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This is a central question in what I do and in years of looking at the literature and talking to statistical experts I have never found an answer. I often get asked which of a set of variables, some of which are dummies, has more impact on a dependent variable than the others. So if there are three predictors this has the most impact on change in the DV followed by this variable. For example, if the dependent variable is income at closure, and you have a spending predictor, and two categorical predictor, which of the three has the most impact on increasing income at closure. As I understand it slopes as normally constructed don't answer this unless they are all measured on exactly the same scale. You can use standardized coefficients, but there appears to be significant doubt in some quarters if using standardized coefficients is valid with dummy variables (many of my variables are categorical). I am surprised how little this issue is addressed in regression, one statistician told me determining relative impact is not the goal of regression.

The whole point is that we would focus on which would raise income (the dependent variable) the most. This is what I mean by relative impact - its not a theoretical issue, it is where we focus resources to make improvements, so we want to find out which variables will generate the biggest increase in a dv when the variables are measured on different scales.

user54285
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  • First you'd have to define what you mean by impact. If you simply mean predictive ability, then you could compare models with different subsets of predictors to get an idea. If you mean something else, then please edit your question to elaborate. – Frans Rodenburg Apr 30 '19 at 01:04
  • [This page](https://stats.stackexchange.com/q/202277/28500) has extensive discussion of the difficulties with assessing predictor importance, That might explain what the statistician noted in your last sentence told you. Please read that page over and consult its links. Then edit this question to state more specifically, in light of that discussion, how you would use an assessment of predictor importance. – EdM Apr 30 '19 at 02:23
  • As is always the case I have cycled back to this issue (I have been pursuing it on and off for 11 years) because it is central to the practical issues I deal with. The business people I work for want to know, given limited resources where will I get the best return. That of course was raised on the previous page. For example we have many services we offer. They want to know, if I offer this service will it have more impact than this service. We measure many definitions of satisfaction and overall satisfaction. They want to know which if we improve it will have the most impact. – user54285 Sep 23 '21 at 02:21
  • I note in passing that one of the articles mentioned on the linked page reviewed the many perspectives/methods to assess this. And beyond the difficulty in doing many of them, including access to software, it is clear from his article that there is no agreement at all which is the best way to do relative impact. A frustrating element, as often for me in statistics, is that they say that there is an issue with "correlated predictors," Given that many predictors are correlated, how much correlations will make such a method of no use. Virtually never is this stated, maybe there is no answer. – user54285 Sep 23 '21 at 02:25

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