I'm trying to create a multi-variate regression model, so far I've found 4 independent variables which are significant below the 0.05 level (p-value). None of the independent variables are normal (2 are categorical), I understand this is not a problem but that the dependent variable should be normal? Is this correct? The dependent variable is actually skewed to the right and looks almost bi-modal, I have tried various transformations but can't get rid of the skew or the bi-modal character. Does this mean I can't use linear regression to create a valid model?

Thanks

-Rob