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I need to calculate MR but my data consists of many dummy variables. I had a question in my survey that asked for the budget/month. But instead of giving the option to fill in a value, I offered ranges (steps of 250, so I have like 0-250; 250.01-500 and so on)

I created dummy variables for these different steps so now I have a total of 6 dummy's and the problem is that I can't calculate the ln-values of these dummy's because all values are either 0 or 1. So any ideas how I can go around this problem?

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    $\begingroup$ I'm not sure I understand what the problem is... why do you want to take the ln of the values exactly? Because the distribution is positively skewed I suspect? Also, to me using 6 dummy variables in this case seems to be something of an overkill. You have the privilege of having your scale start at 0, be ordered, and have equal intervals; with 7 different categories, I just might forget about dummy variables and use it as a continuous variable... $\endgroup$ – Patrick Coulombe May 22 '13 at 17:23
  • $\begingroup$ I want the ln values so I can check whether they are positively skewed or not actually. How should I use it as a continuous variable thought? Add a column with the median value or something? Like use 125 for each one that is between 0-250 etc? $\endgroup$ – user25982 May 22 '13 at 17:44
  • $\begingroup$ If they're dummies, you don't care if they're skewed or not. (And you don't care about the distribution of predictors in MR, only the distribution of residuals - at least for the purpose of testing assumptions). $\endgroup$ – Jeremy Miles May 22 '13 at 18:39
  • $\begingroup$ What's the protocol here, now that I've made my comment into an answer? Do I remove the comment or do I leave it there? $\endgroup$ – Patrick Coulombe Mar 6 '14 at 16:29
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I think using 6 dummy variables in this case is something of an overkill. You have the privilege of having your scale start at 0, be ordered, and have equal intervals; with 7 different categories, I just might forget about dummy variables and use it as a continuous variable. Once you do that, the regression coefficient for your budget variable will be interpretable as the expected change in the dependent variable for each increase of $250 in the budget.

And as @JeremyMiles pointed out, for the sake of testing assumptions, you don't need to worry about whether the distribution of the budget variable is normally distributed, so long as the residuals are.

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