% comes from x2, n% comes from Xn.

This is what I mean contribution of each predictor to target in %.
Thank you.

This is the sort of question that seems like it should have an easy answer, but it is deceptively complex. Regression just doesn’t decompose variance in a way that provides straightforward answers to such questions. In machine learning, the notion of variable importance is common, but less common when dealing with “statistical” models. I would suggest checking out these papers (among many others) for some additional information:

Nathans, L. L., Oswald, F. L., & Nimon, K. (2012). Interpreting multiple linear regression: A guidebook of variable importance. Practical Assessment, Research, and Evaluation , 17 (1), 9.

Grömping, U. (2015). Variable importance in regression models. Wiley interdisciplinary reviews: Computational statistics , 7 (2), 137-152.

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