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I need to find the factors which are most impacting the number of students failed in a class. So, I have a dataset containing number of students failed and variables which are specific to the school, class etc. Essentially, I want to figure out the variables which are affecting "number of students failing".

If the Y-variable was a continuous one I could have run a linear regression and have sorted the variables based on their t-values. But since, I have a discrete dependent variable what methodology should I implement here?

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You could still use linear regression, but it may not perform well when the dependent variable takes on a small number of discrete values. If you have just a 0/1 output, you could use logistic regression. For more than two possible outcomes, it's multinomial logistic regression. Here are some more models to consider: http://www.kellogg.northwestern.edu/faculty/dranove/htm/dranove/coursepages/mgmt%20469/discrete-lhs.pdf

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There is nothing that says you can't use regression on a discrete variable since the residuals could still be normally distributed. Finding the most important variables can be more complex than sorting the t values, though. For example, if you have two highly correlated variables each with a high correlation with the criterion and a third variable uncorrelated with the other two and moderately correlated with the criterion, this third variable may well have the highest t value.

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  • $\begingroup$ 1. It's the conditional distribution of the response (or equivalently the errors) that are assumed normal (when such an assumption is used, which is pretty much when doing tests and intervals that rely on it) 2. The conditional distribution of the response will be discrete, so it is not normal. It is sometimes reasonable to use normal theory inference with discrete variates, but the nature of count variables - especially as they approach boundaries - tends to lead to non-constant variance and non-linear relationships. $\endgroup$ – Glen_b Feb 21 '17 at 22:25

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