I'm doing a multiple regression model on environmental data and am stuck on checking the assumptions. Ultimately, I need to do a model selection for the data. There are various explanatory variables and the response variable is expenditure, so this is a predictive model. There are 5 response variables. One is quantitative and the rest are categorical. For the 4 that are categorical, I have coded with dummy variables. I transformed my quantitative variable and response variable and the residual plot looks better than the original residual plot; however, the qq plot looks skewed. I did a log transformation for both. (It wouldn't make sense to transform the dummy variables right?)
residual plot (original data)
qq plot (original data)
residual plot (transformed data)
qq plot (transformed data)
My question is what should I do? I don't think the assumptions have been met for me to proceed with analysis yet.
The second question I have is how do I deal with the dummy variables? I have coded them to be 1 true, 0 false but how exactly do I deal with them in determining the final model? For example, one variable is permit type, and I have 7 of them so I will need 6 dummy variables. I already coded them in the excel file. Another variable is air quality with 1 being yes and 0 being no. Another one is a document that has 3 types, so I have 2 dummy variables. etc.