How many zeros in an independent variable are too many for regression? I use simple regressions. My independent variable is a count data (# of a drug used per year), and it has too many zeroes. Depending upon a dependent variable, for some simple regressions, I have 13 observations, and there are only 3 non-zero values out of 13. For other simple regressions, I have 150 observations and only 12 are non-zeros out of 150. Is it appropriate to use simple regressions for these data? Is there a rule about how many zeros should be in independent variable to be able to model the relationship? My dependent variable is continuous (weight). 
 A: Regression methods do not make assumptions about the distribution of your independent variable.  Strictly speaking, you would have too many zeros for linear regression when all of your data are zeros.  Instead the issue here is lower statistical power and reduced ability to check your assumptions.  Although it is discussed in terms of the t-test, you might be able to get the main idea from my answer here: How should one interpret the comparison of means from different sample sizes?
A: (1) by simple regression I assume you mean linear regression.
(2) zero values are not to my mind an issue for independent variables (in the same way they are for DV count data).
(3) what is an issue is that you're unlikely to have a linear relationship between IV and DV. There is a whole section in most regression textbook on how to approach this issue. I usually categorize the IV into categories that seem reasonable. Many statisticians dislike this approach - it is data-driven, arbitrary and wastes statistical power - and would recommend:
(a) transforming variable, (b) adding cubic/quadratic terms, (c) using restricted splines, (d) or something even more complex. Depends out what relationship between ID/DV looks like.
