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I performed an ANOVA on my dataset and I have determined which predictors are significant and which are not. Now I need to minimize my response variable in order to predict which combination of 2 categorical variables yields the smallest response. How do I do this? If they were continuous variables this wouldn't be difficult but I'm struggling to conceptualize how to go about doing this with 2 categorical variables. My last resort would be to manually check combinations but I know there has to be a better solution. I know I'm missing the obvious solution here but I just can't solve this issue.

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  • $\begingroup$ You can look at coefficient estimates and choose the two categories which have the largest negative coefficients. $\endgroup$ – Demetri Pananos Aug 5 '19 at 2:04
  • $\begingroup$ @DemetriPananos Thank you! I knew I was completely missing the obvious. $\endgroup$ – regents Aug 5 '19 at 22:25
  • $\begingroup$ @DemetriPananos Why not post that as an answer? $\endgroup$ – mkt - Reinstate Monica Aug 7 '19 at 8:25
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    $\begingroup$ @mkt Ok, I've posted it. $\endgroup$ – Demetri Pananos Aug 7 '19 at 12:28
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You can look at coefficient estimates and choose the two categories which have the largest negative coefficients

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  • $\begingroup$ What if there are interactions between the factors fit in the model? And on the other hand, if only an additive (thus unsaturated) model was fit, does the model need to be correctly specified for this procedure to work (in expectation)? $\endgroup$ – Andrew M Aug 7 '19 at 13:08

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