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I'm building a model that predicts goals scored based on the defenses that a player faces.

From the classes I've taken, you should normalize the response variable. Here is the issue I'm facing: the value for Goals will usually be 0,1,2,3 or 4 resulting in the following QQ plot.

QQ Plot of Goals

This is definitely not normal and I worry that this will affect the results of my model.

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Rather clearly, you are looking at a discrete distribution. You are right to worry that a standard linear model that assumes a continuous response is inappropriate. On first instance, use a Poisson or Negative Binomial regression and you will be fine. This is relatively standard for when computing goal-scoring in football or count data in general. More advanced models (eg. here and here) use an ordered probit regression model that accumulates the probabilities of the related outcome. (ie. for a team to score 3 goals it has to be first score 2 goals, to scores 2 goals it has to first score 1 goal, etc.)

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  • $\begingroup$ Thanks a lot for the resources. Looking at the Poisson Regression Model, it seems as though it's assumptions make it essentially unusable. It doesn't seem common for the variance to be equal to the mean. $\endgroup$ – madsthaks Aug 10 '16 at 13:18
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    $\begingroup$ I am glad I could help. I find Possion restrictive too but OK, usually being approximately equal is good enough; the situation is problematic when they are clearly not the same, eg. different scales of magnitude, etc. I prefer NB-regression for that reason. $\endgroup$ – usεr11852 says Reinstate Monic Aug 10 '16 at 13:25
  • $\begingroup$ I'll keep that in mind. After a quick google search, it seems as though Poisson doesn't increase the precision of the model by much either. I'll stick with NB for this analysis but play around with Poisson at a later time to familiarize myself. Thanks again for the help, the articles you sent on the advanced models are really interesting. $\endgroup$ – madsthaks Aug 10 '16 at 13:59
  • $\begingroup$ So, using the Negative Binomial resource you gave me, I checked the assumptions by using the likelihood test. I got a value of -0.001491238. Does that mean I should be using the Poisson Model instead? $\endgroup$ – madsthaks Aug 11 '16 at 0:36
  • $\begingroup$ I am sure what this value refers at. I would suggest you make a new question particular for NB regression and how to interpreter its results. $\endgroup$ – usεr11852 says Reinstate Monic Aug 11 '16 at 8:27

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