I have a numerical dependent variable, and many independent variables. Most of my independent variables are dummy variables, but I have some categorical and numerical variables, too. I tried forward and backward model selection in R, but R returns my model empty! When I run separate simple regressions, there seems to be a significant relationship between my independent and dependent variables!
My question is: Am I going to have biased results if I run separate simple regressions with each variable, and then run a multiple regression with all the significant variables?