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Consider a model where:

  • Y (response variable): continuous and both positive and negative

  • X1 (explanatory variable): continuous data, but with many zero values

  • X2 (explanatory variable): binomially distributed data [0,100,1], but with many zero values

In planning a good approach I assume that:

  • the many zeros for X1 (the continuous variable) will not be a problem as long as the residuals of my model are roughly normally distributed.

However, I have no idea how to handle X2. I cannot use binomial regression because my Y is both negative and positive. Could somebody point me in the right direction on how to handle this variable?

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  • $\begingroup$ Logistic regression (=binomial) refers solely to the outcome which is assume is your Y. That is not to say that there are no issues with X1 and x2 Can you clarify that Y is indeed the outcome? $\endgroup$ – mdewey Aug 13 '16 at 12:49
  • $\begingroup$ I edited the question, thanks for highlighting the need for clarification. Y is the response variable. $\endgroup$ – Jef Van Alsenoy Aug 13 '16 at 12:52
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If the excess of zeroes in the continuous predictor represent the fact that those cases are fundamentally different then you could consider using two variables, your existing X1 plus a zero/one variable which represents zero versus the rest. So an example might be expense on drugs where if you are well it is zero and of you are ill it can have any value. You might be able to do something similar with X2 as well. You feeling that the residuals are important is of course correct whatever you decide to do.

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