Logistic regression analysis is a fairly advanced statistical technique, designed to analyse the relationships amongst a mass of unconnected binary variables and highlight the most important that might be individually contributing to the end-result.
Basically, if you have this significant association between the mixture of variables and an outcome, logistic regression allows you to withdraw one variable at a time from the mixture and observe whether the level of significance suddenly drops away (ie p goes from .001 to .9). If that does happen, the inference can be made that such a variable is contributing substantially to the outcome. Conversely, if withdrawing a variable doesn’t alter the significance, then it’s possible that variable isn’t involved in the real situation. IIRC the history of the approach is that it was developed during the research into the association between smoking (only one amongst the myriad of other lifestyle factors that could have had an influence) and lung cancer.
I have used such an analysis before in a program called StatView, and it’s very good as long as you enter the data correctly. However I would definitely advise you to consult a statistician for some help; it’s not a standard analysis that you’d expect to find in a stats and curve-fitting program like Prism and I’m surprised you’re advised by the kit manufacturer to do that with simple ELISA results.
If I could ask, what are you trying to measure with this ELISA, and what are the four binary variables (i.e. the +/- parameters)?