I recently encountered this question twice, on my exam. If you fit a full MLR additive, model, can you infer that the insignificant predictors (p-value > 0.05 from lm output) will not be chosen during stepwise regression, such as forward selection. I said no both times. My reasoning is that forward selection only looks at the partial contributions of each predictors after each model size, so sometimtes the non-significant predictors on a full model, might be significant on their own such that its picked by forward selection. So you can't reasonably infer that non-significant predictors will not be chosen by forward selection?
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4$\begingroup$ The question is ill-posed, because "insignificant predictors" makes sense only in the context of the set of other predictors and "lm output" is too vague to be of any use at all, because it could refer to any of the possible models being selected from. $\endgroup$– whuber ♦Commented Apr 30 at 16:20
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1$\begingroup$ This is an ill-defined question; in general the answer is probably “no” because there are so many ways that we can induce pathological behavior (e.g. fix N and let p tend to infinity), but it really doesn’t make sense to talk about significance out of context $\endgroup$– Randy SavageCommented Apr 30 at 16:23
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4$\begingroup$ You may have predictors that have statistically significant effects in univariable models (that thus may be selected by stepwise regression), but non-significant effects in a multivariable model. This is particularly common in the case of correlated predictors $\endgroup$– alan ocallaghanCommented Apr 30 at 16:48
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1$\begingroup$ Do not use step-wise model selection $\endgroup$– AlexisCommented Apr 30 at 16:51
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2$\begingroup$ @alanocallaghan - might want to expand this point and write it up as an answer. $\endgroup$– jbowmanCommented Apr 30 at 17:11
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