How to approach ranking and explaining business driver independent variables? I'm looking at quarterly sales for a fortune 500 company, sales being the dependent target variable. My independent variables include things like marketing spend, sales volume, and competitor market share.
My question is how can I answer what variables influenced why sales increased/decreased the most for the quarter?
I'm currently thinking of running a classic regression model on weekly data for the quarter, then taking the variables that have p values <0.05 to explain shifts. So I would say our marketing spend increased, and for every dollar we spent on marketing we saw a 0.4 increase in sales, with a p value of <0.05.
I was also thinking I could use a random forest to rank the variables that explain the most variance. So if marketing spend and sales volume both increased with sales, which one was more important? I could use the random forest variable ranking to show this.
Can I combine the two approaches, taking a linear regression with low p value variable and their coefficients, then ranking them according to random forest?
Is there a standard way of doing this?

NO
Compared to your linear model, the random forest emphasizes different aspects of how a feature can influence the outcome. For example, a random forest can pick up on an interaction between variables, which you have to specify in a linear model. Consequently, the feature importance from a random forest and the feature importance to a linear model need not coincide.
Further, there are a few issues with your approach.

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*Feature importance and feature selection are unstable. Frank Harrell has discussed this multiple times, such as his keynote at "Why R?" and an answer of his on here.


*Pre-screening with the linear regression influences downstream inferences. For example, if you screen out a variable in the linear model, you never give the random forest a chance to examine that variable, even though the random forest might have found that variable to be important. If you want p-values or confidence intervals, it gets even worse.
