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I have a variable with values strongly skewed towards zero:

table()

     0      1      2      3      4      5      6      7 
488444   9384    557    100     12      2      1      1

summary()

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.0218  0.0000  7.0000  

which plots

enter image description here

I have reason to believe that other two variables might correlate with the skewed variable.

Which strategy should I adopt to build my predictive model, thus with the skewed variable as dependent variable Y? Should I subset my data only to include non zero values for my Y?

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    $\begingroup$ You might want to explore zero-inflated Poisson and zero-inflated negative binomial models. A canonical example of when to use is in predicting how many fish people catch: in order to catch any fish, you have to go fishing. So these models estimate first whether you are going fishing, and then if you are what your catch probabilities are. $\endgroup$ – Alexis Apr 29 '14 at 3:11

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