I am trying to create a model to explain/predict fulfillment ratio of a product by a store i.e orders placed divided by orders delivered.The QQ-plot of the fulfillment ratio is: enter image description here

The QQ-plot of the predictor variables are: enter image description here

I tried linear regression once but that is not of much use since the spread is not really continuous or normal. Variable transformation is not also working as a large percentage of the observation is concentrated at the extremes. Any suggestion on which regression technique should i use for predicting fulfillment ratio?

I was considering categorizing the the predictors and dependent variable to convert them from numerical to ordinal form, and then use linear regression. Will that help?

Any suggestion to solve this is most welcome. I cannot share my dataset due to data privacy issues otherwise i would have.


The distribution of the predictor variables is irrelevant, but that response variable looks very nearly binary. You might consider logistic regression.

  • $\begingroup$ You might want to expand this to suggest what @Arsha should do with the ones in the middle which do show some variation ad also seem to have a small clump at 0.5 $\endgroup$
    – mdewey
    May 12 '16 at 12:57
  • $\begingroup$ I did think about that but can't the business requires that i provide a "ratio". I could split this variable into 10 levels and then develop a model, but cannot use a logistic model. $\endgroup$ May 12 '16 at 12:59
  • $\begingroup$ You could use a beta distribution to model the ones in between. $\endgroup$ May 12 '16 at 13:31
  • $\begingroup$ See the chapter on using ordinal regression for continuous $Y$ in my course notes at biostat.mc.vanderbilt.edu/rms $\endgroup$ May 12 '16 at 14:13

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