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I've a cross sectional model where I want predict number of users that take specific service, to make it I've many variables but have specifically two nominal: isWorkday(0 or 1) and weeday(1,2,3,...,7). When I make the model, taking into account the two variables, generates high multicollinearity. So I've delete one of them, so what's better have many dummies (weeday) or less dummies (isWorkday).

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    $\begingroup$ Have you tried both? Usually when faced with this kind of dilema we perform tests with our available options, unless the amount of tests needed create a effort in which the experiment is not worth of. $\endgroup$ – Pedro Henrique Monforte Apr 13 at 2:35
  • $\begingroup$ @PedroHenriqueMonforte you are right, see what I answered next, and I know that all possible models should be tried, but the question is addressed to multicollinearity. $\endgroup$ – David Salgado Apr 13 at 21:39
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Since your task is to predict something, the better variable is the one that gives you a higher prediction accuracy. So you can simply test both and choose the one with which your model performs better.

However, I would suggest considering to engineer your own feature that incorporates information of both variables. For example, you could create three dummy variables: workday, weekend and holiday and include two of them into your model (to prevent falling into the dummy variable trap). Another option would be to only include the interaction terms between isWorkday and weekday.

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    $\begingroup$ I get it. But if it's the case where I've a dummy variable for isWorkday and six for the days of the weeks(isTuesday,isWednesday,isThurday, isFriday,isSaturday and isSunday) and both in the multicollinearity tests generate conflict , which dummy I should choose isWeekDay or the six dummies?. Remember that I can make a relationship with two variables (multicolineality): isTuesday,isWednesday,isThurday and isFriday mapped to isWorkday(1) and isSaturday and isSunday to isWorkday(0). $\endgroup$ – David Salgado Apr 13 at 21:41
  • $\begingroup$ To make a decision, you first test both options. Case 1: If isWorkday gives you better prediction results, you choose isWorkday. Case 2: If the six weekday-variables give you better prediction results, you choose the six weekday-variables. Case 3: If the six weekday-variables perform equally good as isWorkday, you choose isWorkday, because in this case, you end up with a smaller model. $\endgroup$ – georg-un Apr 13 at 22:18
  • $\begingroup$ Oh, I understand thanks, with that you tell me I'm also convinced that this would be the way to proceed. $\endgroup$ – David Salgado Apr 13 at 22:23
  • $\begingroup$ Awesome, glad I could help. $\endgroup$ – georg-un Apr 13 at 22:27

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