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Good morning, I was after some guidance on the issue of normally distributed data in a multiple regression. There is a lot of contradictory texts out there.
 
I have a number of predictors (independent variables) that I am using to predict 2 outcome variables (2 multiple regressions to be run). Only a handful of predictor variables are normally distributed and my outcome variables are not normally distributed. So...
 
1. I have read that is reasonable to expect that often predictors are not normally distributed (most of which are not)
 
2. The concern would be if the outcome variables are not normally distributed (which mine are not)
 
3. However, some texts claim that even normally distributed outcome variables (dependent variables) should not always be expected and that the focus should be on whether the residuals are normally distributed (which mine are).
 
4. an interesting point is that in my outcome variables there are 2 peaks (above the mean). they represent self reported safety knowledge and safety knowledge where the higher numbers relate to greater knowledge and motivation. it is interesting data in itself in that one group appear to have an 'average' amount of knowledge and motivation and another group have very high levels. Is this is a problem in terms of multiple regressions?
 
Any advice is greatly appreciated.