I can't tell exactly what you're doing, or why, and it seems a little strange, to be honest. I'm guessing that you have a regression model, and believe that those who are above the line are from a different underlying (latent) group from those who are below the line, and hope to find out something about these 'groups'. Perhaps not, but if so, I'm not sure this is a legitimate strategy. I have difficulty imagining how the distance above a regression line can be determined by one set of explanatory variables, and the distance below the line by a different set. There is a great deal of real noise in data and trying to explain it is more likely to lead to phantoms than knowledge. But I don't mean to scold.
Perhaps a tobit model would be appropriate. The tobit is based on a probit model with an underlying normal distribution, but where some proportion of the data have been censored. Recognize that this means the model is assuming the other half of the data are a part of the picture, but just have been hidden from the model, which is true in your case. The non-zero level of intrinsically unexplainable variance that must exist in your data necessitates that some proportion of the negative residuals really belong to the set of your positive residuals and vice versa, so the assumption the model is making is justifiable. Nonetheless, running two tobits would allow you to try to model your residuals with different explanatory variables.
I have no idea how to conduct a tobit regression in SPSS; I'm not sure the software supports that analysis. If you want to know a little bit more about it, and how to conduct it with other software, UCLA's website has a nice, concise, clear description (of course) of it for R. If you want more theoretical background on it, J Scott Long's book is very accessible. It requires calculus, but he steps through it very gently.