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I have 8 predictors and for 4 of them, the AV plots have a slope close to 0. Is that enough information for me to leave out these predictors in my model?

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If there's not otherwise pattern (such as a nonlinear trend), lack of slope in an added-variable plot would tend to indicate that the variable wouldn't help you explain the response over what was in the model.

However, note that this is still a form of model selection, and will have a similar effect on your inferences* that other forms of stepwise selection would have.

* (on test significance levels, confidence interval coverage, bias of estimates and standard errors and so on)

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  • $\begingroup$ Thank you for responding. So if I'm understanding you correctly, a model that excludes the predictors that had near zero slopes in its AV plot should be compared to other models generated using, for example, stepwise regression? $\endgroup$ – mistersunnyd Mar 7 '17 at 22:10
  • $\begingroup$ Definitely not saying that. I'm pointing out that variable selection in whatever form, when done on the same data as you're using for your hypothesis tests, confidence intervals, predictions etc has an impact on the properties of those procedures -- they no longer behave "as advertised". If you don't have to do selection (e.g. if you can reasonably include all your variables, which is sometimes true) then that's a way to avoid the problem; or if you need to do selection, there are ways to go about it (but they cost you something in effective sample size). $\endgroup$ – Glen_b Mar 7 '17 at 22:26
  • $\begingroup$ If you'd add a variable that showed a strong relationship in the AV plot, and would avoid adding it if it did not, you're doing variable selection. If you redo AV plots after you add a variable, you're doing stepwise selection (specifically, forward selection) -- if less formally; the impact will be the same. $\endgroup$ – Glen_b Mar 7 '17 at 22:31
  • $\begingroup$ In regression analysis, is what I'm doing (variable selection) appropriate? I am also planning on using stepwise selection, so I suppose I should skip variable selection if it's redundant and less formal? $\endgroup$ – mistersunnyd Mar 7 '17 at 22:43
  • $\begingroup$ "Appropriate" is a tricky word. I'm not saying "don't do variable selection". I'm saying that if you do do it, you will incur some costs and you have some control over the kinds of costs you'll pay and how big they might be. If you do it in some ways the costs are mostly hidden and potentially severe; if you do it in other ways the costs are up front and usually modest. There are many questions on this issue. .... as to whether there's a particular problem with both looking at AV plots and doing variable selection more formally, I don't see any additional issue. $\endgroup$ – Glen_b Mar 7 '17 at 22:52

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